tag:blogger.com,1999:blog-87347442910405054502024-03-13T03:38:53.399-07:00The Art of LogicEssays on education, debate, and math instruction; neat math problems; and whatever else I get around to.Russell Haneshttp://www.blogger.com/profile/13594411930757264086noreply@blogger.comBlogger124125tag:blogger.com,1999:blog-8734744291040505450.post-69538268344621751372024-01-16T10:42:00.000-08:002024-01-16T10:42:48.876-08:00Hexagonal city grids<p>Many years ago I posted about hexagonal city grids: <a href="https://art-of-logic.blogspot.com/2014/12/hexagonal-grid-city-life.html">https://art-of-logic.blogspot.com/2014/12/hexagonal-grid-city-life.html</a>. I recently saw City Beautiful's <a href="https://www.youtube.com/watch?v=Lgio_ygetbo&ab_channel=CityBeautiful" target="_blank">YouTube video</a> about hexagonal city grids, which rekindled my interest in them. Apparently, hexagonal city grids aren't just my fantasy.</p><p><br /></p><p>How do you plat houses in hexagonal grids? Don't they create weird-shaped lots? Perhaps, but the problem is mitigated substantially by using the "superblock" strategy. The idea, which was developed by Barcelona, was to merge multiple blocks together into one superblock; through-traffic would be pushed to the perimeter of the superblock, whereas streets in the interior of the block would be only for residents. Here's what this could look like for hexagons:</p><p><br /></p><div class="separator" style="clear: both; text-align: center;"><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEiysthQrjdymuXqPVjgfU_2h8QEm7lmF1e5iMKD3NkR1BcqTIhNMR7tRF6SD3EyWHlUHTlOrH9ef8_Liahr90XQMb75J7oKtz5XkR4QVy3OUEcdWVPuT3vTQIm67w_TOG5E3tTEWQKtJEgqUHF6ybKQ-9zz7AXbdBgOw7CKVUcchVE9LHrZ7kYiImphDKHv/s2880/hexagonal%20block.png" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" data-original-height="1694" data-original-width="2880" height="376" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEiysthQrjdymuXqPVjgfU_2h8QEm7lmF1e5iMKD3NkR1BcqTIhNMR7tRF6SD3EyWHlUHTlOrH9ef8_Liahr90XQMb75J7oKtz5XkR4QVy3OUEcdWVPuT3vTQIm67w_TOG5E3tTEWQKtJEgqUHF6ybKQ-9zz7AXbdBgOw7CKVUcchVE9LHrZ7kYiImphDKHv/w640-h376/hexagonal%20block.png" width="640" /></a></div><br /><p>Each triangular grid line is 200 ft. Commercial/apartment building lots are marked in red. Residential lots of approximately 50x100 ft are marked in blue. The residential streets are marked in black, whereas bike/walking paths are dashed lines. A park in the center is marked in green.</p><p><br /></p><p>The hexagonal city block pictured is about 1,000,000 sq ft, or about 23 acres. A typical city block in most cities is somewhere about 4–5 acres, so the superblock above is about 5–6 typical city blocks.</p><p><br /></p><p>As you can see, a few lots end up as triangles, but for the most part, rectangular lots can be preserved for most residential development.</p><p><br /></p><p>Each residential street has only one inlet, limiting car traffic on the street to residents and residential services like trash collection, while bike/walking paths allow everyone else easy cut-throughs and connection.</p><p><br /></p><p>However, commercial properties could have limited (by hours of business and total volume) loading docks and trash collection via the residential streets behind them, thus improving the flow of traffic on the main thoroughfares on the hexagon's perimeter.</p>Russell Haneshttp://www.blogger.com/profile/13594411930757264086noreply@blogger.com0tag:blogger.com,1999:blog-8734744291040505450.post-89537775042817854302021-11-19T16:44:00.003-08:002021-11-19T16:44:32.551-08:00Judge intervention<p>"[W]hen people argue they move back and forth between strong claims that are weakly defended and weaker claims that are strongly defended." ~ Ross Douthat, https://www.vox.com/21760348/trump-2020-election-republican-party-ross-douthat</p><p><br /></p><p><b>What is judge intervention?</b></p><p><br /></p><p>Let's start out first by explaining what judge intervention is NOT:</p><p><br /></p><p>-<span style="white-space: pre;"> </span>Judge intervention is not when a judge prefers your opponents' argument to yours. This is, <i>ya know</i>, "judging."</p><p>-<span style="white-space: pre;"> </span>Judge intervention is not when a judge ridicules your argument. This is rude, but that's about all it is.</p><p>-<span style="white-space: pre;"> </span>Judge intervention is not when a judge jokingly says, "Extra points to anyone who can avoid saying the President's name," or some such. Silly, and perhaps annoying, but that's about all it is.</p><p>-<span style="white-space: pre;"> </span>Judge intervention is not when a judge declines to discuss their decision after the debate. In some cases, talking after the debate is disallowed by a tournament; in other case, it may just be the judge's personal preference. So be it.</p><p>-<span style="white-space: pre;"> </span>Judge intervention is not when a judge grants your opponent favorable treatment (e.g., more prep time than is allowed by the tournament, advice, extra speech time or do-overs, etc.). This is unacceptable behavior and should be reported to an adult in charge of the tournament.</p><p>-<span style="white-space: pre;"> </span>Judge intervention is not when a judge ignores the debate, falls asleep, or in other ways is derelict in their duty to be a full participant and educator. This is unacceptable behavior and should be reported to an adult in charge of the tournament.</p><p>-<span style="white-space: pre;"> </span>Judge intervention is not when a judge demeans you personally. This is unacceptable behavior and needs to be brought to an adult's attention, preferably your coach and/or the tournament.</p><p>-<span style="white-space: pre;"> </span>Judge intervention is not when a judge votes based on the school, sex, gender, sexual orientation, race, ethnicity, or socio-economic class of the debaters, and not the arguments. Let's point out that it's beyond unacceptable and could be illegal.</p><p>-<span style="white-space: pre;"> </span>Judge intervention is not when a judge creates a hostile environment of harassment or fear or sexual joking. Or implies wins or speaker points can be traded for personal favors unrelated to debate. Beyond unacceptable and definitely illegal.</p><p><br /></p><p>As you can see, judge intervention is not a catch-all term for rude or inappropriate judging behavior. Judge intervention falls somewhere in the middle of the spectrum: beyond merely rude, but well short of truly inappropriate behavior. Judge intervention is perhaps in some cases murkily unethical, although it would be very, very hard to prove any specific instance as unethical and will probably never result in an overturned ballot.</p><p><br /></p><p>In many cases, judge intervention is the inevitable result of how YOU debated; it is, in at least some key ways, an inevitable part of judging even good debates.</p><p><br /></p><p>So, what it judge intervention? Simply put, judge intervention is when a judge has to use their own prior knowledge to resolve an issue in the debate. Consider the following exchange:</p><p><br /></p><p>Team A: "X is a fact" [no evidence provided]</p><p>Team B: "X is not a fact" [no evidence provided]</p><p>Judge: "… fudge you all"</p><p><br /></p><p>In this instance, neither team provided any evidence to back up this point. If X is a crucial fact for the debate, then the judge will have to insert their prior knowledge to resolve it. (If X isn't important, then most judges will happily ignore it as irrelevant so as to avoid intervening.) Of course, this example is not the only one where a judge might be forced to intervene:</p><p><br /></p><p>Team A: "The sky is green" [no evidence provided]</p><p>Team B: "…"</p><p>Judge: "Come on, team B!"</p><p><br /></p><p>While the judge should be open minded, this doesn't extend to being completely gullible. We expect everyone to bring at least some prior knowledge into the debate with them. To assume the judge knew nothing would actually be an exhausting way to debate; in every round, you would spend the bulk of your time explaining how the government worked, that people were bipedal and how they used language to communicate, and so on. To paraphrase the T.V. show <i>Archer</i>, "Why is there conflict in the Middle East? Well, a long time ago there were dinosaurs, then they died, and their bones are what your car uses for food." Giving every bit of backstory would slow debates to a crawl. The judge should be allowed to have some degree of common sense without being accused of wrongdoing, even though it's technically intervening to ignore Team A's insane green-sky claim.</p><p><br /></p><p>There are in fact many instances in which we should actually expect the judge to intervene and reject your argument, even if the opposing team said nothing against it. Looking at Toulmin's model will help us delineate all the ways. Toulmin's model of an argument contains the following parts:</p><p><br /></p><p>Claim: your argument</p><p>Evidence: your supporting facts or expert opinion</p><p>Warrant: the logical connection between evidence and claim</p><p>Relevance: the meaning of your claim to the debate</p><p><br /></p><p>A judge might reject your claim because it's muddled and unintelligible; they might reject it because it contradicts claims you make in other parts of the flow. A judge might reject your claim because it's of the wrong type. There are four types of claims: (1) factual, "X is true"; (2) causal, "If X happens, then Y will result"; (3) value, "X is right and good" or "X is more important than Y"; and (4) definitional, "The word X means…" These types of claims are not interchangeable, so don’t go answering a moral question with a factual claim. Definitions don't really address cause and effect questions…</p><p><br /></p><p>A judge might reject your argument because you provide no or weak evidence. What if you argue the economy is doing well and your evidence is several years old? What if your source is, unbeknownst to you, a widely discredited conspiracy theorist? There are some real gray areas here. In some instances, we might say, "The other team didn't point that out, so the judge merely needs to accept any evidence I provided at face value," but in other cases, that feels absurdly deferential to a team reading, say, neo-Nazi propaganda or other gibberish. The judge should accept most reasonable seeming sources at face value, even if they perhaps know of a specific flaw with the evidence or source, but what is a reasonable source? Judges may have to walk a very fine line here because, though they are no experts on the topic, they may know more than you do. The line I often draw is,"What would be reasonable for a student at your age and experience level to know?" Do I expect you to know an insane conspiracy theory website when you see one? Yes. Do I expect you to know how respected an academic at a good university is in their field? Not really. So I would throw out the conspiracy website, even if it's unchallenged, while allowing the academic—even if I know something specific about their work—if your opponent says nothing. But if your opponent does say something, I will definitely let my skepticism fly free. My initial, naive presumption you shouldn't know something at your age goes right out the window when your opponent knows it.</p><p><br /></p><p>A judge might reject your argument for lacking a warrant connecting the evidence back to the claim; the evidence might appear senseless and irrelevant. But the judge might also reject some kinds of warrant that you do provide. We don't expect judges to be subject matter experts in every single field a debate might touch on: they are not scientific experts, legal scholars, linguists, logicians, political theorists and strategists, pollsters and statisticians, and foreign policy gurus and intelligence analysts, all rolled into one. It's quite possible our explanations are too "inside baseball" for a lay judge to follow. Debating is a communicative act, so we need to do a bit of audience analysis. Our explanations, our reasoning, and our warrants need to assume that we are persuading an intelligent but lay audience; after all, our judge is not a subject matter expert but a smart generalist. In other words, yes, it's reasonable that a judge could reject a warrant you've provided that's perfectly intelligible and correct simply because it's over the judge's head—and it's reasonable to expect you to know it would have been.</p><p><br /></p><p>A judge might believe everything about your argument but simply not get why you believe it's relevant to the debate.</p><p><br /></p><p>In short, there are many, many reasons why a judge may intervene in a debate. Rather than the problem being that judges intervene, the problem is that you think it's an aberration. Judge intervention isn't an aberration. It happens all the time. It's the norm. It's a normal part of human decision-making to use one's prior knowledge and common sense to evaluate arguments in holistic ways. It's called critical thinking, yo. Judges don't accept everything you spoon-feed to them, and if they did, they wouldn't be able to reach decisions. A truly blank slate judge would be like a computer program that fritzes out before returning an answer; a spinning rainbow; a blue screen of death. Judges are thinking human beings with their own life experiences and assumptions who are trying to be—but not always succeeding at being—open minded to your arguments.</p><p><br /></p><p>The problem with judge intervention is not that it happens in the first place but that you don't know how to use that fact to your advantage. A great debater knows how any judge, any human being, likes to reason; knows when, why, and how a judge is likely to intervene; and uses that knowledge to win. To be clear, I'm not talking about judge adaptation (changing your speed, style, or argument selection in order to appeal to the judge's preference). I'm talking about using the human psychology of decision making so as to find ways to "stitch" the inevitable gaps in arguments so that the judge won't notice them as flaws.</p><p><br /></p><p>A winning debater is ultimately a good storyteller, and those stories operate on the micro level (warrants and reasoning) and on the macro level (relevance and voting issues). Those stories are crucial to winning over a judge. Judges need cohesive stories to justify their ballot, and if you don't supply it, the judge will. While you might not do a perfect job on every issue and position in the debate, telling a good macro story enables you to persuade the judge that you are, overall, winning. Likewise, not every claim or piece of evidence is perfect, so a good micro level story enhances your credibility; you paper over any holes in logic by demonstrating an overall cohesive understanding of the disadvantage or the case.</p><p><br /></p><p>Lacuna in your arguments and direct contradiction by opponents are just inevitable in close debates. The latter, because your opponents are good; the former, because under the pressure of a close debate, you won't get to everything. There will be holes; the judge has to intervene to pull together a cohesive picture.</p><p><br /></p><p>Consider a close football game, where the final score difference is less than 7 points between the teams. Either team could have won. A bobbled pass that was caught, a different penalty call, a timeout left—any of these could have made the difference in the game. Both teams had a near 50% chance of winning.</p><p><br /></p><p>So too in debate. In a blowout debate, you are able to put together full, complete arguments and full, complete strategies. Your opponent isn't able to contradict you and isn't prepared to put together a competing narrative. You perhaps have a 90% or 95% chance of winning; there is but a slim chance that your opponent successfully throws a Hail Mary and makes a lucky good argument or that your judge happens to find one of your arguments completely unbelievable (i.e., you've unknowingly used a conspiracy website, so far as the judge is concerned). Pure judge intervention like the latter is rare, but it's just a part of human reasoning. Take the 90% or 95% chance of winning and be glad. There's no way to be 100% airtight in front of a thinking human being with experiences different than your own. They will have different assumptions and thought processes than you do. Mostly airtight is good enough.</p><p><br /></p><p>A close debate, however, is like the close football game. Any play or argument could make the difference. Your efforts to complete every argument, although valiant, are impossible under the time pressure and constant barrage from your opponents. There will be holes. Therefore, the most important thing you can do is to tell good stories to paper over any holes. You want the inevitable judge intervention to slide your way. You won’t be able to increase your odds to 80% or 90%, but you can perhaps up them to 60% from 50%. In this instance, judge intervention isn't a bad thing, either; it's just part of the round being so close, so use it to your advantage.</p><p><br /></p><p>When the round isn't close, out-of-clear-blue-sky judge intervention should be rare. It stinks, but all you can do is build your arguments as carefully and as air-tightly as you can—and learn from judges' rare interventions how to improve upon your techniques.</p><p><br /></p><p>When the round is close, and judge intervention become inevitable, do your best to push the judge to intervene for you. Do this by using solid evidence, being clear and consistent in your positions, and most of all, telling compelling logical stories and impact analyses. Credibility and persuasion matter.</p>Russell Haneshttp://www.blogger.com/profile/13594411930757264086noreply@blogger.com0tag:blogger.com,1999:blog-8734744291040505450.post-85583301593090953192021-11-03T14:39:00.001-07:002022-01-28T16:16:47.273-08:00Repairing the SenateIt should come as no surprise to anyone that the U.S. federal government is in need of serious Constitutional reform, as it is barely functional these days, but most people would probably ascribe the problem to gerrymandering, to executive orders, or to an activist Supreme Court. But the worst problem is the Senate.<br /><br />And I'm not talking about the filibuster (though by all means, please get rid of the filibuster). The Senate's problems are much deeper. The real problem is that the Senate has become a place for ambitious young politicians to prove they can win statewide elections and boost their brand by single handedly blocking legislation. "Senator" literally implies old, as it comes from the same root as "senile." A Senate of the extremely aged is going too far, but a Senate composed mostly of party elders and states-people would function better than today's Senate's too-ambitious, too-many-extremists mix.<br /><br />Half the problem is that many senators are more afraid of the primary than the general election because of the dominance of their party in the state. This means more party-line votes in the Senate and less compromise.<br /><br />There's no way to redraw state lines nor a way to marshal a proportional system (what would that even mean in the Senate, where the states aren't even close to the same population). But there's a way to make most Senators focus on the general election all the same: elect both senators from a state at once.<br /><br />If states use an instant runoff style method—say, ranked choice—it's easy to fairly choose the top two vote-getters. In some states that are extremely left-leaning or right-leaning, both Senators might be from the same party. But in quite a lot of states—and not just the battlegrounds—the likeliest result is one Senator from each party. The critical waterline would be that two-thirds or more of the voters in a state prefer one party in order to elect two senators from the same party. At this moment, about five Republican and five Democratic-dominated states cross this waterline, leaving the other 40 states as possible splits. Democrats might have a chance to elect one Senator in Texas; Republicans might have a chance to win one Senator in California.<br /><br />And running both seats in one race would help increase the representativeness of the Senate. Currently, 49% of people in a given state might disagree with both of their Senators, but with a top-two system, people have a greater chance to like at least one of their Senators.<br /><br />Wait, you ask: How would we divide the Senate races into three classes, so only one-third of Senators are chosen each election? The easiest answer is putting each state into a class based on order of admission to the union: Delaware was first, so class 1; Pennsylvania second, class 2; New Jersey third, class 3; Georgia fourth, class 1, and so on. The order of admission actually divides the country pretty nicely: each class would have states from every region of the country.<br /><br /><div class="separator" style="clear: both; text-align: center;"><a href="https://blogger.googleusercontent.com/img/a/AVvXsEh5s7aYmbtHENhgsFSJC2M3_dgUsLfhL0-lfEUiSgpucAudPfPDw_od4hLUnn0KYnxa0UZNQNs5CX7m4rawCSmspY38api_NAQhE-j0CZCn8MFzQrI1H-xVVXSBPDMHXx0dlZN44vDiA5rIm24lj1OS6njqbQ2WEdThuM9nFMIg_A_N11gB0P2NP7gF5w=s5285" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" data-original-height="3762" data-original-width="5285" height="285" src="https://blogger.googleusercontent.com/img/a/AVvXsEh5s7aYmbtHENhgsFSJC2M3_dgUsLfhL0-lfEUiSgpucAudPfPDw_od4hLUnn0KYnxa0UZNQNs5CX7m4rawCSmspY38api_NAQhE-j0CZCn8MFzQrI1H-xVVXSBPDMHXx0dlZN44vDiA5rIm24lj1OS6njqbQ2WEdThuM9nFMIg_A_N11gB0P2NP7gF5w=w400-h285" width="400" /></a></div><br />This would help immensely with the too-many-extremists problem, but there also needs to be a solution to the too-many-ambitious-types problem. Whenever there are too many ambitious types jockeying around, it's because there isn't enough work to do. But we can make Senators work harder. The Senate went from the cooling saucer of democracy to a stone-cold funeral slab under McConnell.<br /><br />The simplest solution: change the Senate's rules so the majority leader can't bottle up everything. Perhaps the Senate should be forced to vote on any bill that passes the House. Maybe the Senate should have to vote on any legislation that addresses an executive order or a Supreme Court decision. A co-equal branch of government shouldn't just twiddle its thumbs. The specifics are less important than the outcome: making the ambitious young things vote on more legislation. Every Senator should have a substantive record on important issues, rather than getting to hide behind the majority leader's apron. The Senate would look less and less like a way to vault your presidential campaign and more like a job that actually requires legislating.Russell Haneshttp://www.blogger.com/profile/13594411930757264086noreply@blogger.com0tag:blogger.com,1999:blog-8734744291040505450.post-33334339040415347062019-03-24T13:24:00.001-07:002019-03-24T17:00:31.824-07:00Scheduled elimination tournament calculator<b>Single-elimination</b> tournaments have one particular flaw: The tournament can only break powers of 2--i.e., 2, 4, 8, 16, 32, etc., teams can make it into the elimination rounds, unless the tournament decides to do a partial elimination round. For example, let's say the tournament decides to break 20 teams. So, the partial elimination round will involve eight teams debating, with twelve teams sitting around and waiting for two hours. The eight teams debating turns into four teams advancing to the first full elimination round, plus the twelve teams that sat around, making for a perfect bracket of sixteen. It works, but... meh. I don't like that the <i>majority</i> of the elimination-qualified teams did nothing for a whole round--it's kind of unfair that they could scout, plan a new strategy, or go get a nice meal and relax. And I especially don't like it, as a tournament director, that instead of just doing one big elimination round right after preliminary rounds and being done with it, I've got to drag it out into two smaller rounds. Let me explain this one a bit.<br />
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Ideally, a tournament breaks exactly one-third of its preliminary teams into elimination rounds. This is the ideal because preliminary rounds use one judge, elimination rounds use three, and well, you get the math. Assuming I have just enough judges for prelims, then breaking one-third of teams will use up all my judges perfectly for the first elimination round. The tournament director can say to every judge, "You must stick around for at least the first elimination round. I need everyone. Then I will start to dismiss judges whose schools have been eliminated." It works out brilliantly if every judge is used in elim round 1, half are needed in elim round 2, a quarter are needed in elim round 3... Smooth and simple.<br />
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Now consider the 20 teams breaking to elimination rounds problem. That means I have about 60 teams in prelims, and therefore 30 judges. In the partial elimination round, eight teams debate, so that is four rounds... therefore I need to use twelve of my 30 judges. In the first full elimination round, sixteen teams debate, so eight rounds, meaning I need 24 of my 30 judges. Notice how awkward and weird this has become? Some judges must judge both elim rounds--whom to pick? No one can go home until the first full elimination round is through, so that requires every judge to stay an extra two hours. Many of those judges will have nothing to do for the first two hours--I don't need them for a round. They just have to wait. Is there a better way to break a number of teams that isn't a power of 2?<br />
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<b>Double-elimination</b> tournaments can take on any even number of teams, so the above case of 20 is no particular problem, but they run into a different problem very quickly: the double elimination rule usually produces odd numbers of teams during the tournament for some rounds. If the tournament is run with brackets, then you can see how the math works quite easily. With 20 teams to start, ten will be undefeated and ten once-defeated after round 1. After round 2, five will be undefeated, ten will be once-defeated, and five twice-defeated and eliminated. That leaves fifteen teams and the perennial problem: some team has got to get a bye in round 3. Round 3! This is less fair than a team getting a bye in the partial elimination round in the single-elimination tournament. Is there no other option?<br />
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My proposed solution is the <b>scheduled-elimination</b> tournament. The plan is quite simple:<br />
<ol>
<li>Do not eliminate teams that are undefeated.</li>
<li>You must eliminate teams that are twice-defeated.</li>
<li>Decide which once-defeated teams to keep based on speaker points or preliminary seed.</li>
<li>Always keep an even number of teams.</li>
<li>Undefeated teams must debate undefeated teams; once-defeated teams must debate once-defeated teams; one pull-up is allowed.* (see note below for fun substitution!)</li>
</ol>
In practice, a scheduled-elimination tournament would look quite similar to a double-elimination tournament. Any (even) number of teams could break. There's an undefeated and once-defeated bracket going on in elimination rounds, just like in a double-elimination tournament.* (not necessarily--see note below!) But in many ways, the scheduled-elimination tournament is more similar to a single-elimination tournament: losing one round makes a team <u>eligible</u> for elimination. The tournament could decide to keep most of the once-defeated teams around, or eliminate most of them. It's up to the tournament. A once-defeated team might stick around to win the tournament, but only if the team had high enough speaker points or preliminary seed in order to never be eliminated. This being a mathematical problem, I made a graph to illustrate.<br />
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<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEj3MXPyhb1nmd6rdZgG0wv6WHkbWW43xByNbG8YgRicMJDx1FRW-sztpusrK5xNuBtQCQRanDVFjWsK3eKnMvqmuDqQqbTjuvnO7j8i9L3XUuArq5ZnsPIfnj6paZL5B9dbklod4FopMo-0/s1600/graphic1.png" imageanchor="1" style="clear: left; float: left; margin-bottom: 1em; margin-right: 1em;"><img border="0" data-original-height="671" data-original-width="1209" height="354" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEj3MXPyhb1nmd6rdZgG0wv6WHkbWW43xByNbG8YgRicMJDx1FRW-sztpusrK5xNuBtQCQRanDVFjWsK3eKnMvqmuDqQqbTjuvnO7j8i9L3XUuArq5ZnsPIfnj6paZL5B9dbklod4FopMo-0/s640/graphic1.png" width="640" /></a></div>
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The single-elimination option (green) and the double-elimination option (red) create a lower and upper boundary on possibilities for the scheduled-elimination tournament (anything in the gray area--and yes, I chose gray for its symbolism). So long as the tournament keeps the remaining number of teams in the gray zone, then it has abided by condition 1 and 2 that I specified above. The gray zone represents all the once-defeated teams in the tournament. If the tournament cuts closer to the green curve, it eliminates most of the once-defeated teams. If the tournament goes closer to the red curve, it keeps most of the once-defeated teams. As you can see, the red curve is flat at first--no one in a double-elimination tournament is eliminated after only one round.<br />
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You might wonder what the two marked points, (3.32, 2) and (6.16, 2), are. This represents how many rounds each type of tournament will need to have, because two teams remaining leads immediately into the final round. The single-elimination tournament needs to have 3.32 rounds, plus the championship round. About one-third of teams participate in the partial round (eight out of 20), thus the 0.32, then the first full elim round will be sixteen teams, the second round will be eight, the third round will be four, and the fourth round will be two teams--the championship round. Four rounds, plus a partial. Similarly, the double-elimination tournament will need to have 6.16 rounds, plus the championship round. That means you're looking at seven or eight total rounds, including the championship round, depending on how the byes and pull-ups go. The scheduled-elimination tournament would have more than the four plus partial (so really five) elimination rounds of the single-elim tournament but fewer than the seven elimination rounds of the double-elim tournament.<br />
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There is considerable choice in that gray zone for how to run a scheduled-elimination tournament. One option would be to run what is almost a single-elimination tournament--but with no partial elimination round to start. Here's an example:<br />
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<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEghtczvMIdefyx-AHRZBKwbMHU6jeQKz1XjKEnzCjcMHddvFsUtSG2oORrtJ6qL7lMmV5vDosk6zZCWsABljpBThOWtCKg_i6ztvINYi3VexIyrSEpNeFCdfkjJLYjPL5LV7xGIR1blRrt1/s1600/graphic2.png" imageanchor="1" style="clear: left; float: left; margin-bottom: 1em; margin-right: 1em;"><img border="0" data-original-height="671" data-original-width="1209" height="354" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEghtczvMIdefyx-AHRZBKwbMHU6jeQKz1XjKEnzCjcMHddvFsUtSG2oORrtJ6qL7lMmV5vDosk6zZCWsABljpBThOWtCKg_i6ztvINYi3VexIyrSEpNeFCdfkjJLYjPL5LV7xGIR1blRrt1/s640/graphic2.png" width="640" /></a></div>
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The tournament starts with 20 teams entering: (0, 20). Ten team remain after round 1: (1, 10). (The round itself is really the line segment from (0, 20) to (1, 10): starting with 20 and ending with 10 is round 1's effect.) After round 2, there are five undefeated teams, but the tournament keeps one once-defeated team for a total of six teams: (2, 6). There could be as many as three undefeated teams after round 3, but the tournament keeps four teams on just in case: (3, 4). After round 4, only two teams remain (4, 2), and then round 5 will be the championship round between those two teams. By keeping on perhaps <i>two</i> teams that are once-defeated (after rounds 2 and 3), this method eliminates having the partial elimination round where <i>twelve</i> teams sit around pointlessly, and it has made managing the judging pool much, <u>much</u> more predictable. The tournament will use: 100% of its judging pool for round 1, 50% for round 2, 30% for round 3, 20% for round 4, and 10%--the final three judges--to decide the championship round.<br />
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Another option is that a tournament could basically hew as close as possible to running a double-elimination tournament, yet avoid the problem of byes, by using a scheduled-elimination tournament. Here's an example:<br />
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<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEiJWDDK3HHyfWl7BgMuJRUjDe4g-Zzw6dmen0klt9BBxYekVe3lwoWdfAiHuI6mKBU-sh0Uzalmapmt9yL4j_mlO8yj_2qmmXVpjlzv9SduxJvjGhtyVubaPX_WCVyV50HnQVmZ7u3wir9Z/s1600/graphic3.png" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" data-original-height="671" data-original-width="1209" height="355" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEiJWDDK3HHyfWl7BgMuJRUjDe4g-Zzw6dmen0klt9BBxYekVe3lwoWdfAiHuI6mKBU-sh0Uzalmapmt9yL4j_mlO8yj_2qmmXVpjlzv9SduxJvjGhtyVubaPX_WCVyV50HnQVmZ7u3wir9Z/s640/graphic3.png" width="640" /></a></div>
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As you can see, this tournament eliminates no team after round 1 (all twenty remain), eliminates six teams after round 2 for fourteen remaining, eliminates four teams after round 3 for ten remaining, eliminates four after round 4 for six remaining, eliminates two after round 5 for four remaining, and eliminates two more after round 6 for two remaining. The championship round will be round 7 between the two final teams. (In practice, because of pull-ups, this could potentially violate my second condition in the list above--some twice-defeated teams might stay in. The tournament should probably not cut quite so close to the red curve if it wants to respect this condition. The sequence 20-20-12-8-4-2 might be better in this regard.)<br />
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This option lengthened the tournament by two rounds compared to the previous option, but the trade-off is that this tournament eliminated almost no once-defeated teams. In general, it's possible that a once-defeated team goes on to win a scheduled-elimination tournament (e.g., they defeat the remaining undefeated team in the final round and beat them on points) if somewhat unlikely. It's also possible that a once-defeated team survives the cut after round 3, yet even though it wins round 4, the team doesn't survive that post-round 4 cut because its speaker points aren't high enough. This outcome seems reasonable enough to me. Being eliminated based on one loss and low points seems fine to me, although I would generally want my tournaments to stay closer to the two loss and done side of the gray zone. But--it's up the tournament to decide what makes sense for their goals and available time and judges.<br />
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I think I would add one other condition to a scheduled-elimination tournament, for a total of six. <b>Condition #6 is:</b> "Once the tournament begins eliminating teams, never increase the number of teams cut after a round above how many were cut after the previous round." In other words, the curve of cuts should flatten out. In the example graph immediately above, the cuts go: -6, -4, -4, -2, and -2. This seems reasonable and straightforward. It seems beyond silly to have the cuts go: -6, -8, -4, -2, -4, -2. Put them in a more sensible order.<br />
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I've made the applet available for you to use here: <a href="https://ggbm.at/dx9kgnbb">https://ggbm.at/dx9kgnbb</a>. You can change the number of teams, and move the number of teams remaining after each round up or down. The line segments between each round will only show if you meet my sixth condition of eliminating fewer (or the same) number of teams after each round than the previous round.<br />
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* <b>Fun addendum:</b> This condition can be swapped out for a different one. The teams do not need to debate within brackets--i.e., several undefeated teams could debate once-defeated teams--so long as no cut is ever more than one-half of the teams remaining (which just seems reasonable and fair). The "no-more-than-half" rule can be substituted for the bracket condition without any risk of violating the first condition to not eliminate undefeated teams. The proof of this is fairly elementary, but let's think through an example first. Say 100% of the teams still in the tournament are undefeated (because you eliminated all the once-defeated teams). After one additional round, 50% will be once-defeated. That turns out to be the worst possible case, so the "no-more-than-half" rule keeps us on the happy side of condition #1.<br />
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Let's do this more conclusively with a bit of algebra. Say x% of the teams were undefeated and y% were once-defeated (and obviously x+y=100). If x><y 50="" after="" at="" be="" can="" hand="" has="" if="" less="" more="" most="" on="" one="" other="" remain="" round.="" since="" teams="" than="" the="" then="" to="" undefeated="" x="" y=""><y 50="" all="" an="" and="" as="" be="" debate="" hand="" less="" many="" might="" must="" of="" on="" other="" remain="" remember="" say="" so="" team="" teams="" than="" that="" the="" then="" undefeated.="" undefeated="" x="" y="">y, then y undefeated teams might debate y once-defeated teams, leading to y% of teams remaining undefeated. The remainder of undefeated teams, x-y, will have to debate themselves. So (1/2) (x-y) will also be undefeated through that pathway. That means we have y + (1/2) (x-y) undefeated teams, which simplifies to (1/2) x + (1/2) y, or (1/2) (x+y). Since x+y=100, that means 50% will be undefeated. The worst case scenario is that as many as 50% of the teams are undefeated. Never eliminate more than half of the teams remaining after a round, and the bracket condition can be dropped. It's a huge benefit to be able to drop it! This makes many more rounds possible--so you can avoid schools debating themselves, or opponents debating each other multiple times, until the very end of the tournament. Yay!</y></y>Russell Haneshttp://www.blogger.com/profile/13594411930757264086noreply@blogger.com0tag:blogger.com,1999:blog-8734744291040505450.post-78582375584900241832019-03-21T10:31:00.002-07:002019-03-21T10:31:04.726-07:00Daylight Savings TimeWhy do we bother with daylight savings time? And... why do we call it "daylight savings" anyway? There's a simple answer that becomes apparent when one looks at a graph of available daylight throughout the year.<br />
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The data below is pulled from wunderground for Portland, Oregon, but adapted by me. I looked up the statistic of actual time day length for each month (on the 21st day), which roughly tells us how many hours of daylight there are (it's sunrise to sunset, so it ignores twilight time). I adapted it by imagining that solar noon--when the sun is at its highest point of the day--is clock noon--when the clocks say 12:00. Solar noon is NOT usually clock noon, but here's what it would look like if it were:<br />
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The solid line in the center is both solar and clock noon.<br />
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As you can see, this is going to work out fairly well in the late fall and winter months. Sunrise in October is just a bit before 7 am and sunset is after 5 pm. Dark December has a sunrise just before 8 am and a sunset just after 4 pm--at least young children can go to and return from school before it is dark. Given that there's so little daylight, it's hard to imagine how we'd want to split things up differently in winter. What should we do with December? Have sunrise at 9 am so we can have sunset after 5 pm? This seems absurd. Have sunrise at 7 am and then have sunset at 3 pm? Even more ridiculous. Solar noon = clock noon seems like the best solution.<br />
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The solar noon = clock noon is called STANDARD time, and it is what we do in the winter in the U.S. On December 21st, the sunrise was at 7:49 am, the sunset was at 4:30 pm, which means solar noon was at 12:10 pm. Easy peasy, so why not keep STANDARD time all year?<br />
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Look again at the chart above, specifically at June. Does it make sense to have the sunrise at nearly 4 am? Are many people going to enjoy the extra hours of sunlight then? Probably not many. It makes more sense to move the clocks forward one hour so 4 am sunrise on June 21st becomes instead a 5 am sunrise--but that also shifts sunset from 8 pm to 9 pm, an extra hour of sunlight in the evening when people are awake and can enjoy it. This is called daylight SAVINGS time because we're "saving" the time from the morning, when few are awake to enjoy it, and then "spending" the time in the evening, when nearly everyone can benefit from it. In truth, Portland, Oregon is far enough north that we could benefit from two hours of a clock shift--5 am sunrise to 7 am and 8 pm sunset to 10 pm sunset--but the one hour of clock shift is a compromise with more southerly states.<br />
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Because the day lengths change very little near the equator, it makes no sense for countries located in the tropics to do anything other than standard time. Sunrise will be approximately 6 am, and sunset will be approximately 6 pm, month after month. For lower/mid-latitude countries, a one-hour shift in the summer--so the extra sunlight is "SAVED" for the evening hours--makes some sense. For higher/mid-latitude countries, perhaps two hours or more of a shift makes sense, but beyond perhaps two hours, you've maxed out the benefit. Who cares if daylight goes to 11 pm or midnight? Very few people would want to be awake to enjoy the sunlight.<br />
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In fact, beyond even a certain high latitude, even shifting clocks an hour is pointless. If you're inside the Arctic or Antarctic Circles, you're going to get 24 hours of sunlight. Why change the clocks at all from standard time? You don't need to "save" morning sunlight for the evening--you're going to get sunlight all evening anyway.<br />
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To sum up, if people were to decide this rationally based on latitude alone:<br />
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Equator - standard time all year<br />
Mid-latitude - standard time in winter, one or two hour later shift in summer<br />
Arctic circle - standard time all yearRussell Haneshttp://www.blogger.com/profile/13594411930757264086noreply@blogger.com0tag:blogger.com,1999:blog-8734744291040505450.post-60676304983493175042018-12-12T14:26:00.001-08:002018-12-12T14:26:43.612-08:00Tabulation softwareHi all,<br />
<br />
I've been thinking about how to run tournaments for many years and publishing articles on it. My published ideas have ranged from <a href="https://docs.wixstatic.com/ugd/9896ec_156a2e5255b84c9e9decdfab98108ec5.pdf" target="_blank">geographic mixing</a>, <a href="https://docs.wixstatic.com/ugd/9896ec_0b38e3ce8fb74e3c85ca1c5f110c1d47.pdf" target="_blank">logit</a> <a href="https://docs.wixstatic.com/ugd/9896ec_0b38e3ce8fb74e3c85ca1c5f110c1d47.pdf" target="_blank">scores</a>, and new methods for <a href="https://docs.wixstatic.com/ugd/9896ec_86a784f59a1e43a2b2263e67f6cbaf7a.pdf" target="_blank">strength-of-schedule pairing and constrained side equalization assignment</a>.<br />
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I've finally gotten around to putting all the ideas into a single, programming-ready document. I'm putting it out there as a Creative Commons Attribution (BY) license, version 4.0. Please feel free to use any ideas contained herein, as long as you attribute me.
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<div style="display: block; font-family: "helvetica" , "arial" , sans-serif; font-size: 14px; font-stretch: normal; font-style: normal; font-variant: normal; font-weight: normal; line-height: normal; margin: 12px auto 6px auto;">
<a href="https://www.scribd.com/document/395567556/Tabulation-Software-Description#from_embed" style="text-decoration: underline;" title="View Tabulation Software Description on Scribd">Tabulation Software Descrip...</a> by <a href="https://www.blogger.com/undefined#from_embed" style="text-decoration: underline;" title="View 's profile on Scribd"></a> on Scribd</div>
<iframe class="scribd_iframe_embed" data-aspect-ratio="null" data-auto-height="true" frameborder="0" height="600" scrolling="no" src="https://www.scribd.com/embeds/395567556/content?start_page=1&view_mode=scroll&show_recommendations=true&access_key=key-Zrj0gvoIPnT81BDJdhSS" title="Tabulation Software Description" width="100%"></iframe>Russell Haneshttp://www.blogger.com/profile/13594411930757264086noreply@blogger.com0tag:blogger.com,1999:blog-8734744291040505450.post-22877434913855940112018-08-07T13:09:00.000-07:002018-08-07T13:09:31.387-07:00Approval voting and primariesCalifornia and Washington both use the top-two, open primary method in their elections: voters get to pick from, regardless of party, any primary contender to go onto the general election. The top two vote getters in the primary, regardless of party, move on to the general. One consequence of this is that a party could get "locked out" of a particular race if none of its candidates qualify for the top two spots. As a result, the parties have been especially concerned with having too many candidates in a race and splitting its voters into too-small factions, thus depriving any of the party's candidates from making it onto the general ballot. See this <a href="https://www.vox.com/2018/8/7/17649564/washington-primary-results">article for a description of the problem</a>.<br />
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There's a very easy, very simple fix for the second part of this problem: approval voting. Here's my two-sentence description of approval voting:<br />
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<blockquote class="tr_bq">
Each voter can put a check next to as many candidates as they approve of, leaving disapproved-of candidates blank. The candidate(s) with the most votes win(s).</blockquote>
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That's it. Ballots look the same. It's not complicated to explain. And approval voting lends itself to virtually no strategic voting (i.e., faking your preferences on the ballot to try to induce your desired outcome to happen).<br />
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In the top-two primary, everything would work the same, except that voters wouldn't get one choice; they could vote for as many candidates as they like. ABBAs could vote for every ABBA candidate, and BeeGees could vote for every BeeGee candidate. Or ABBAs could vote for most ABBA candidates and some centrist BeeGees. Or a centrist could vote for some centrist ABBAs and some centrist BeeGees. Let's imagine a scenario in which a district is 51% ABBA voter and 49% BeeGees. Let's say each side nominates three candidates: A, B, and C for the ABBAs, and X, Y, and Z for the BeeGees.<br />
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In a hyper-partisan environment, 100% of ABBA voters approve of A, B, and C, and 0% approve of X, Y, and Z; vice versa for all the BeeGee voters. Because there are slightly more ABBA voters (51-to-49), therefore the top two candidates will always be some combination of A, B, and C (more on this in a second). The BeeGee would be locked out. However, this lock-out has nothing to do with how many candidates the BeeGees nominated. It would have happened whether they nominated two, three, four, or a hundred candidates. The lock-out is the result of the hyper-partisan environment, not the number of candidates nominated splitting the vote. No matter how many candidates the BeeGees nominate, they all get 49% of the vote and fall short of the general ballot.<br />
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Let's go back to that issue of which two of A, B, and C make the general ballot in the hyper-partisan environment. If it is truly a tie--all three got exactly the same number of votes--then some tie-breaking mechanism would have to be employed. They could draw straws, or the ABBA party chairperson could decide because all of the candidates are its own. But this three-way tie seems fairly unlikely. Would primary ABBA voters be so united in support of all three candidates that they give 100% approval to each? I guess this is an argument that such hyper-partisanship seems unlikely; it's more likely A gets 95% approval from ABBA voters, B gets 90%, and C gets 70% or some such split. If there aren't at least two of ABBA's candidates that get 100% approval from ABBA voters, it opens up the possibility that a BeeGees candidate can make it to the general election.<br />
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Furthermore, it seems unlikely that there are no unaffiliated voters exist and that none of the partisans ever cross-over. Even in today's highly partisan environment, people can and do split tickets, switch parties, and cross-over. (I reserve hyper-partisanship to mean zero behavior exists.) Some ABBA voters might approve of A, B, and Z. Some centrist voters might approve of B and X. Having unaffiliated voters and cross-over votes doesn't guarantee ABBA candidates or BeeGee candidates won't be locked out--but it does make it less likely. Even in a highly partisan environment, candidates with cross-over appeal might be at somewhat of a practical advantage. Winning 99% of 51% of the total votes (almost all ABBA voters) is 50.49% of the total; winning 90% of 51% of the total votes (most ABBA voters) and 10% of 49% of the total votes (a smattering of BeeGee voters) is 50.8% of the total votes. As a real-world matter, I think it's harder to get complete party unity behind a candidate (that is, 99%) than it is to attract a couple percentage points from the other party. Maybe I'm wrong, but look at this <a href="http://www.pewresearch.org/fact-tank/2018/08/01/trumps-approval-ratings-so-far-are-unusually-stable-and-deeply-partisan/">graph of presidential approval ratings</a>. Of the twelve presidents of the modern era, nine were able to pick up more support from the opposition party than they lost from their own. Only two were better able at holding their own party together than at attracting opponents (Barack and the Donald). The twelfth case, Jimmy, did dismally with both parties. The average trend is that pulling in opposition is easier than preventing any defections.<br />
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In an approval voting scheme for a top-two primary, it's possible that a party gets locked out, but the cause would not be how few or many candidates they nominate. A party would get locked out if (1) the other party had more voters and had at least two candidates they completely unified behind or if (2) the other party had at least two candidates with cross-over appeal. Scenario 1 seems unlikely as an empirical matter; scenario 2 seems like it fulfills the exact purpose of top-two primaries of selecting the two best candidates overall--who just happen to be from the same party, but expanded their support beyond it.<br />
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By the way, the approval voting scheme makes sense for regular primaries too, or any time voters have more than two choices they need to whittle down. I use it in meetings whenever we have more than two options to consider to find out where the general consensus lays.<br />
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There's not much an individual voter can do to vote strategically. Some might consider giving an approval vote to the candidate I find least objectionable from the party I disagree with, if I think it's inevitable that the other party will get one candidate in. (In other words, it's inevitable, so chose the weakest opposition.) This seems an unlikely scenario, however, and a risky strategy. When do I know the other party is nearly guaranteed a spot in the general election? Only when my party has nominated only one candidate or only one strong candidate (so, unlikely). And it's a risky strategy: my approval vote for the weakest opposition might be enough to push TWO of the opposition party's candidates into the general election, excluding my candidate entirely. Let's say the standings look like this, including my vote for my candidate but not yet voting for the opposition candidate:<br />
<br />
<blockquote class="tr_bq">
My candidate - 51%<br />Opposition candidate I hate - 49%<br />Opposition candidate I would prefer - 49%</blockquote>
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In this case, I do get to decide which opposition candidate we face in the general election. But the scenario could just as easily be this:<br />
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<blockquote class="tr_bq">
My candidate - 49%<br />Opposition candidate I hate - 51%<br />Opposition candidate I would prefer - 49%</blockquote>
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In this case, the opposition candidate I hate is inevitable. My vote for the opposition candidate I prefer knocks out my candidate. (At least before, my candidate might have won the tie-breaker for second place.)</div>
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<br /></div>
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Who can say which scenario is likely to happen in a close race before the voting is done? This strategy is incredibly risky when everyone votes before votes are tallied.</div>
Russell Haneshttp://www.blogger.com/profile/13594411930757264086noreply@blogger.com0tag:blogger.com,1999:blog-8734744291040505450.post-18708930851069116012018-07-27T12:38:00.000-07:002018-07-27T12:38:34.215-07:00Random matching in debate tournamentsEvery debater knows the predicted number of teams with each record when power-matching is used:<br />
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<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEheybv2wl7u1kR4-Qrdanft3q5xnC-jrBfbLjb78Uc_ov6Vho4alrkr5HRmPqfMail6xV7GEa0AB0kZ2Wl5NNMl0CzeBbo-0dX5Y17Nbukb5NEoKENvloKoyNMW2HyFkUPDz09Yxc7ejfR1/s1600/img0.jpeg" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" data-original-height="157" data-original-width="735" height="85" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEheybv2wl7u1kR4-Qrdanft3q5xnC-jrBfbLjb78Uc_ov6Vho4alrkr5HRmPqfMail6xV7GEa0AB0kZ2Wl5NNMl0CzeBbo-0dX5Y17Nbukb5NEoKENvloKoyNMW2HyFkUPDz09Yxc7ejfR1/s400/img0.jpeg" width="400" /></a></div>
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and so on. But how would it work without power-matching? What if teams were paired at random? The easy part is using the laws of probability to figure out which matches happen by chance. That's listed in column F.<br />
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The hard part is figuring out which team wins. If both teams have the same record, then whichever team wins, the outcome is the same. For example, in round two, the 25 teams in 1-0 vs. 1-0 rounds (ignore the fact that this is odd--it makes no difference in the end) and the 25 teams in 0-1 vs. 0-1 rounds guarantees that 12.5 teams will have a 2-0 record; 25 will be 1-1; and 12.5 will be 0-2. These guaranteed outcomes are listed in column I.<br />
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But what happens if the two teams have different records? One possibility is that there are no upsets at all. For example, in round two, of the 50 teams in 1-0 vs. 0-1 rounds, exactly half are 1-0s. These 25 teams might all win--no upsets--and become 2-0s. The 25 teams that are 0-1s all become 0-2s. These no-upset results are listed in column J.<br />
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The other possibility is that all rounds with mixed records have upsets. In round two, of the 50 teams with 1-0 vs. 0-1 rounds, the 25 teams that are 0-1s could all win, becoming 1-1s, while the 25 teams with 1-0s all lose, become 1-1s. Thus all 50 teams end up 1-1. These all-upset results are listed in column K.<br />
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Of course, neither no-upsets or all-upsets is realistic. From other research I've done, it turns out the upset rate is more like 20%, so I blended the two results 80:20 no-upsets:all-upsets in column L. As you can see, the ultimate outcome is that each record is nearly balanced with the others, though slightly more in the mediocre results. For example, after three rounds, a 20% upset rate results in about 17 teams that are 4-0s; 22 teams that are 3-1s; 23 teams that are 2-2s; etc.<br />
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Yet the 20% upset rate is probably conservative. It is unlikely that an 0-3 team has a 20% chance against a 3-0 team. As the teams are farther apart in record in later rounds, the overall upset rate must drop. If this is so, the final outcomes flatten. It turns out that if the upset rate is 1/6 for round two, drops to 1/8 for round three, and further drops to 1/10 for round four, then the final outcome is that exactly 20 teams are 4-0s; 20 are 3-1s; etc.<br />
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<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgvCB9mrtV3Sc2fJy4eZSzPBbj6MZMgET71MHHmfPPNkrniEJ1nzbRKTPMcjgj1yTK27bprQ8nxDpdn8Fx1ibJe4xp5nige5JQB0avI05rdW_IhDQttpKYbDhVA9A3l_-_XNDnWL7_HXV6u/s1600/img2.jpeg" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" data-original-height="499" data-original-width="803" height="247" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgvCB9mrtV3Sc2fJy4eZSzPBbj6MZMgET71MHHmfPPNkrniEJ1nzbRKTPMcjgj1yTK27bprQ8nxDpdn8Fx1ibJe4xp5nige5JQB0avI05rdW_IhDQttpKYbDhVA9A3l_-_XNDnWL7_HXV6u/s400/img2.jpeg" width="400" /></a></div>
<br />
What happens if teams are paired at random? It depends on the upset rate. If it's exactly 50% (which is far too high), then the final outcomes look exactly like it would with power-matching:<br />
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<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEiNM8xGgklkqnPiKNXSZu6ucpXqFvfSnSrLK8l4mz9VIjTWPJtIh-MzTOQI6P11z-hr_5BDgEDELz7PqG3RG7yULxOANPIbJaOR0Unws_i9yLV0dD7DiaHNQiTLVUeJIV9EonOsOlXaJ-ro/s1600/img3.jpeg" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" data-original-height="507" data-original-width="807" height="251" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEiNM8xGgklkqnPiKNXSZu6ucpXqFvfSnSrLK8l4mz9VIjTWPJtIh-MzTOQI6P11z-hr_5BDgEDELz7PqG3RG7yULxOANPIbJaOR0Unws_i9yLV0dD7DiaHNQiTLVUeJIV9EonOsOlXaJ-ro/s400/img3.jpeg" width="400" /></a></div>
<br />
If the upset rate is a more realistic, empirically justified 20%, then the outcomes are much flattened and nearly equally distributed:<br />
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<br />
Here's the <a href="https://drive.google.com/open?id=1MwJSzea7SPolpGWzlOHwdoLyC6hG8sEM">sheet</a> for anyone who'd like to play around with it.Russell Haneshttp://www.blogger.com/profile/13594411930757264086noreply@blogger.com0tag:blogger.com,1999:blog-8734744291040505450.post-48483834186563226552018-05-16T21:52:00.000-07:002018-07-10T08:31:24.437-07:00Why debate tournaments have been doing side assignment wrongSide assignment is easy, right? In odd rounds, assign teams to sides at random. In even rounds, assign each team to the opposite side as the previous round. What could be easier?<br />
<br />
The problem is that this makes even rounds harder to pair. Any tournament director can tell you that even rounds often "lock up" and that one has to break brackets to make matches. I know I've sat at a screen, wishing the two 5-0s that are both due Aff could hit, instead of each getting a pull-up.<br />
<br />
I stumbled on an alternative, what I call the constrained side equalization (C.S.E.) method. Instead of balancing Aff-Neg rounds at the end of even rounds, this method works its magic at the end of odd rounds. Here's the C.S.E. in action:<br />
<br />
<b>Rd 1</b> - paired at random<br />
<b>Rd 2</b> - paired at random, ignoring sides. If both teams were Aff in round 1, or both Neg in round 1, it's a computer flip-for-sides. If one team was Aff and the other was Neg, then the sides are equalized.<br />
<br />
<i>At the end of round 2, about 25% of teams will have two Affs, 25% two Negs, and 50% will be balanced. (It depends on the random pairings.)</i><br />
<br />
<b>Rd 3</b> - Teams with two Affs must go Neg; teams with Negs must go Aff. The balanced teams are not assigned to either side. If a balanced team is matched against a two-Aff team, then the two-Aff team goes Neg. Likewise, if a balanced team is matched against a two-Neg team, then the two-Neg team goes Aff. If a two-Aff team is matched against a two-Neg team, then the sides are equalized. And if a balanced team is matched against a balanced team, then it's a computer flip-for-sides.<br />
<br />
<i>At the end of round 3, every team will either have had two Affs and one Neg, or two Negs and one Aff. In other words, at the end of an odd round, the sides are "equalized."</i><br />
<br />
The cycle repeats. <b>Round 4</b> is paired at random, ignoring sides. <b>Round 5</b> has the constraint that teams with three Affs must go Neg and teams with three Negs must go Aff; otherwise, any team can be paired against any other. If the tournament ends on an odd round, there's no special other consideration. If the tournament ends on an even round, you'd want to pair teams in the typical way for the final prelim.<br />
<br />
Mathematically, it is as simple as this rule:<br />
<blockquote class="tr_bq">
<u>If the Aff rounds - Neg rounds is 2 or -2, then the team is assigned a </u><b style="text-decoration-line: underline;">side</b> <i style="text-decoration-line: underline;">first</i><u>, </u><i style="text-decoration-line: underline;">then</i><u> paired with an </u><b style="text-decoration-line: underline;">opponent</b><u>; otherwise, a team is assigned an <b>opponent</b> <i>first</i>, <i>then</i> assigned a <b>side</b> (to equalize if necessary)</u>.</blockquote>
This works in odd or even rounds.<br />
<br />
But why go to all this bother? The reason is simple: constraints.<br />
<div style="text-align: left;">
<br /></div>
<table border="1" cellspacing="0" style="color: #222222; font-family: arial, sans-serif; font-size: small; text-align: left; width: 50%px;"><tbody>
<tr><td style="margin: 0px; text-align: center;"></td><td style="margin: 0px; text-align: center;"> Odd</td><td style="margin: 0px; text-align: center;">Even </td><td style="margin: 0px; text-align: center;">Avg. </td></tr>
<tr><td style="margin: 0px; text-align: center;"> Trad.</td><td style="margin: 0px; text-align: center;"> 100%</td><td style="margin: 0px; text-align: center;">50% </td><td style="margin: 0px; text-align: center;">75% </td></tr>
<tr><td style="margin: 0px; text-align: center;">Alt. </td><td style="margin: 0px; text-align: center;"> 87.5%</td><td style="margin: 0px; text-align: center;">100% </td><td style="margin: 0px; text-align: center;">94% </td></tr>
</tbody></table>
<div style="text-align: center;">
<br /></div>
<div>
In a traditional method, in odd rounds, 100% of possible matches-- 0.5 * (n (n - 1)) --could be considered. There are no side constraints in odd rounds, so anyone could be matched against anyone. But in an even round, a tournament is limited to a fourth of (n (n - 1)). A due-Aff team can only be matched against a due-Neg team. This is a <i>huge</i> constraint.</div>
<div>
<br /></div>
<div>
Using the C.S.E. method, in odd rounds, teams with more Affs must go Neg and vice versa. Aside from this small constraint (only about one-eighth of possible matches ruled out), nearly anyone can debate anyone. And in even rounds, it's 100% of possible matches that can be considered. The C.S.E. method has much lower overall constraints than the traditional method.</div>
<div>
<br /></div>
<div>
In other words, the odd C.S.E. round is considerably easier to pair than the even traditional round (21 times better odds of finding a good pairing, in fact). If a side assignment for C.S.E. happens to not turn up a suitable pairing, why, you can reshuffle the teams--switching some randomly selected teams' side, excepting the couple side-constrained teams--and try again. This works whether it's an odd or an even round. In the traditional method, you can only reshuffle with an odd round. You're stuck with the even round side assignments you get with the traditional method. This inability to reshuffle the teams means the tournament can lock up. In the C.S.E. method, because any round can be reshuffled, there's always another chance to find a good pairing.</div>
<div>
<br /></div>
<div>
I worked out <a href="http://www.mediafire.com/file/8lm4kuqs5auqcsn/side_constraints.xlsx">an example here</a>. At the end of five rounds of C.S.E., every team had either two or three Affs. The method yielded side "equivalence."<br />
<br />
But, intriguingly, the teams took different paths to get there. Some went Aff two times in a row. Some alternated. Although all the paths end with one of two correct results--two or three Affs--there were more path types to get there and thus more options to pair the teams. More paths = more flexibility. We've been doing side assignment the hard way!</div>
Russell Haneshttp://www.blogger.com/profile/13594411930757264086noreply@blogger.com0tag:blogger.com,1999:blog-8734744291040505450.post-32987646167062062018-04-07T20:35:00.000-07:002018-04-07T20:35:01.408-07:00Experimental verification of the logit scoreOne method for ranking teams that I <a href="http://art-of-logic.blogspot.com/2017/02/the-logit-score-new-way-to-rate-debate.html">introduced to the debate community is the logit score</a>. The logit score is derived from a logistic regression. The logit score combines a team's record, speaker points, and its opponents' strength into a single number. Because the logit score factors in record and points, it is performance-based, but that record is adjusted by opponent strength, making the logit score more fair than record alone. A win against a good team is "worth" more than a win against a weak team. If you take the worst opponent a team beat and the best opponent it lost to, and average those together along with the team's average speaker points, then you're approximating the team's logit score. Due to how the logit score is calculated, it is the likeliest team strength that explains its results: its record and its points.<br />
<br />
I had previously looked for <a href="http://art-of-logic.blogspot.com/2017/02/the-logit-score-new-way-to-rate-debate.html">empirical support for the logit score</a> in a college debate season. I took the real results for the entire season and used them to calculate each team's logit score. I then used those to retrodict the winner in every single match-up that had actually happened, with the higher ranked by logit score team retrodicted to win the round. The logit score did this better than every other ranking method I also tested, slightly edging out median speaker points, and doing better by a goodly margin than the win-loss record. Despite this success, there was the nagging concern that the logit score was being derived from an entire season's worth of information. This empirical support could not show if the logit score would work for a single tournament.<br />
<br />
Therefore I set out to do an experiment. I created a <a href="https://docs.wixstatic.com/ugd/9896ec_d268e65460f74551b1101c6574a48814.pdf">simulation tournament in a program</a>, and ran and re-ran it hundreds of times. I tested various tournament conditions, from random prelims to a typical method of power-matching to pre-matching (like a round robin). I looked to see whether in these kind of conditions--using only the information available in a tournament--the logit score fared as well in comparison to record-based rankings and to speaker point-based rankings.<br />
<br />
The results are that, in any condition, the <a href="https://docs.wixstatic.com/ugd/9896ec_d268e65460f74551b1101c6574a48814.pdf">logit score is a vast improvement</a> on the win-loss record, but not quite as good as speaker points. It may surprise people to realize that speaker points, even though they vary considerably from judge to judge, are the best information to rank teams. A team's median speaker points isn't affected too much by one judge. Speaker points are rich data when you only have six or eight rounds to rank a team.<br />
<br />
However, I believe many in the community would not prefer to use speaker points alone. If nothing else, ignoring wins and losses gives a perverse incentive to teams to speak pretty and ignore winning key arguments. The logit score is a solid, thoughtful compromise. The logit score is based on both wins and points, so there's no perverse incentive to ignore key arguments--nor is there an incentive to ignore effective, mellifluous communication. Although the logit score is slightly less accurate for a single tournament than speaker points alone, the logit score is far more accurate than win-loss record is. The logit score is, in other words, a <a href="https://docs.wixstatic.com/ugd/9896ec_d268e65460f74551b1101c6574a48814.pdf">vast improvement on the status quo method</a>--a compromise in name only.Russell Haneshttp://www.blogger.com/profile/13594411930757264086noreply@blogger.com0tag:blogger.com,1999:blog-8734744291040505450.post-7939450825463128752017-11-11T14:33:00.000-08:002017-11-11T14:33:30.901-08:00Mixed member HouseI've written about <a href="http://art-of-logic.blogspot.com/2017/02/gerrymandering.html" target="_blank">gerrymandering</a> before (and <a href="http://art-of-logic.blogspot.com/2014/05/hands-off-redistricting.html" target="_blank">solutions</a> to it), but the more I think about it, the best way to fix the problem is to remove the incentive. <a href="http://art-of-logic.blogspot.com/2012/02/proportional-representation.html" target="_blank">Proportional representation</a> is good (and <a href="http://art-of-logic.blogspot.com/2012/07/proportional-representation-2.html" target="_blank">here</a>), but the simplest change to the system is mixed member representation.<br />
<br />
Here's how the system could work:<br />
<br />
<ol>
<li>Expand the size of the House to 540 districted members. This means the smallest district (Wyoming's) is everyone's size--about 600,000 constituents. The current number of House districts--435--has been fixed since <i><b>1911</b></i>. Some things have changed since then... (I guess this isn't strictly necessary to a mixed-member system.)</li>
<li>Have independent commissions in each state draw the districts, with a first priority to keep communities of interest together, although districts need to have the same 600,000 people, so it won't be perfect. This means you'll have some heavily African-American districts, heavily Latino districts, and big rural districts. Geographical compactness can take a back seat. Yes, that's right--we might have some ugly, squiggly districts. Trust me, this will work. Independent commissions' proposal should be approved by 2/3 of the votes in the state legislature, which should be easily achieved because everyone can recognize that districts are reasonable communities of interest.</li>
<li>Modify ballots to include two questions for the House races: (a) <i>Which candidate do you support for your House district?</i> This could use approval voting to allow selection of more than one candidate in multi-candidate races. (b) <i>Which party would you like to see control the House?</i> This must be a single selection.</li>
<li>Winners on question 1 win their district and get the seat. Because of the way we've drawn the districts, we're more likely to see black representatives run and get elected, Latino representatives, etc.</li>
<li>We've got district races done and can look at the composition of the entire House so far. For example, the House might be 290 seats for party A, 250 for party B. This establishes the <b><i>seat share</i></b> for party A of 53.7%. In the next stage--the mixed member part--votes on <i>question 2</i> are now compiled nationally. If the <i><b>vote share</b></i> and the <b><i>seat share</i></b> are not the same, then the party that is underrepresented in the House has at-large seats added. Seats are added until the seat share is within 1% of the vote share. In our example, let's say party A won 55% of the vote. Party A would have 4 seats added: 294 out of 544 seats is 54.04%. If two or more parties are underrepresented, whichever one is farther behind has a seat added first. Two parties might ping-pong back and forth in adding seats.</li>
<li>Once the total number of at-large seats each party gets is decided, then those new members are selected. The at-large members are chosen from the party's candidates who lost but received the most votes. In other word, party A's four additional seats would go to whichever of its candidates lost very close district races.</li>
</ol>
<br />
Stop and think about the incentives of this proposal. There's actually a triple incentive to draw fair districts. Independent commissions want to get the districting plans to supermajority status; there's no reason to draw unfair districts, as you'll lose any gains in the at-large seats part of the plan; and having several competitive districts might increase your state's representation in Congress. States would want to draw at least a few competitive districts to get one over on the neighboring states.<br />
<br />
In theory, it's possible that you have to seat 519 additional members (party A wins 49.9999% percent of national House votes but loses every single district race), but in all likelihood, we're talking about an extra 5% of seats--perhaps 20-30 additional seats. Altogether, a 570-member House is about 30% larger than today's. It's big but still manageable. And it's gerrymander-proof. The incentive to gerrymander disappeared.<br />
<br />
And here's the most exciting part: You can vote for a third-party to have seats in Congress, even if no one runs (or has a shot) in your district. Let's say you want to vote for the Democratic candidate but throw your party support to the Greens. Or for the Republican candidate and put party support behind the Libertarians. Nationally, those parties will pick up enough votes to amount to at least a few seats. All they have to do is field some candidates in some districts, who will lose, but get picked up in the at-large representatives process.<br />
<br />
My hope would be that third parties win enough support to deny either of the two major parties an outright majority, forcing the major parties to form coalition governments with third parties. Suddenly, we're looking at a system that doesn't freeze third parties out of power entirely; we're looking at a system that gives third parties enough seats in Congress to be involved in some leadership decisions. Support for a major party's Speaker might come at the cost of a committee leadership position. The Green party might demand leadership of the Natural Resources committee to support a Democratic speaker. The Libertarian party might demand leadership of Judiciary to support a Republican speaker. It seems likely, though, that this system creates more third party involvement.Russell Haneshttp://www.blogger.com/profile/13594411930757264086noreply@blogger.com0tag:blogger.com,1999:blog-8734744291040505450.post-36837774965380344052017-03-23T18:20:00.000-07:002017-03-23T22:39:12.210-07:00Naming streetsI believe in that simple things done right are the bedrock of society: the bus line that's always running; the convenience store around the corner that's never out of bread, milk, or toilet paper, even during the worst snowstorms; or the reliable local newspaper. But there's perhaps no greater collective failure in this country than our massively incompetent ability to name streets properly. Naming streets should be as simple as 1-2-3:<br />
<br />
<ol>
<li>A contiguous street gets a single name.</li>
<li>A name is used only on one street per city.</li>
<li>Name them in a pattern that's helpful for navigation.</li>
</ol>
<br />
To be clear, I'm talking about street names, not route designations, like U.S. 52 or State Route 39. A road could have a street name as well as a route designation, or even two route designations or more if geography forces the routes to consolidate for a stretch: Johnson Pass Rd. could be U.S. 52 and S.R. 39 all at the same time.<br />
<br />
These rules seem clear, right? Rule 1 requires a little definition: a "street" may pass through multiple intersections in a straight or gently curving manner but must actually cross the other street. In other words, a "street" doesn't take a right angle at an intersection. Rule 2 requires a little clarification; let's allow "Maple Avenue" and "Maple Place" as two separate names, provided that they follow rule 3 by being close together--maybe even intersecting. But I don't believe cardinal indicators--"West Maple Avenue" and "East Maple Avenue"--ought to be allowed for separate streets. Those should be reserved for different sections of the same road.<br />
<br />
The most common way the rules are violated is that two non-contiguous streets will get the same name. On a map, they're a straight shot, right in line with each other, but maybe there's a natural obstacle in the way, like a river. If I can't drive (or at least walk) from one end to another without turning, it's not one street; it's two. Give the two streets on the opposite river banks two different names.<br />
<br />
You may think this doesn't seem like a big deal, but maybe I'll change your mind when I present to you the worst named street in the United States: Old Hickory Boulevard in Nashville, Tennessee. Look upon these maps and despair for your sanity. Our journey begins at Whites Creek, to the north of Nashville.<br />
<br />
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<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEj2GV_QwjJHFNXrFBq7QQj6i3vShipvq6DtE1SwXNKpYU3gFSYua7XeNw-mFerIWLZVbfNMu44utvMAB8ugHdBqWxkhLAwcfsekATIxFsyMva7FBUjUrvw48ffzPidYUwqAOFBTG2-Tirht/s1600/map1.jpg" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" height="454" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEj2GV_QwjJHFNXrFBq7QQj6i3vShipvq6DtE1SwXNKpYU3gFSYua7XeNw-mFerIWLZVbfNMu44utvMAB8ugHdBqWxkhLAwcfsekATIxFsyMva7FBUjUrvw48ffzPidYUwqAOFBTG2-Tirht/s640/map1.jpg" width="640" /></a></div>
<br />
Crossing Eatons Creek Rd:<br />
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<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjWn0izOVPzK_vQvXTIkMnGMFvEHLKH7U06A3Vt8GtgF221K8z7KAEnxZpvEFeX_wSt6zOPfXXI-H_kLQ3hhuEcwSOQGJnG7gyQXMX5eN2pfSX-0M-g1YEC5WiNxGdSrDEsgkpxHR05ewhn/s1600/map2.jpg" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" height="640" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjWn0izOVPzK_vQvXTIkMnGMFvEHLKH7U06A3Vt8GtgF221K8z7KAEnxZpvEFeX_wSt6zOPfXXI-H_kLQ3hhuEcwSOQGJnG7gyQXMX5eN2pfSX-0M-g1YEC5WiNxGdSrDEsgkpxHR05ewhn/s640/map2.jpg" width="486" /></a></div>
<br />
Crossing route 12, you may start to get an ominous feeling, noticing the Cumberland River to both the west and east:<br />
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<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhmsJvOkmbh4BP5LYJlbIT02SwQxlmdm6uONfOztggMndQrzoa4xoTLLrltQGFFMVuUiSwEvuRkX1lPNATChl0l-0pbzWH0NANRgZJ7dRl6PIgqE91UAKRT2dI8b_bQpS8TmutFtrkElicM/s1600/map3.jpg" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" height="640" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhmsJvOkmbh4BP5LYJlbIT02SwQxlmdm6uONfOztggMndQrzoa4xoTLLrltQGFFMVuUiSwEvuRkX1lPNATChl0l-0pbzWH0NANRgZJ7dRl6PIgqE91UAKRT2dI8b_bQpS8TmutFtrkElicM/s640/map3.jpg" width="612" /></a></div>
<br />
Sure enough, you've hit a dead end:<br />
<br />
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<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhw_jNRaE2s2Y9s9N7s8iWvcK-GV00nASsigqyOZSS6ufrbhr1zZJ-_AtN5X34voYTdTcuhSY7ODh7LUXHsCnnflmF9y-uSq7RGMfqqFvK8nBouu6RW57y2fC8A7lztxaOOEuIKLS2iQqW7/s1600/map4.jpg" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" height="582" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhw_jNRaE2s2Y9s9N7s8iWvcK-GV00nASsigqyOZSS6ufrbhr1zZJ-_AtN5X34voYTdTcuhSY7ODh7LUXHsCnnflmF9y-uSq7RGMfqqFvK8nBouu6RW57y2fC8A7lztxaOOEuIKLS2iQqW7/s640/map4.jpg" width="640" /></a></div>
<br />
This is west of Nashville.<br />
<br />
Old Hickory Boulevard now jumps the river:<br />
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<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjCCYZlLBHjCHytS2ImJn3m34aOhlpedfFaBvGNXnHoKO2C3Czi2fJFBHqD9pSeUidsIWbN6ivfje7kLsLTwrvQgBeYWW_bwMGkU4ywAMjxlMerCGrq-XtHwKTdkyKMqC_A0eeI-3oWVUa4/s1600/map5.jpg" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" height="640" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjCCYZlLBHjCHytS2ImJn3m34aOhlpedfFaBvGNXnHoKO2C3Czi2fJFBHqD9pSeUidsIWbN6ivfje7kLsLTwrvQgBeYWW_bwMGkU4ywAMjxlMerCGrq-XtHwKTdkyKMqC_A0eeI-3oWVUa4/s640/map5.jpg" width="474" /></a></div>
<br />
Please note: route 251 <b><i>south</i></b> of Old Charlotte Pike is Old Hickory Boulevard. Route 251 north of Old Charlotte Pike is a different road.<br />
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<div class="separator" style="clear: both; text-align: center;">
<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjAYZhakh42B9OOBBo0futm77HDUCkb2bPSnlPrAC5JDB4CfroKmeuTsOCgrDIXizfd46aZQexe2VGni79zOr3XCCsr6Am_YNgzSrybXs5-G6bmD8f-Th6PJv4kL44L7KqW_KVmrGBHO7nj/s1600/map6.jpg" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" height="640" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjAYZhakh42B9OOBBo0futm77HDUCkb2bPSnlPrAC5JDB4CfroKmeuTsOCgrDIXizfd46aZQexe2VGni79zOr3XCCsr6Am_YNgzSrybXs5-G6bmD8f-Th6PJv4kL44L7KqW_KVmrGBHO7nj/s640/map6.jpg" width="492" /></a></div>
<br />
Old Hickory Boulevard jumps here, and gets a new route designation: route 254.<br />
<br />
Next, OHB meanders along the south side of Nashville. Granny White is not exactly due south, but pretty close.<br />
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<div class="separator" style="clear: both; text-align: center;">
<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgCFvIV0VM8Cd3KIZea5acUvUefknjAW86owmDtjUCfbncrpGFYV5JK6cafGvp_vL-ob_xwpVzbVNrnfyZK-G_O-OuB1t7CvQhp_CZ7Mo42tdebydYf5rCLvvd2y7XgqetdBNtgBvj3hOKJ/s1600/map7.jpg" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgCFvIV0VM8Cd3KIZea5acUvUefknjAW86owmDtjUCfbncrpGFYV5JK6cafGvp_vL-ob_xwpVzbVNrnfyZK-G_O-OuB1t7CvQhp_CZ7Mo42tdebydYf5rCLvvd2y7XgqetdBNtgBvj3hOKJ/s1600/map7.jpg" /></a></div>
<br />
OHB now winds through Brentwood.<br />
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<div class="separator" style="clear: both; text-align: center;">
<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEj3aC7XVgQAnjoFg4u8mYhqg46387QEmd6MC0lgxTjoxrx2AeScRnw91O2vYoO3mjvd8IPpz3pnuVg68magDOzHIs4nNxR-S2WdQ2UifFOFp6DyV5R0lzW61o1u7doRsouB-LKS-2zyHBNH/s1600/map8.jpg" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEj3aC7XVgQAnjoFg4u8mYhqg46387QEmd6MC0lgxTjoxrx2AeScRnw91O2vYoO3mjvd8IPpz3pnuVg68magDOzHIs4nNxR-S2WdQ2UifFOFp6DyV5R0lzW61o1u7doRsouB-LKS-2zyHBNH/s1600/map8.jpg" /></a></div>
<br />
True story: I remember sitting in a Pargo's in Brentwood as a child when a tourist came into the restaurant in tears. "I've driven from one end of Old Hickory Boulevard to the other and I can't find this address!"<br />
<br />
The manager took one look at her address. "Oh, this address is Whites Creek. That's the north side of town. This here's the south side." Hope you aren't in a hurry...<br />
<br />
Now, watch what happens carefully after crossing 41A.<br />
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<div class="separator" style="clear: both; text-align: center;">
<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhCOwhuJX_cZ9Pffaye7tPgPvu8o3JfE09GnPfbMvgXa_GctG4d8IZnM7BlygdJEpNLjeOFm04KweTo_553rPxVe6uD6XvoYjA6QqzqMgHnA6jrNUmBK4fK6KQiOFZZjfTjy13kQTaToHQK/s1600/map9.jpg" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" height="400" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhCOwhuJX_cZ9Pffaye7tPgPvu8o3JfE09GnPfbMvgXa_GctG4d8IZnM7BlygdJEpNLjeOFm04KweTo_553rPxVe6uD6XvoYjA6QqzqMgHnA6jrNUmBK4fK6KQiOFZZjfTjy13kQTaToHQK/s640/map9.jpg" width="640" /></a></div>
<br />
Did you see it? Old Hickory, which was route 254, took a right turn. Route 254 is now Bell Road.<br />
<br />
OHB takes another jump:<br />
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<div class="separator" style="clear: both; text-align: center;">
<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgah-YGuyoEUMD4d07qpSqO_dLYV2ljGJe7CJADMSt-uSzGDnF0Jwos9b3qrCHVSWIxtnDskNiYWImfoxnRGTJgcTPRL-jAZFcSaESnKqE8S_t49yGXCMBtNXn7YnUiNQm3Z8gOFQKOzgSW/s1600/map10.jpg" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" height="578" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgah-YGuyoEUMD4d07qpSqO_dLYV2ljGJe7CJADMSt-uSzGDnF0Jwos9b3qrCHVSWIxtnDskNiYWImfoxnRGTJgcTPRL-jAZFcSaESnKqE8S_t49yGXCMBtNXn7YnUiNQm3Z8gOFQKOzgSW/s640/map10.jpg" width="640" /></a></div>
<br />
As far as I can tell, that little section there is Pettus Rd.<br />
<br />
Keep your eyes peeled:<br />
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<div class="separator" style="clear: both; text-align: center;">
<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjxRyxUQwyXZA9omisTBVC7eYREjedxWuDtzFt4e5bdrtAkcTe_KgapS2Yh5MM2UrRkYX3fHM1cLxuXaqgo6YokBoQYTh888DiSydXY8bE5uFhzChBcRnNbMMw95vOR8Aa7iRQcBLaf0Mf2/s1600/map11.jpg" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" height="332" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjxRyxUQwyXZA9omisTBVC7eYREjedxWuDtzFt4e5bdrtAkcTe_KgapS2Yh5MM2UrRkYX3fHM1cLxuXaqgo6YokBoQYTh888DiSydXY8bE5uFhzChBcRnNbMMw95vOR8Aa7iRQcBLaf0Mf2/s640/map11.jpg" width="640" /></a></div>
<br />
Boom! Another right turn for you! Can't you just imagine a couple driving south on Old Hickory after getting off I-24 and the navicomputer is telling them to turn right onto OHB?<br />
<br />
<i>"But TomTom, I'm already on Old Hickory!"</i> as they just breeze right onto Burkitt Road.<br />
<br />
Maybe they'd have better luck if they got off I-24 going north on Old Hickory?<br />
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<div class="separator" style="clear: both; text-align: center;">
<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEix99XD8wTH4nHyfndCxrzd76gpVc6_YQmGegwS8F1sUmCDKJ1KnorsRTPah9iWX6i5vXIwatNhmWStClVT6W0fgtt6h7x1bt8-aViJe2-dYpSZO0kJSpmX4aWTJX3kWadshQ7yNh85Rr3T/s1600/map12.jpg" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" height="640" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEix99XD8wTH4nHyfndCxrzd76gpVc6_YQmGegwS8F1sUmCDKJ1KnorsRTPah9iWX6i5vXIwatNhmWStClVT6W0fgtt6h7x1bt8-aViJe2-dYpSZO0kJSpmX4aWTJX3kWadshQ7yNh85Rr3T/s640/map12.jpg" width="476" /></a></div>
<br />
Nope.<br />
<br />
BTW, Route 171 is now the third route designation. So what happens after that right turn off 171?<br />
<br />
<div class="separator" style="clear: both; text-align: center;">
<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEg2QgYj9bu6dAVLb0VHuvO4Lxzh5EvaZEYgleYfF0WSmvlAY3MLsWWqg-tdzD9LtnfDRpD7lr5-lKMVbaPDoQsV9arbUhzFDkefIjp6Mp5nIqVV80SEeYZOk7KphAwTScUVSdoK1qClVAtA/s1600/map13.jpg" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" height="320" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEg2QgYj9bu6dAVLb0VHuvO4Lxzh5EvaZEYgleYfF0WSmvlAY3MLsWWqg-tdzD9LtnfDRpD7lr5-lKMVbaPDoQsV9arbUhzFDkefIjp6Mp5nIqVV80SEeYZOk7KphAwTScUVSdoK1qClVAtA/s640/map13.jpg" width="640" /></a></div>
<br />
Old Hickory Boulevard vanishes at the star. The road used to continue, but then T.V.A. built a dam on the Cumberland river, creating Percy Priest lake to the southeast of Nashville. A section of OHB still exists under that lake. Does it confuse boat tourists as much as the land sections confuses car tourists?<br />
<br />
Wait, Old Hickory was a ring road. Does it continue on the other side?<br />
<br />
<div class="separator" style="clear: both; text-align: center;">
<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhdcFACic356Non0HL-MLhaGC6t0SBjhYW3OnTfFq2A_ATsl9uy9Y5jUOY1vpl3axMhlAaPU1zjefoz12gO_Di-8XS_Iwyh92q_2JXi7oxygewHoHLs3WB-tQcNGL3TSvJwFVCaMUh3MQ-D/s1600/map14.jpg" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" height="640" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhdcFACic356Non0HL-MLhaGC6t0SBjhYW3OnTfFq2A_ATsl9uy9Y5jUOY1vpl3axMhlAaPU1zjefoz12gO_Di-8XS_Iwyh92q_2JXi7oxygewHoHLs3WB-tQcNGL3TSvJwFVCaMUh3MQ-D/s640/map14.jpg" width="312" /></a></div>
<br />
Hello? Anyone seen a crappily named road?<br />
<br />
<div class="separator" style="clear: both; text-align: center;">
<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjkHBkXrxFvBIrbBj6PlPWwiW6hxHaQzUSCnzhEhcMlIEvuzELBGpSi8AP6BJPltZmUQuxMBZ-DJxqEwN0o9qwkrn5lkLsSZyKCdhklbotnS5A-NYGktYlTxn-s_FKFyTHFNSmRyAcTii5Q/s1600/map15.jpg" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" height="640" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjkHBkXrxFvBIrbBj6PlPWwiW6hxHaQzUSCnzhEhcMlIEvuzELBGpSi8AP6BJPltZmUQuxMBZ-DJxqEwN0o9qwkrn5lkLsSZyKCdhklbotnS5A-NYGktYlTxn-s_FKFyTHFNSmRyAcTii5Q/s640/map15.jpg" width="614" /></a></div>
<br />
Oh, there you are!<br />
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<div class="separator" style="clear: both; text-align: center;">
<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEiGcqPldC-cCuyQMp6K2tDCXX6BM77lWXwRg0t_JvjL4Q-5bO8-Yame0oCAZZLklY0KcpCL0ffS6gUwJGg94VYEUBBjy0mGw9MEXzZb4sXkTvYpHqW1JNA8s1Q7FrcvRJ__orKFnlKbgpTt/s1600/map16.jpg" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" height="640" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEiGcqPldC-cCuyQMp6K2tDCXX6BM77lWXwRg0t_JvjL4Q-5bO8-Yame0oCAZZLklY0KcpCL0ffS6gUwJGg94VYEUBBjy0mGw9MEXzZb4sXkTvYpHqW1JNA8s1Q7FrcvRJ__orKFnlKbgpTt/s640/map16.jpg" width="504" /></a></div>
<br />
And another jump!<br />
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<div class="separator" style="clear: both; text-align: center;">
<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEirfY1Zg2o0L8WqeIqarPLXyMSOvVXJjQh1c-CarqHoM6tsKedHCxw9yEhSrJpZ0ubHi1YdC3T3lPW46nd9Rp5gee08mW_N4XKursudd3IP9FDvOEStxntQ7gC19oIaD-CHxkUgBo85JCzq/s1600/map17.jpg" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" height="640" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEirfY1Zg2o0L8WqeIqarPLXyMSOvVXJjQh1c-CarqHoM6tsKedHCxw9yEhSrJpZ0ubHi1YdC3T3lPW46nd9Rp5gee08mW_N4XKursudd3IP9FDvOEStxntQ7gC19oIaD-CHxkUgBo85JCzq/s640/map17.jpg" width="458" /></a></div>
<br />
And we're back on solid land. You'll notice Old Hickory now has its fourth route designation, route 265.<br />
<br />
We'll just cross I-40. Now you'll recall that OHB already crossed I-40 once before (when OHB was route 251). That means we're now on the opposite side of Nashville: the east.<br />
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<div class="separator" style="clear: both; text-align: center;">
<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEiCmZYhCeZhuG5Nj5GGqYIc5ZnRFpg28Q3IsrdhECq_RlcEsxT0U4n0s1dKvelP7W7X7aZRe2EQrdN6H9cp7NHQ3IM4K3x5-h6DATLK5CWXAc9Ah_CgQIdwyCIiCf0e34TXe2OjvM7fVokH/s1600/map18.jpg" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" height="640" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEiCmZYhCeZhuG5Nj5GGqYIc5ZnRFpg28Q3IsrdhECq_RlcEsxT0U4n0s1dKvelP7W7X7aZRe2EQrdN6H9cp7NHQ3IM4K3x5-h6DATLK5CWXAc9Ah_CgQIdwyCIiCf0e34TXe2OjvM7fVokH/s640/map18.jpg" width="632" /></a></div>
<br />
We just follow OHB north for a bit.<br />
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<div class="separator" style="clear: both; text-align: center;">
<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhipuF_mSMJQTFStU7fwTdG1pxqROXxpv8YaNhB5FbQ123u7SB4DC6bjsidIiru5LTQPux8mVudlSUvoQl8vlsds0e_W6R6WtPQ51m2REBq4Oq7YkXFPSdTXYqk2k9jXRllNqkTaUPP6XDx/s1600/map19.jpg" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" height="640" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhipuF_mSMJQTFStU7fwTdG1pxqROXxpv8YaNhB5FbQ123u7SB4DC6bjsidIiru5LTQPux8mVudlSUvoQl8vlsds0e_W6R6WtPQ51m2REBq4Oq7YkXFPSdTXYqk2k9jXRllNqkTaUPP6XDx/s640/map19.jpg" width="454" /></a></div>
<br />
Hermitage, by the way, is the name of Andrew Jackson's house/plantation. Andrew Jackson was nicknamed Old Hickory because he was nuttier than a squirrel's poop.<br />
<br />
Let's see... we'll just keep going north.<br />
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<div class="separator" style="clear: both; text-align: center;">
<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhmBK522UzwB0C29Ej7vfK-P6JwLvHN4yhSfetxsDsPTU1m8PWABybKZa7ttMtMwjWYVJIQws3R9E73AVcxPJnXRYZ7ZTZvywhSn4_NRlEeyAnCKJAnNRYKEH-S_aJQgQJi0Zr5Zm0TjHUl/s1600/map20.jpg" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" height="640" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhmBK522UzwB0C29Ej7vfK-P6JwLvHN4yhSfetxsDsPTU1m8PWABybKZa7ttMtMwjWYVJIQws3R9E73AVcxPJnXRYZ7ZTZvywhSn4_NRlEeyAnCKJAnNRYKEH-S_aJQgQJi0Zr5Zm0TjHUl/s640/map20.jpg" width="300" /></a></div>
<br />
<i>"Wait, WTF? We're on route 45 now? I thought we were on route 265... We must've changed back there. TomTom still says we're on Old Hickory, hon. Good ole Old Hickory won't let us down, right?"</i><br />
<br />
OHB, now route 45, takes a northwest hook here because of the Cumberland river on both sides. (Like Old Hickory, it's everywhere in Nashville.) Here's the map:<br />
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<div class="separator" style="clear: both; text-align: center;">
<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjG47EliQMwsiw4RErnz6UdzsFX1Kxe1Nfpgeb309Ts5tqFnQIpuVeD-zA0nPTtXTr09y8C9XTRpb0GD4fD-qm17PYYRFQoUnpErY3YyjAVxoSfdvZhDbe6rY86YacaO9u73DBxqOv0aiE8/s1600/map21.jpg" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" height="536" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjG47EliQMwsiw4RErnz6UdzsFX1Kxe1Nfpgeb309Ts5tqFnQIpuVeD-zA0nPTtXTr09y8C9XTRpb0GD4fD-qm17PYYRFQoUnpErY3YyjAVxoSfdvZhDbe6rY86YacaO9u73DBxqOv0aiE8/s640/map21.jpg" width="640" /></a></div>
<br />
<i>"Oh look, dear, there's a neighborhood called Old Hickory! Oh, how cute."</i><br />
<i>"Son of a..."</i><br />
<br />
Now, it happens to be worth zooming in a little bit on Lakewood neighborhood first:<br />
<br />
<div class="separator" style="clear: both; text-align: center;">
<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEg_8uYxDeQ6xVgkR_Vx_eVkyOzn55s1K1GvPpFsCEPzzIoheKxHiZeNVQHcths00bExR3VGDmPoSRnoLLqXCXaqzG1DfJ7B3z8OM7Qk5ADPVpbdU16Vvo1OTjzT3QFGuMb6j0ah2lZLrwzK/s1600/map22.jpg" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" height="354" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEg_8uYxDeQ6xVgkR_Vx_eVkyOzn55s1K1GvPpFsCEPzzIoheKxHiZeNVQHcths00bExR3VGDmPoSRnoLLqXCXaqzG1DfJ7B3z8OM7Qk5ADPVpbdU16Vvo1OTjzT3QFGuMb6j0ah2lZLrwzK/s640/map22.jpg" width="640" /></a></div>
<br />
That's right, folks. It has two names. Hadley Avenue and OHB. It's officially broken all the simple naming convention rules and spiked the ball in the end zone.<br />
<br />
But now, let's see what happens a little to the north, in Old Hickory neighborhood:<br />
<br />
<div class="separator" style="clear: both; text-align: center;">
<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEh5kSYmCSQhHtMyIXs1Y4PuWlctKmg0k_5CDXptSrO8vRPL7waNX9HthCNfTN6Eth5Y9beofFH_DsgsW2msoychI9ZjTfBxZPCpw_-Af6T3gXu0ZpHPw7szs17n_brNeY9oGRh87VE0Ri2p/s1600/map23.jpg" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" height="506" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEh5kSYmCSQhHtMyIXs1Y4PuWlctKmg0k_5CDXptSrO8vRPL7waNX9HthCNfTN6Eth5Y9beofFH_DsgsW2msoychI9ZjTfBxZPCpw_-Af6T3gXu0ZpHPw7szs17n_brNeY9oGRh87VE0Ri2p/s640/map23.jpg" width="640" /></a></div>
<br />
Nothing good for our tourists. OHB just disappears. (Hadley Avenue, the jerk, continues to the right.) Why is the neighborhood called "Old Hickory" when <i><b>Old Hickory Boulevard doesn't run through it!!</b></i><br />
<br />
Where did that wascally street go?<br />
<br />
<div class="separator" style="clear: both; text-align: center;">
<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEiqOM2TCKY9eY1rD_6Smc5B4Mo3gvEuyMUgFtfEP9q1W58SzrfIua-eeQEaHGQyX9TIRc_oLxghkMvRZ7fPPfbb0GgaH_91WZzVBmsIBuU3ezEkE1OuPlZLyiSlWfrSf-6zp3E0546sG9sL/s1600/map24.jpg" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" height="480" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEiqOM2TCKY9eY1rD_6Smc5B4Mo3gvEuyMUgFtfEP9q1W58SzrfIua-eeQEaHGQyX9TIRc_oLxghkMvRZ7fPPfbb0GgaH_91WZzVBmsIBuU3ezEkE1OuPlZLyiSlWfrSf-6zp3E0546sG9sL/s640/map24.jpg" width="640" /></a></div>
<br />
Oh, it magicked itself across its eponymous neighborhood. Right. To be clear, that whole section of route 45 I haven't marked is all Robinson Road. All the time. Sure, the locals who are just running down to the Piggly Wiggly know they turn on OHB which then becomes Robinson. But streets aren't named for locals, are they?<br />
<br />
In case you're wondering, Old Hickory Community is where all the lost tourist children go to live, if their mums or dads can't navigate the streets of Nashville and pick them up by closing time.<br />
<br />
Surely, surely, surely, OHB has pulled its last trick?<br />
<br />
<div class="separator" style="clear: both; text-align: center;">
<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhWG_OG5vjzuxJDyxwgXjlgTaA3f21GICK_2tCFAQFiD52BrG8CCdy7XjY7qhnZW-jR48HKw1lOz4SPuClap6s4oAx33j94QJPBQ7YLQ-Q3j8F3fCCk8_5t2FVrwFK4U-sA6swINvt6SqfC/s1600/map25.jpg" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhWG_OG5vjzuxJDyxwgXjlgTaA3f21GICK_2tCFAQFiD52BrG8CCdy7XjY7qhnZW-jR48HKw1lOz4SPuClap6s4oAx33j94QJPBQ7YLQ-Q3j8F3fCCk8_5t2FVrwFK4U-sA6swINvt6SqfC/s1600/map25.jpg" /></a></div>
<br />
This one is a doozy. You'll notice an <i>East</i> Old Hickory Boulevard to the <i><b>south</b></i> of route 45. That's odd. Why would the East OHB be south of regular OHB?<br />
<br />
Because route 45 ain't OHB any more.<br />
<br />
East OHB is it. The best part is what happens inside that star. The name jumps from 45 to the surface street--but there's no physical connection. (Also, let's point out the East OHB goes around its corner, and that non-intersection changes its name to Sandhurst Drive.)<br />
<br />
<i>"Getting lost is... just a way to have an adventure, dear! Just... um, wasn't planning this and we're low on gas..."</i><br />
<i>"Oh look, hon, an Old Hickory Community. Maybe they can help us!"</i><br />
<br />
If there's an East OHB, is there a West OHB? Indeed there is:<br />
<br />
<div class="separator" style="clear: both; text-align: center;">
<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhFNpJuNA9e-cb7dWjmkYdePv4YCSGmgMAoXG8thUczj_cPm8PDWVCrI3ef5tEx2tDazeCtTz8AXrVY3oXpPu3v6Ipw5h8mYK_UIYO0_EDZv-fp4f2Opmo2_g1RhKOtlOPXax8OrROiPjTU/s1600/map26.jpg" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" height="193" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhFNpJuNA9e-cb7dWjmkYdePv4YCSGmgMAoXG8thUczj_cPm8PDWVCrI3ef5tEx2tDazeCtTz8AXrVY3oXpPu3v6Ipw5h8mYK_UIYO0_EDZv-fp4f2Opmo2_g1RhKOtlOPXax8OrROiPjTU/s640/map26.jpg" width="640" /></a></div>
<br />
but you gotta take another jump.<br />
<br />
OHB is nearly out of tricks, though:<br />
<br />
<div class="separator" style="clear: both; text-align: center;">
<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjlQPsYZBj0e3vzc5aDuz1zpiz2eeKfXlowB1qLAxnSH_4IKkJ9eET64IQeuA-PGEZLvzVuLYQzmtDy3MP3y0YYfk1PXQy3YcY3sV1s_PqOlhpF9177l4G9Wmv1F4c5sSsnym5qbDCcz4mb/s1600/map27.jpg" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" height="278" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjlQPsYZBj0e3vzc5aDuz1zpiz2eeKfXlowB1qLAxnSH_4IKkJ9eET64IQeuA-PGEZLvzVuLYQzmtDy3MP3y0YYfk1PXQy3YcY3sV1s_PqOlhpF9177l4G9Wmv1F4c5sSsnym5qbDCcz4mb/s640/map27.jpg" width="640" /></a></div>
<br />
At the star, it changes names from West OHB just back to plain vanilla Old Hickory Boulevard. BTW, crossing I-65 a second time means that we're on the north side of Nashville again.<br />
<br />
A few more miles--crossing I-24 a second time--and we're back to Whites Creek:<br />
<br />
<div class="separator" style="clear: both; text-align: center;">
<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjfHhubxVxZI5r-S9W3OqXuiWDjPsGhshsCKllgsDqlOAJvNyK_16YNZy7I1t0_-Dhe-DZJ_dbkNE81maQWwUdVn_Nl_818tQVYDriV8Qcvb00fFqADBnBiptknzELtjzGTHPh4cx2Bx8Iv/s1600/map28.jpg" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" height="226" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjfHhubxVxZI5r-S9W3OqXuiWDjPsGhshsCKllgsDqlOAJvNyK_16YNZy7I1t0_-Dhe-DZJ_dbkNE81maQWwUdVn_Nl_818tQVYDriV8Qcvb00fFqADBnBiptknzELtjzGTHPh4cx2Bx8Iv/s640/map28.jpg" width="640" /></a></div>
<br />
You can almost hear the tourists wailing: <i>"I just wanted... [sob] just to see... some country music stars' homes! I didn't want to drive all around creation!"</i><br />
<i>"And where are our children?!"</i><br />
<br />
Let's do the numbers:<br />
<br />
<u>Route designations</u>: Five (251, 254, 171, 265, and 45)<br />
<u>Two street names simultaneously</u>: Yes (OHB and Hadley)<br />
<u>Street takes a right turn</u>: Three times (all between 41A, I-24, and 171 in southeast Nashville)<br />
<u>Jumps over water</u>: Three (Cumberland river, Percy Priest lake twice)<br />
<u>Jumps over other roads</u>: Four (251 to 254; over Pettus Rd.; from route 45 to East OHB; from East OHB to West OHB)<br />
<u>Jumps over neighborhoods</u>: One--but double points because it's eponymous<br />
<u>Switching names while driving down the same street, not otherwise covered</u>: Two (West OHB turning back into OHB; East OHB turning into Sandusky Rd. The West OHB to regular OHB could be OK, I guess... No one is going to get lost if the numbering makes sense... <i>which it doesn't</i>.)<br />
<br />
I think this deserves a total of 15 naming violation points: +1 for two names simultaneously, +3 for right turns, +9 for jumps, +2 for two name switches. (Or maybe 14 points, if you're cool with West OHB to OHB.)<br />
<br />
I defy anyone to come up with a worse named street in the U.S. Map-based proof required.<br />
<br />
BTW, in case you couldn't tell, I'm originally from Nashville. No offense is intended; I think it's fair to poke a little fun at your hometown.Russell Haneshttp://www.blogger.com/profile/13594411930757264086noreply@blogger.com0tag:blogger.com,1999:blog-8734744291040505450.post-45481876434732645702017-02-26T15:57:00.000-08:002017-02-26T15:57:02.780-08:00GerrymanderingA federal court recently struck down a gerrymandering scheme in Wisconsin in a case that could set a major precedent for the country. Once every ten years, after each Census is completed, the boundaries for House of Representatives districts have to be re-drawn to keep their populations equal. The U.S. Constitution leaves it to state legislatures to decide how to draw these districts. Gerrymandering is the intentional abuse of that power; legislatures might gerrymander to keep minority groups out of power or to benefit one political party. The longtime practice of gerrymandering has always had its critics. As President Obama recently said, “Politicians should not pick their voters; voters should pick their politicians,” though Obama didn’t coin the phrase and wasn’t the first to express exasperation about gerrymandering.<br /><br />Contrary to popular opinion, gerrymandering isn’t about protecting incumbents by giving them safe districts. The actual process of gerrymandering involves two steps: packing and cracking. Packing is the placement of your opposition’s voters into a few, concentrated districts. Cracking is the distribution of the remaining opposition voters into districts that they can’t win. Here’s what a gerrymandering scheme using packing and cracking could look like:<br /><div class="MsoNormal">
<br /></div>
<div align="center">
<table border="0" cellpadding="0" cellspacing="0" class="MsoTableGrid" style="border-collapse: collapse; border: none; mso-border-insideh: none; mso-border-insidev: none; mso-padding-alt: 0in 5.4pt 0in 5.4pt; mso-yfti-tbllook: 1184;">
<tbody>
<tr>
<td colspan="4" style="padding: 0in 5.4pt 0in 5.4pt;">
<div class="MsoNormal" style="line-height: 150%; margin-bottom: 2pt; margin-top: 2pt;">
<i>Possible
party B gerrymander<o:p></o:p></i></div>
</td>
</tr>
<tr>
<td style="padding: 0in 5.4pt 0in 5.4pt;">
<div align="center" class="MsoNormal" style="margin-bottom: 2pt; margin-top: 2pt; text-align: center;">
<br /></div>
</td>
<td colspan="2" style="padding: 0in 5.4pt 0in 5.4pt;">
<div align="center" class="MsoNormal" style="margin-bottom: 2pt; margin-top: 2pt; text-align: center;">
<u>Votes for party<o:p></o:p></u></div>
</td>
<td style="padding: 0in 5.4pt 0in 5.4pt;" valign="top">
<div align="center" class="MsoNormal" style="margin-bottom: 2pt; margin-top: 2pt; text-align: center;">
<br /></div>
</td>
</tr>
<tr>
<td style="border-bottom: solid windowtext 1.0pt; border: none; mso-border-bottom-alt: solid windowtext .5pt; padding: 0in 5.4pt 0in 5.4pt;">
<div align="center" class="MsoNormal" style="margin-bottom: 2pt; margin-top: 2pt; text-align: center;">
District<o:p></o:p></div>
</td>
<td style="border-bottom: solid windowtext 1.0pt; border: none; mso-border-bottom-alt: solid windowtext .5pt; padding: 0in 5.4pt 0in 5.4pt;">
<div align="center" class="MsoNormal" style="margin-bottom: 2pt; margin-top: 2pt; text-align: center;">
A<o:p></o:p></div>
</td>
<td style="border-bottom: solid windowtext 1.0pt; border: none; mso-border-bottom-alt: solid windowtext .5pt; padding: 0in 5.4pt 0in 5.4pt;">
<div align="center" class="MsoNormal" style="margin-bottom: 2pt; margin-top: 2pt; text-align: center;">
B<o:p></o:p></div>
</td>
<td style="border-bottom: solid windowtext 1.0pt; border: none; mso-border-bottom-alt: solid windowtext .5pt; padding: 0in 5.4pt 0in 5.4pt;" valign="top">
<div align="center" class="MsoNormal" style="margin-bottom: 2pt; margin-top: 2pt; text-align: center;">
Winner<o:p></o:p></div>
</td>
</tr>
<tr>
<td style="border: none; mso-border-top-alt: solid windowtext .5pt; padding: 0in 5.4pt 0in 5.4pt;">
<div align="center" class="MsoNormal" style="margin-bottom: 2pt; margin-top: 2pt; text-align: center;">
1<o:p></o:p></div>
</td>
<td style="border: none; mso-border-top-alt: solid windowtext .5pt; padding: 0in 5.4pt 0in 5.4pt;">
<div align="center" class="MsoNormal" style="margin-bottom: 2pt; margin-top: 2pt; text-align: center;">
95<o:p></o:p></div>
</td>
<td style="border: none; mso-border-top-alt: solid windowtext .5pt; padding: 0in 5.4pt 0in 5.4pt;">
<div align="center" class="MsoNormal" style="margin-bottom: 2pt; margin-top: 2pt; text-align: center;">
5<o:p></o:p></div>
</td>
<td style="border: none; mso-border-top-alt: solid windowtext .5pt; padding: 0in 5.4pt 0in 5.4pt;" valign="top">
<div align="center" class="MsoNormal" style="margin-bottom: 2pt; margin-top: 2pt; text-align: center;">
A<o:p></o:p></div>
</td>
</tr>
<tr>
<td style="padding: 0in 5.4pt 0in 5.4pt;">
<div align="center" class="MsoNormal" style="margin-bottom: 2pt; margin-top: 2pt; text-align: center;">
2<o:p></o:p></div>
</td>
<td style="padding: 0in 5.4pt 0in 5.4pt;">
<div align="center" class="MsoNormal" style="margin-bottom: 2pt; margin-top: 2pt; text-align: center;">
45<o:p></o:p></div>
</td>
<td style="padding: 0in 5.4pt 0in 5.4pt;">
<div align="center" class="MsoNormal" style="margin-bottom: 2pt; margin-top: 2pt; text-align: center;">
55<o:p></o:p></div>
</td>
<td style="padding: 0in 5.4pt 0in 5.4pt;" valign="top">
<div align="center" class="MsoNormal" style="margin-bottom: 2pt; margin-top: 2pt; text-align: center;">
B<o:p></o:p></div>
</td>
</tr>
<tr>
<td style="padding: 0in 5.4pt 0in 5.4pt;">
<div align="center" class="MsoNormal" style="margin-bottom: 2pt; margin-top: 2pt; text-align: center;">
3<o:p></o:p></div>
</td>
<td style="padding: 0in 5.4pt 0in 5.4pt;">
<div align="center" class="MsoNormal" style="margin-bottom: 2pt; margin-top: 2pt; text-align: center;">
45<o:p></o:p></div>
</td>
<td style="padding: 0in 5.4pt 0in 5.4pt;">
<div align="center" class="MsoNormal" style="margin-bottom: 2pt; margin-top: 2pt; text-align: center;">
55<o:p></o:p></div>
</td>
<td style="padding: 0in 5.4pt 0in 5.4pt;" valign="top">
<div align="center" class="MsoNormal" style="margin-bottom: 2pt; margin-top: 2pt; text-align: center;">
B<o:p></o:p></div>
</td>
</tr>
<tr>
<td style="padding: 0in 5.4pt 0in 5.4pt;">
<div align="center" class="MsoNormal" style="margin-bottom: 2pt; margin-top: 2pt; text-align: center;">
4<o:p></o:p></div>
</td>
<td style="padding: 0in 5.4pt 0in 5.4pt;">
<div align="center" class="MsoNormal" style="margin-bottom: 2pt; margin-top: 2pt; text-align: center;">
45<o:p></o:p></div>
</td>
<td style="padding: 0in 5.4pt 0in 5.4pt;">
<div align="center" class="MsoNormal" style="margin-bottom: 2pt; margin-top: 2pt; text-align: center;">
55<o:p></o:p></div>
</td>
<td style="padding: 0in 5.4pt 0in 5.4pt;" valign="top">
<div align="center" class="MsoNormal" style="margin-bottom: 2pt; margin-top: 2pt; text-align: center;">
B<o:p></o:p></div>
</td>
</tr>
<tr>
<td style="border-bottom: solid windowtext 1.0pt; border: none; mso-border-bottom-alt: solid windowtext .5pt; padding: 0in 5.4pt 0in 5.4pt;">
<div align="center" class="MsoNormal" style="margin-bottom: 2pt; margin-top: 2pt; text-align: center;">
5<o:p></o:p></div>
</td>
<td style="border-bottom: solid windowtext 1.0pt; border: none; mso-border-bottom-alt: solid windowtext .5pt; padding: 0in 5.4pt 0in 5.4pt;">
<div align="center" class="MsoNormal" style="margin-bottom: 2pt; margin-top: 2pt; text-align: center;">
45<o:p></o:p></div>
</td>
<td style="border-bottom: solid windowtext 1.0pt; border: none; mso-border-bottom-alt: solid windowtext .5pt; padding: 0in 5.4pt 0in 5.4pt;">
<div align="center" class="MsoNormal" style="margin-bottom: 2pt; margin-top: 2pt; text-align: center;">
55<o:p></o:p></div>
</td>
<td style="border-bottom: solid windowtext 1.0pt; border: none; mso-border-bottom-alt: solid windowtext .5pt; padding: 0in 5.4pt 0in 5.4pt;" valign="top">
<div align="center" class="MsoNormal" style="margin-bottom: 2pt; margin-top: 2pt; text-align: center;">
B<o:p></o:p></div>
</td>
</tr>
<tr>
<td style="border: none; mso-border-top-alt: solid windowtext .5pt; padding: 0in 5.4pt 0in 5.4pt;">
<div align="center" class="MsoNormal" style="margin-bottom: 2pt; margin-top: 2pt; text-align: center;">
Total<o:p></o:p></div>
</td>
<td style="border: none; mso-border-top-alt: solid windowtext .5pt; padding: 0in 5.4pt 0in 5.4pt;">
<div align="center" class="MsoNormal" style="margin-bottom: 2pt; margin-top: 2pt; text-align: center;">
275<o:p></o:p></div>
</td>
<td style="border: none; mso-border-top-alt: solid windowtext .5pt; padding: 0in 5.4pt 0in 5.4pt;">
<div align="center" class="MsoNormal" style="margin-bottom: 2pt; margin-top: 2pt; text-align: center;">
225<o:p></o:p></div>
</td>
<td style="border: none; mso-border-top-alt: solid windowtext .5pt; padding: 0in 5.4pt 0in 5.4pt;" valign="top">
<div align="center" class="MsoNormal" style="margin-bottom: 2pt; margin-top: 2pt; text-align: center;">
<br /></div>
</td>
</tr>
</tbody></table>
</div>
<div class="MsoNormal">
<br /></div>
District 1 is packed with party A supporters. Party A’s remaining voters are cracked across the other four districts, which they can’t win. Even though party A received 275 out of 500 votes, or 55%, they win only one district out of five, or 20%. There’s no way party B could have gerrymandered this any better. Four districts are safe enough that party B will likely never lose those races, even in a bad election year for their party. Trying to give their party a bigger margin in any of those races would only make another race closer. Getting the right vote totals in each district may require drawing some unusual shape districts. Gerrymandering gets its name from an 1812 Massachusetts district map, approved by Governor Gerry, with one district that looked like a salamander. The map benefited his party, even though Gerry lost his own office for it.<br /><br />The U.S. Supreme Court has never struck down a gerrymandering scheme that attempted partisan gain, only gerrymandering done to deprive minority groups of voting power. The Voting Rights Act prohibits racially motivated gerrymandering, and justices have also looked to the Equal Protection Clause of the Fourteenth Amendment. The Court has allowed the creation of districts where a minority group is a near majority of the voters to ensure that minority groups can elect their own representatives to Congress. In southern states, for example, African Americans vote so heavily Democratic, and white people vote so heavily Republican, that some districts must approach a 50-50 racial mix in order to elect black congresspeople. The Supreme Court has allowed this as long as race isn’t the primary factor in making the districts. Two racial gerrymandering cases will be heard by the Court soon, Bethune-Hill v. Virginia State Board of Elections and McCrory v. Harris, so the standards might be changing soon.<br /><br />Partisan gerrymanders, however, have long been ignored, although Justice Kennedy has indicated that if a clear standard for judging gerrymandering’s severity could be found, he would rule against partisan gerrymandering as well. Along with the four liberal justices on the Court, Kennedy might bring forth a new Supreme Court precedent. The Court, by the way, cannot decline to make some ruling on the Wisconsin case.<br /><br />The Wisconsin case is the result of an unlikely group of statisticians, political scientists, and lawyers attempting to serve up to Justice Kennedy a standard for judging gerrymandering. Their work is premised on the concept of a “wasted vote”: any votes above 51% or any vote in a lost race are considered “wasted.” In the hypothetical gerrymandering scenario, this is what the wasted votes look like:<br /><div class="MsoNormal">
<br /></div>
<div align="center">
<table border="0" cellpadding="0" cellspacing="0" class="MsoTableGrid" style="border-collapse: collapse; border: none; mso-border-insideh: none; mso-border-insidev: none; mso-padding-alt: 0in 5.4pt 0in 5.4pt; mso-yfti-tbllook: 1184;">
<tbody>
<tr>
<td colspan="6" style="padding: 0in 5.4pt 0in 5.4pt;">
<div class="MsoNormal" style="line-height: 150%; margin-bottom: 2pt; margin-top: 2pt;">
<i>Wasted
votes in party B gerrymander<o:p></o:p></i></div>
</td>
</tr>
<tr>
<td style="padding: 0in 5.4pt 0in 5.4pt;">
<div align="center" class="MsoNormal" style="margin-bottom: 2pt; margin-top: 2pt; text-align: center;">
<br /></div>
</td>
<td colspan="2" style="padding: 0in 5.4pt 0in 5.4pt;">
<div align="center" class="MsoNormal" style="margin-bottom: 2pt; margin-top: 2pt; text-align: center;">
<u>Votes for party<o:p></o:p></u></div>
</td>
<td style="padding: 0in 5.4pt 0in 5.4pt;" valign="top">
<div align="center" class="MsoNormal" style="margin-bottom: 2pt; margin-top: 2pt; text-align: center;">
<br /></div>
</td>
<td colspan="2" style="padding: 0in 5.4pt 0in 5.4pt;" valign="top">
<div align="center" class="MsoNormal" style="margin-bottom: 2pt; margin-top: 2pt; text-align: center;">
<u>Wasted votes for<o:p></o:p></u></div>
</td>
</tr>
<tr>
<td style="border-bottom: solid windowtext 1.0pt; border: none; mso-border-bottom-alt: solid windowtext .5pt; padding: 0in 5.4pt 0in 5.4pt;">
<div align="center" class="MsoNormal" style="margin-bottom: 2pt; margin-top: 2pt; text-align: center;">
District<o:p></o:p></div>
</td>
<td style="border-bottom: solid windowtext 1.0pt; border: none; mso-border-bottom-alt: solid windowtext .5pt; padding: 0in 5.4pt 0in 5.4pt;">
<div align="center" class="MsoNormal" style="margin-bottom: 2pt; margin-top: 2pt; text-align: center;">
A<o:p></o:p></div>
</td>
<td style="border-bottom: solid windowtext 1.0pt; border: none; mso-border-bottom-alt: solid windowtext .5pt; padding: 0in 5.4pt 0in 5.4pt;">
<div align="center" class="MsoNormal" style="margin-bottom: 2pt; margin-top: 2pt; text-align: center;">
B<o:p></o:p></div>
</td>
<td style="border-bottom: solid windowtext 1.0pt; border: none; mso-border-bottom-alt: solid windowtext .5pt; padding: 0in 5.4pt 0in 5.4pt;" valign="top">
<div align="center" class="MsoNormal" style="margin-bottom: 2pt; margin-top: 2pt; text-align: center;">
Winner<o:p></o:p></div>
</td>
<td style="border-bottom: solid windowtext 1.0pt; border: none; mso-border-bottom-alt: solid windowtext .5pt; padding: 0in 5.4pt 0in 5.4pt;" valign="top">
<div align="center" class="MsoNormal" style="margin-bottom: 2pt; margin-top: 2pt; text-align: center;">
A<o:p></o:p></div>
</td>
<td style="border-bottom: solid windowtext 1.0pt; border: none; mso-border-bottom-alt: solid windowtext .5pt; padding: 0in 5.4pt 0in 5.4pt;" valign="top">
<div align="center" class="MsoNormal" style="margin-bottom: 2pt; margin-top: 2pt; text-align: center;">
B<o:p></o:p></div>
</td>
</tr>
<tr>
<td style="border: none; mso-border-top-alt: solid windowtext .5pt; padding: 0in 5.4pt 0in 5.4pt;">
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1<o:p></o:p></div>
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<div align="center" class="MsoNormal" style="margin-bottom: 2pt; margin-top: 2pt; text-align: center;">
95<o:p></o:p></div>
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<div align="center" class="MsoNormal" style="margin-bottom: 2pt; margin-top: 2pt; text-align: center;">
5<o:p></o:p></div>
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<div align="center" class="MsoNormal" style="margin-bottom: 2pt; margin-top: 2pt; text-align: center;">
A<o:p></o:p></div>
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<td style="border: none; mso-border-top-alt: solid windowtext .5pt; padding: 0in 5.4pt 0in 5.4pt;" valign="top">
<div align="center" class="MsoNormal" style="margin-bottom: 2pt; margin-top: 2pt; text-align: center;">
44<o:p></o:p></div>
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<div align="center" class="MsoNormal" style="margin-bottom: 2pt; margin-top: 2pt; text-align: center;">
5<o:p></o:p></div>
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<td style="padding: 0in 5.4pt 0in 5.4pt;">
<div align="center" class="MsoNormal" style="margin-bottom: 2pt; margin-top: 2pt; text-align: center;">
2<o:p></o:p></div>
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<td style="padding: 0in 5.4pt 0in 5.4pt;">
<div align="center" class="MsoNormal" style="margin-bottom: 2pt; margin-top: 2pt; text-align: center;">
45<o:p></o:p></div>
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<td style="padding: 0in 5.4pt 0in 5.4pt;">
<div align="center" class="MsoNormal" style="margin-bottom: 2pt; margin-top: 2pt; text-align: center;">
55<o:p></o:p></div>
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<td style="padding: 0in 5.4pt 0in 5.4pt;" valign="top">
<div align="center" class="MsoNormal" style="margin-bottom: 2pt; margin-top: 2pt; text-align: center;">
B<o:p></o:p></div>
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<td style="padding: 0in 5.4pt 0in 5.4pt;" valign="top">
<div align="center" class="MsoNormal" style="margin-bottom: 2pt; margin-top: 2pt; text-align: center;">
45<o:p></o:p></div>
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<td style="padding: 0in 5.4pt 0in 5.4pt;" valign="top">
<div align="center" class="MsoNormal" style="margin-bottom: 2pt; margin-top: 2pt; text-align: center;">
4<o:p></o:p></div>
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<div align="center" class="MsoNormal" style="margin-bottom: 2pt; margin-top: 2pt; text-align: center;">
3<o:p></o:p></div>
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45<o:p></o:p></div>
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<div align="center" class="MsoNormal" style="margin-bottom: 2pt; margin-top: 2pt; text-align: center;">
55<o:p></o:p></div>
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<td style="padding: 0in 5.4pt 0in 5.4pt;" valign="top">
<div align="center" class="MsoNormal" style="margin-bottom: 2pt; margin-top: 2pt; text-align: center;">
B<o:p></o:p></div>
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<td style="padding: 0in 5.4pt 0in 5.4pt;" valign="top">
<div align="center" class="MsoNormal" style="margin-bottom: 2pt; margin-top: 2pt; text-align: center;">
45<o:p></o:p></div>
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<td style="padding: 0in 5.4pt 0in 5.4pt;" valign="top">
<div align="center" class="MsoNormal" style="margin-bottom: 2pt; margin-top: 2pt; text-align: center;">
4<o:p></o:p></div>
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<div align="center" class="MsoNormal" style="margin-bottom: 2pt; margin-top: 2pt; text-align: center;">
4<o:p></o:p></div>
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<div align="center" class="MsoNormal" style="margin-bottom: 2pt; margin-top: 2pt; text-align: center;">
45<o:p></o:p></div>
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<div align="center" class="MsoNormal" style="margin-bottom: 2pt; margin-top: 2pt; text-align: center;">
55<o:p></o:p></div>
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<td style="padding: 0in 5.4pt 0in 5.4pt;" valign="top">
<div align="center" class="MsoNormal" style="margin-bottom: 2pt; margin-top: 2pt; text-align: center;">
B<o:p></o:p></div>
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<td style="padding: 0in 5.4pt 0in 5.4pt;" valign="top">
<div align="center" class="MsoNormal" style="margin-bottom: 2pt; margin-top: 2pt; text-align: center;">
45<o:p></o:p></div>
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<td style="padding: 0in 5.4pt 0in 5.4pt;" valign="top">
<div align="center" class="MsoNormal" style="margin-bottom: 2pt; margin-top: 2pt; text-align: center;">
4<o:p></o:p></div>
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<div align="center" class="MsoNormal" style="margin-bottom: 2pt; margin-top: 2pt; text-align: center;">
5<o:p></o:p></div>
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<td style="border-bottom: solid windowtext 1.0pt; border: none; mso-border-bottom-alt: solid windowtext .5pt; padding: 0in 5.4pt 0in 5.4pt;">
<div align="center" class="MsoNormal" style="margin-bottom: 2pt; margin-top: 2pt; text-align: center;">
45<o:p></o:p></div>
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<div align="center" class="MsoNormal" style="margin-bottom: 2pt; margin-top: 2pt; text-align: center;">
55<o:p></o:p></div>
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<td style="border-bottom: solid windowtext 1.0pt; border: none; mso-border-bottom-alt: solid windowtext .5pt; padding: 0in 5.4pt 0in 5.4pt;" valign="top">
<div align="center" class="MsoNormal" style="margin-bottom: 2pt; margin-top: 2pt; text-align: center;">
B<o:p></o:p></div>
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<td style="border-bottom: solid windowtext 1.0pt; border: none; mso-border-bottom-alt: solid windowtext .5pt; padding: 0in 5.4pt 0in 5.4pt;" valign="top">
<div align="center" class="MsoNormal" style="margin-bottom: 2pt; margin-top: 2pt; text-align: center;">
45<o:p></o:p></div>
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<div align="center" class="MsoNormal" style="margin-bottom: 2pt; margin-top: 2pt; text-align: center;">
4<o:p></o:p></div>
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<div align="center" class="MsoNormal" style="margin-bottom: 2pt; margin-top: 2pt; text-align: center;">
Total<o:p></o:p></div>
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<div align="center" class="MsoNormal" style="margin-bottom: 2pt; margin-top: 2pt; text-align: center;">
275<o:p></o:p></div>
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<div align="center" class="MsoNormal" style="margin-bottom: 2pt; margin-top: 2pt; text-align: center;">
225<o:p></o:p></div>
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<td style="border: none; mso-border-top-alt: solid windowtext .5pt; padding: 0in 5.4pt 0in 5.4pt;" valign="top">
<div align="center" class="MsoNormal" style="margin-bottom: 2pt; margin-top: 2pt; text-align: center;">
<br /></div>
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<td style="border: none; mso-border-top-alt: solid windowtext .5pt; padding: 0in 5.4pt 0in 5.4pt;" valign="top">
<div align="center" class="MsoNormal" style="margin-bottom: 2pt; margin-top: 2pt; text-align: center;">
224<o:p></o:p></div>
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<td style="border: none; mso-border-top-alt: solid windowtext .5pt; padding: 0in 5.4pt 0in 5.4pt;" valign="top">
<div align="center" class="MsoNormal" style="margin-bottom: 2pt; margin-top: 2pt; text-align: center;">
21<o:p></o:p></div>
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</div>
<div class="MsoNormal">
<br /></div>
Party B gerrymandered the districts to waste 224 of party A’s 275 votes. Party A’s wasted votes almost equal the total votes party B received! Of course, the plaintiffs would also have to prove that gerrymandering happened intentionally, but proving too many votes are wasted is the necessary first step. No mathematical evidence, no case.<br /><br />Using the wasted votes standard proposed in the Wisconsin case, seven states have Congressional districts that are suspicious: Florida, Michigan, North Carolina, Ohio, Pennsylvania, Texas, and Virginia—all of them pro-Republican gerrymandering. In Pennsylvania, the Republican Senate candidate won 51% of the two-party vote, as did Trump. The Pennsylvania House delegation, on the other hand, will be thirteen Republicans to five Democrats, or 72% Republican. One reason all the current gerrymandering schemes are Republican is that the G.O.P. controlled more state legislatures after 2010, when the last re-districting was done.<br /><br />Another standard proposed for measuring gerrymandering is to look at the median district. In the hypothetical gerrymander given before, the median district—the middle in a list from party A’s worst to best district—is a 55% to 45% result in favor of party B. Yet party A received 55% of the overall votes. This gap of 10 percentage points between the median district and statewide total is sizable.<br /><br />Packing isn’t necessarily bad. A district could reflect a real community of interest, a group of people with similar social, economic, and political interests. For example, in Oregon, the Democratic candidate for Portland’s congressional district ran unopposed. The people of Portland share a similar enough view with the Democratic candidate that it deterred any Republicans from challenging the seat. The Supreme Court has ruled that predominantly African American or Hispanic districts can ensure minority representation in Congress and can serve a community of interest’s needs.<br /><br />Likewise, cracking isn’t necessarily bad either. It depends on the ratio. A 50-50 split district is competitive. Even a 52-48 split could swing to the other party in some years. The real question is about one party being systematically disadvantaged by packing and cracking. So how does Oregon fare?<br /><div class="MsoNormal">
<br /></div>
<div align="center">
<table border="0" cellpadding="0" cellspacing="0" class="MsoTableGrid" style="border-collapse: collapse; border: none; mso-border-insideh: none; mso-border-insidev: none; mso-padding-alt: 0in 5.4pt 0in 5.4pt; mso-yfti-tbllook: 1184;">
<tbody>
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<td colspan="6" style="padding: 0in 5.4pt 0in 5.4pt;">
<div class="MsoNormal" style="line-height: 150%; margin-bottom: 2pt; margin-top: 2pt;">
<i>Oregon
2016 results in U.S. congressional races<sup><o:p></o:p></sup></i></div>
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<br /></div>
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<u>% votes for</u> <sup>*</sup><u><o:p></o:p></u></div>
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<br /></div>
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<div align="center" class="MsoNormal" style="margin-bottom: 2pt; margin-top: 2pt; text-align: center;">
<u>% wasted votes for<o:p></o:p></u></div>
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District<o:p></o:p></div>
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Democrat<o:p></o:p></div>
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Republican<o:p></o:p></div>
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Winner<o:p></o:p></div>
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Democrat<o:p></o:p></div>
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Republican<o:p></o:p></div>
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<div align="center" class="MsoNormal" style="margin-bottom: 2pt; margin-top: 2pt; text-align: center;">
1<o:p></o:p></div>
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<td style="border: none; mso-border-top-alt: solid windowtext .5pt; padding: 0in 5.4pt 0in 5.4pt;">
<div align="center" class="MsoNormal" style="margin-bottom: 2pt; margin-top: 2pt; text-align: center;">
62<o:p></o:p></div>
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<td style="border: none; mso-border-top-alt: solid windowtext .5pt; padding: 0in 5.4pt 0in 5.4pt;">
<div align="center" class="MsoNormal" style="margin-bottom: 2pt; margin-top: 2pt; text-align: center;">
38<o:p></o:p></div>
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<td style="border: none; mso-border-top-alt: solid windowtext .5pt; padding: 0in 5.4pt 0in 5.4pt;" valign="top">
<div align="center" class="MsoNormal" style="margin-bottom: 2pt; margin-top: 2pt; text-align: center;">
D<o:p></o:p></div>
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<td style="border: none; mso-border-top-alt: solid windowtext .5pt; padding: 0in 5.4pt 0in 5.4pt;" valign="top">
<div align="center" class="MsoNormal" style="margin-bottom: 2pt; margin-top: 2pt; text-align: center;">
11<o:p></o:p></div>
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<div align="center" class="MsoNormal" style="margin-bottom: 2pt; margin-top: 2pt; text-align: center;">
38<o:p></o:p></div>
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<td style="padding: 0in 5.4pt 0in 5.4pt;">
<div align="center" class="MsoNormal" style="margin-bottom: 2pt; margin-top: 2pt; text-align: center;">
2<o:p></o:p></div>
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<div align="center" class="MsoNormal" style="margin-bottom: 2pt; margin-top: 2pt; text-align: center;">
28<o:p></o:p></div>
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<td style="padding: 0in 5.4pt 0in 5.4pt;">
<div align="center" class="MsoNormal" style="margin-bottom: 2pt; margin-top: 2pt; text-align: center;">
72<o:p></o:p></div>
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<td style="padding: 0in 5.4pt 0in 5.4pt;" valign="top">
<div align="center" class="MsoNormal" style="margin-bottom: 2pt; margin-top: 2pt; text-align: center;">
R<o:p></o:p></div>
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<div align="center" class="MsoNormal" style="margin-bottom: 2pt; margin-top: 2pt; text-align: center;">
28<o:p></o:p></div>
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<td style="padding: 0in 5.4pt 0in 5.4pt;" valign="top">
<div align="center" class="MsoNormal" style="margin-bottom: 2pt; margin-top: 2pt; text-align: center;">
21<o:p></o:p></div>
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<td style="padding: 0in 5.4pt 0in 5.4pt;">
<div align="center" class="MsoNormal" style="margin-bottom: 2pt; margin-top: 2pt; text-align: center;">
3<o:p></o:p></div>
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<td style="padding: 0in 5.4pt 0in 5.4pt;">
<div align="center" class="MsoNormal" style="margin-bottom: 2pt; margin-top: 2pt; text-align: center;">
100<o:p></o:p></div>
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<td style="padding: 0in 5.4pt 0in 5.4pt;">
<div align="center" class="MsoNormal" style="margin-bottom: 2pt; margin-top: 2pt; text-align: center;">
-<o:p></o:p></div>
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<td style="padding: 0in 5.4pt 0in 5.4pt;" valign="top">
<div align="center" class="MsoNormal" style="margin-bottom: 2pt; margin-top: 2pt; text-align: center;">
D<o:p></o:p></div>
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<td style="padding: 0in 5.4pt 0in 5.4pt;" valign="top">
<div align="center" class="MsoNormal" style="margin-bottom: 2pt; margin-top: 2pt; text-align: center;">
49<o:p></o:p></div>
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<td style="padding: 0in 5.4pt 0in 5.4pt;" valign="top">
<div align="center" class="MsoNormal" style="margin-bottom: 2pt; margin-top: 2pt; text-align: center;">
0<o:p></o:p></div>
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<td style="padding: 0in 5.4pt 0in 5.4pt;">
<div align="center" class="MsoNormal" style="margin-bottom: 2pt; margin-top: 2pt; text-align: center;">
4<o:p></o:p></div>
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<td style="padding: 0in 5.4pt 0in 5.4pt;">
<div align="center" class="MsoNormal" style="margin-bottom: 2pt; margin-top: 2pt; text-align: center;">
58<o:p></o:p></div>
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<td style="padding: 0in 5.4pt 0in 5.4pt;">
<div align="center" class="MsoNormal" style="margin-bottom: 2pt; margin-top: 2pt; text-align: center;">
42<o:p></o:p></div>
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<td style="padding: 0in 5.4pt 0in 5.4pt;" valign="top">
<div align="center" class="MsoNormal" style="margin-bottom: 2pt; margin-top: 2pt; text-align: center;">
D<o:p></o:p></div>
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<td style="padding: 0in 5.4pt 0in 5.4pt;" valign="top">
<div align="center" class="MsoNormal" style="margin-bottom: 2pt; margin-top: 2pt; text-align: center;">
7<o:p></o:p></div>
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<td style="padding: 0in 5.4pt 0in 5.4pt;" valign="top">
<div align="center" class="MsoNormal" style="margin-bottom: 2pt; margin-top: 2pt; text-align: center;">
42<o:p></o:p></div>
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<td style="border-bottom: solid windowtext 1.0pt; border: none; mso-border-bottom-alt: solid windowtext .5pt; padding: 0in 5.4pt 0in 5.4pt;">
<div align="center" class="MsoNormal" style="margin-bottom: 2pt; margin-top: 2pt; text-align: center;">
5<o:p></o:p></div>
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<td style="border-bottom: solid windowtext 1.0pt; border: none; mso-border-bottom-alt: solid windowtext .5pt; padding: 0in 5.4pt 0in 5.4pt;">
<div align="center" class="MsoNormal" style="margin-bottom: 2pt; margin-top: 2pt; text-align: center;">
55<o:p></o:p></div>
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<td style="border-bottom: solid windowtext 1.0pt; border: none; mso-border-bottom-alt: solid windowtext .5pt; padding: 0in 5.4pt 0in 5.4pt;">
<div align="center" class="MsoNormal" style="margin-bottom: 2pt; margin-top: 2pt; text-align: center;">
45<o:p></o:p></div>
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<td style="border-bottom: solid windowtext 1.0pt; border: none; mso-border-bottom-alt: solid windowtext .5pt; padding: 0in 5.4pt 0in 5.4pt;" valign="top">
<div align="center" class="MsoNormal" style="margin-bottom: 2pt; margin-top: 2pt; text-align: center;">
D<o:p></o:p></div>
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<td style="border-bottom: solid windowtext 1.0pt; border: none; mso-border-bottom-alt: solid windowtext .5pt; padding: 0in 5.4pt 0in 5.4pt;" valign="top">
<div align="center" class="MsoNormal" style="margin-bottom: 2pt; margin-top: 2pt; text-align: center;">
4<o:p></o:p></div>
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<td style="border-bottom: solid windowtext 1.0pt; border: none; mso-border-bottom-alt: solid windowtext .5pt; padding: 0in 5.4pt 0in 5.4pt;" valign="top">
<div align="center" class="MsoNormal" style="margin-bottom: 2pt; margin-top: 2pt; text-align: center;">
45<o:p></o:p></div>
</td>
</tr>
</tbody></table>
</div>
<div class="MsoNormal">
<br /></div>
* This is the two-party vote share; third party and write-in results excluded for simplicity.<br /><br />District 3 is “packed” for the Democratic candidate who ran unopposed. Offsetting this is the fact that District 2—all of eastern Oregon—is packed for the Republican. However, Republican voters seem to be “cracked” into Districts 4 and 5, central-west and southwest Oregon respectively.<br /><br />How does Oregon look on either measures of gerrymandering? The Democrats took 58% of the two-party vote share. The median district is district 4, and Democrats won 58% there, so the gap is zero. However, on the wasted votes measure, Oregon is not doing as well. Democrats wasted 326,030 out of 991,008 votes statewide, or 33% wasted. Republicans wasted 524,332 out of 709,716 votes, or 74% wasted. Ideally, both parties would waste about 50%. The divergence between the two measures of gerrymandering—one good, one not-so-good—is why the Supreme Court wants to settle on one standard, not two or more competing definitions, of partisan gerrymandering.<br /><br />Based on Oregon Republicans winning 42% of the two-party vote, the state might be expected to have about two Republican congresspeople out of five. One could imagine an alternative to the current district 4 and 5 arrangement that shuffled counties into two new districts: a greater Willamette Valley district comprising Salem, Albany, Corvallis, and Eugene, solidly Democratic; and a U-shaped Cascades, south-central, and coastal Oregon district, leaning Republican. This would move one of the districts into the Republican column. However, it’s often difficult to shift a few voters around and create balance as measured by wasted votes. The standards that people have proposed only kick in when gerrymandering creates a two-seat difference or more because it isn’t always possible in small states to make districts balanced. Geography can get in the way.<br /><br />Some political scientists have proposed using computer programs to draw district boundaries, but this doesn’t solve the root of the problem. For example, a program might try to create more compact districts. That tends to pack Democrats into small, round city districts, wasting Democratic votes. Alternatively, a program might try to create short, straight-line district boundaries, cutting a state into districts like you might cut a cake into irregular polygons. That tends to pack Republicans into large, rectangular rural districts, wasting Republican votes. The bias in the program comes from preferring one type of shape to another. Natural and human geography can necessitate all different shapes to reflect real communities of interest. An eastern Oregon district makes sense, as does a coastal Oregon one, but one district is a near square and the other would be pencil-shaped.<br /><br /> The best hope is for states to put non-partisan commissions, not state legislatures, in charge of drawing reasonable boundaries. Iowa has a long-standing commission; Arizona, California, and New Jersey have newer commissions. There are strengths and weaknesses to each state’s set up for its commission, but the outcomes have been better with commissions than without. Perhaps the threat of losing a federal case for gerrymandering will persuade more state legislatures to enact a non-partisan option, only 204 years after Governor Gerry learned his lesson the hard way at the hand of Massachusetts voters.<style>
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</style>Russell Haneshttp://www.blogger.com/profile/13594411930757264086noreply@blogger.com0tag:blogger.com,1999:blog-8734744291040505450.post-34853238770073326332017-02-11T09:26:00.000-08:002018-04-07T20:35:45.410-07:00The Logit Score: a new way to rate debate teamsI recently published an <a href="https://docs.wixstatic.com/ugd/9896ec_0b38e3ce8fb74e3c85ca1c5f110c1d47.pdf" target="_blank">article on a new debate team-rating method</a> I invented, called the logit score. I hope the logit score will take its place among win-loss record, average speaker points, median speaker points, opponent wins, ranks, and so on as an effective way to rate (and thus rank) debate teams at a tournament.<br />
<br />
<h2>
What is the logit score?</h2>
<br />
The basic idea is simple: the logit score combines win-loss record, speaker points, and opponent strength into one score using a probability model. In other words, the logit score is the answer to the question, "Given these speaker points and these wins and losses to those particular opponents, what is the likeliest strength of this team?"<br />
<br />
Let's take a step back and acknowledge a truth not universally acknowledged in debate: <a href="http://art-of-logic.blogspot.com/2012/07/probability-of-upsets.html" target="_blank">results should be thought of as probabilities, not certainties</a>. A good team won't always beat a bad team--just usually. Off days, unusual arguments, mistakes, and odd judging decisions all contribute to a slight risk of the bad team winning. The truly better team won't always prevail. That means actual rounds need to be thought of as suggesting but not definitively proving which team is better. Team A beats team B. Team A is probably better, but then again, they could have had off day, been surprised by a weird argument, or had a terrible judge. If team A got much, much higher speaker points, it was very likely the better team. If team A only edged out team B by a little bit, then the uncertainty grows.<br />
<br />
That's where the logit score comes in. Estimating team A's actual, true strength depends on putting together all of those probabilities and uncertainties into one model. I won't get into the specifics (the details are in the article), but the basic idea is using a logistic regression to put the probabilities for wins and losses to specific opponents as well as specific speaker points received together. The logit score for a team means: "If team A were estimated to be stronger, these results would be a bit more likely, but those other results would be far less likely. If team A were estimated to be weaker, these results would be far less likely, even though those other results would be a bit more likely. This logit score is the proper balance that makes all the results most likely overall." Because it factors in all the results in one probability model, the logit score isn't sensitive to outliers: unusually high or low speaker points, losses to outstanding teams, and wins over terrible teams don't affect the logit score much at all.<br />
<br />
<h2>
Does the logit score have any empirical results to back it up?</h2>
<br />
Yes. This is the <a href="https://docs.wixstatic.com/ugd/9896ec_0b38e3ce8fb74e3c85ca1c5f110c1d47.pdf" target="_blank">bulk of my article</a>.<br />
<br />
I took a past college debate season, used those results to give every team a logit score, and then looked to see how well logit scores "retrodicted" the actual results in a season. That is to say, how often did the higher logit scoring team win rounds against the lower logit scoring team? As a baseline of comparison, I also did the same kind of analysis by ranking the teams by win-loss record.<br />
<br />
<i><b>The logit score rankings got slightly more rounds correct than the win-loss record rankings.</b></i><br />
<br />
The slightly higher accuracy is not, on its own, a reason to rush to adopt logit scores. It merely proves that the logit scores aren't doing anything crazy. For the most part, the logit scores reshuffles teams ever so slightly with their nearest peers. The moves are slight ups or downs, not drastic shifts.<br />
<br />
The real reason to consider using logit scores is that (a) they are less sensitive to outliers, which can matter a lot for a six or eight round tournament; and (b) they factor in more information. Win-loss records only use speaker points as a tiebreaker; it's secondary. Measures of opponent strength usually come third. In other words, a team with a really tough random draw and goes 4-2 as a result of dropping the first two rounds might miss out on breaking if no 4-2s break--win-loss record comes first and opponent strength won't factor in in that scenario. The logit score on the other hand--because wins, points, and opponents are all factored in at once--could reflect that this team is in fact very strong because it only lost two rounds to very good opponents. (See how important it is to be less sensitive to outliers?) More information also rewards well-rounded teams: those that win rounds on squeakingly close decisions and don't receive great speaker points are penalized more under a logit score system than a win-loss-then speaker points-system.Russell Haneshttp://www.blogger.com/profile/13594411930757264086noreply@blogger.com2tag:blogger.com,1999:blog-8734744291040505450.post-25514186671481868992016-03-31T10:28:00.001-07:002016-03-31T10:28:51.550-07:00Standards-based grading; standardized testingIt's been a while since I've written anything--life gets in the way. Mostly, I've been working on my new book, <i>Statistics for Debaters and Extempers</i>, which is 23/29 written. I keep writing chapters but adding one new ones to the list. It's like the Winchester House. However, I do have some thoughts I want to share about teaching.<br />
<br />
One post I'm proud of is the <a href="http://art-of-logic.blogspot.com/2014/01/the-decathlon-and-grading.html" target="_blank">one about grading</a>. Percent grades are not very informative for teachers. Standards-based grading (SBG) is far better. If you're not familiar with SBG, let me explain it really briefly. The idea is to note for each standard (skill or knowledge students are supposed to learn) for each assignment, you mark a score that the student earns. These scores are often 1 to 4, where 1 is "not demonstrated at all"; 2 is "developing"; 3 is "demonstrated"; and 4 is "mastery". Or some such other scheme. For example, on a math test on fractions, a student might receive a 4 on the adding fractions standard but a 3 on the multiplying fractions standard. All the other standards for the year for that test would be left "N/A". SBG can exist side-by-side with a percent grade, too.<br />
<br />
Ideally, students would be assessed on each standard multiple times. They could demonstrate mastery on the standard on tests, homework, or projects. Students should be able to show at least a 3 on a standard multiple times, say three times, to earn an overall 3 on it. A SBG scheme might also look only at the most recent three times a standard has been assessed. For example, a {2, 3, 3} could be coded as a 2, a {3, 4, 3} coded as a 3, and a {3, 4, 4} coded as a 4. The student earning a 2 wouldn't be penalized; they'd be given another chance to earn a 3. The other two students who earned 3's and 4's wouldn't need another assessment.<br />
<br />
One thing I hadn't thought about before: SBG opens the door to indicating to students which test, quiz, and homework questions reveal which level. For example, one could mark questions as 2's, 3's, and 4's. A teacher could explain that getting all the 2's right is a necessarily developmental step but not an endpoint. A student who can answer all the 2-level questions right should recognize the achievement but push himself or herself to do the 3-level questions. Likewise, a student getting all the 3-level questions right should recognize the achievement but push to do 4's. It basically, to use a buzzword, allows the teacher and student to differentiate the work they do. Kids at the top could be told, "When you do your homework, spend half the time on 3's to prove you can do them, and spend the rest of your time doing the 4's for exercise." Kids in the middle could be told, "Spend a third of your time on 2's to prove you can do them, a third on 3's to really exercise, and a third on 4's to see if you can really stretch." Kids at the bottom could be told to spend equal time on 2's and 3's. It gives every ability kid a chance to do comfortable practice and also practice time for growth.<br />
<br />
<div style="text-align: center;">
* * *</div>
<br />
A completely random idea: why do we have the S.A.T.? I think the biggest reason colleges want to keep it is because it is hard to know what schools' curricula cover and what their grading means. Grades from one school aren't really comparable to grades from another.<br />
<br />
But what if the S.A.T. 1 format (you know, one hour each of math, reading, and writing) was basically ditched in favor of the S.A.T. 2 / A.P. subject style tests? Colleges could verify what each schools' transcript actually meant. Even if the tests aren't necessarily accurate for individual kids, they would be accurate for an entire schools' worth of test-takers.<br />
<br />
Here's how I imagine it working. Gone are Saturday tests. Gone are students being solely responsible to sign up (this harms poor kids and kids who are the first in their families to go to school). It is the school's responsibility to look at the different test options and sign the kids up for the right tests. These tests would happen in May, during the school day, just like the A.P. tests do.<br />
<br />
Math, English, and foreign languages would only need to be tested in the May of junior year. Obviously there would need to be a different exam for each foreign language. The English exam could have two options, say, a regular level exam and an honors level exam. (I imagine a vast chunk of material that overlaps between the two so that scores are comparable.)<br />
<br />
Math would be a bit tricky. There would need to be several different exams reflecting the fact that juniors end up in very different places. The school would be responsible for guiding students in the different classes to pick the right exam. I imagine these tests would be about three hours, like the current A.P. tests are.<br />
<br />
Sciences and history would be even trickier. Every student basically takes biology, chemistry, and physics but the order differs from school to school. Most schools do biology in freshman year, but some start with physics. In history, the usual sequence is world history, European history, and U.S. history, but there are many deviations from that pattern. However, this seems like it is a surmountable problem for the test designers. The bigger problem to me is making sure that these subject tests don't get bloated and require extensive cramming of facts and instead test higher level scientific and historical reasoning skills. (These subjects are the A.P. tests that come in for the most abuse for this issue.) To keep things balanced and prevent bloat, each of these tests would be kept to one hour.<br />
<br />
Basically, I'm talking about expanding the A.P. tests for all students, not just at the honors level but also at the regular level. Everyone submits ten scores: math, English, foreign language, three sciences, three history, plus one more of their choice (could be computer science, or economics, or art history--whatever they want). Junior year, we're talking about a week of testing, but in sophomore and freshman year, it would only be two hours of testing (science plus history), so they would more or less have normal classes during that week. It's even possible to devise a basic schedule:<br />
<br />
Monday - English<br />
Tuesday - Sciences + optional tests<br />
Wednesday - Languages<br />
Thursday - History + optional tests<br />
Friday - Mathematics<br />
<br />
People complain about the inequity of A.P. testing, and I agree. But making the A.P. tests mandatory and putting the burden on schools solves that problem. And my system obviates the need for giving the S.A.T. 1, which is inequable because preparing for it requires work outside of school. This hurts the poor kids who won't be able get any additional help for it.Russell Haneshttp://www.blogger.com/profile/13594411930757264086noreply@blogger.com0tag:blogger.com,1999:blog-8734744291040505450.post-53661576747805761242015-10-18T11:28:00.002-07:002016-02-04T21:08:33.832-08:00Houses and Algebra<script src="http://cdn.mathjax.org/mathjax/latest/MathJax.js?config=TeX-AMS-MML_HTMLorMML" type="text/javascript">
</script>Buying and selling a house are major financial decisions, but ones where I believe a lot of people do the math wrong and do not properly determine their net profit or loss of homeownership. It is also a good example where students in an Algebra 1 class could understand how to build an equation.<br />
<br />
In a traditional Algebra 1 class, an equation would be presented to students first, like so:<br />
<br />
<div style="text-align: center;">
<math xmlns="http://www.w3.org/1998/Math/MathML"><mi>m</mi><mfenced><mrow><mi>x</mi><mo>-</mo><mi>y</mi></mrow></mfenced><mo>+</mo><mn>0</mn><mo>.</mo><mn>94</mn><mi>f</mi><mo>-</mo><mi>i</mi><mo>=</mo><mi>n</mi></math></div>
<br />
where m is the months of occupancy, x is the monthly savings of owning over renting, y is the monthly interest on the downpayment, f is the final sale price, i is the initial price, and n is the net profit. Got that? No? Who cares - here's 10 problems, plug in the numbers and go. I fail to see the point of it.<br />
<br />
<h2>
A better way to do it</h2>
<br />
Basically, let the students build the equation.<br />
<br />
There are two things to consider, both related to opportunity costs. The first is the monthly cost to own a house - the mortgage, insurance, and property taxes - compared to monthly cost to rent. Utilities would be the same, so both columns of the ledger should ignore utilities. Let's define this as x, where x = monthly rental cost minus monthly cost to own. Students could work with some specific examples and determine what the sign of x indicates. This is knowledge students in Algebra 1 are still reinforcing. (A positive x indicates that it is cheaper to own. A negative x indicates that it is cheaper to rent.)<br />
<br />
The second thing to consider is that buying a house necessarily entails tying up a down payment that could have been an investment. Call the monthly return on this investment y, the opportunity cost of not investing the money elsewhere. If the down payment is $50,000 and the interest rate one can get in a safe account is 3%, then y is about $125 per month. This variable is, of course, always positive. In Algebra 1, students wouldn't know how to calculate the monthly interest, but it is worth them knowing where that variable is coming from.<br />
<br />
Next, I would ask students to think about the true monthly benefit to owning, giving them several different examples. After that, I would ask them to write a general expression for it (the true monthly benefit to owning is x - y) and ask them to explain what the sign of this quantity shows them. If this quantity is positive, the homeowner is saving money each month. If it's negative, the renter is saving money each month. This quantity needs to multiplied by the period of occupancy to come up with total savings or total costs to the homeowner.<br />
<br />
Now onto sale price.<br />
<br />
There are four possibilities. There are the two trivial-to-understand ones: (a) the homeowner both makes money on the sale AND saves money each month by owning, in which case the person clearly had made money by owning; and (b) the homeowner both loses money on the sale and on the monthly cost compared to renting, in which case the person has clearly lost money by owning.<br />
<br />
The other possibilities are more tricky to understand: (c) the sale price is negative but the monthly cost is positive, and (d) the sale price is positive but the monthly cost is negative. In both cases, it depends on the specific amounts. Let's have the students work with some specific numbers to make sure that they see what's going on.<br />
<br />
Let's say the homeowner is saving $400 a month on the mortgage compared to renting. The downpayment was $50,000, so that's $125 per month in foregone interest, so the actual monthly benefit to owning is $275. Now let's say the person lives in the house for 7 years. Perhaps the loss on the sale of the house is $20,000. (Don't forget to multiply the final sale price by 0.94 because of the real estate transaction fees when calculating the net profit or loss!) Did this homeowner come out ahead?<br />
<br />
<div style="text-align: center;">
<math xmlns="http://www.w3.org/1998/Math/MathML"><mn>7</mn><mo>·</mo><mn>12</mn><mo>·</mo><mn>275</mn><mo>></mo><mn>20</mn><mo>,</mo><mn>000</mn></math></div>
<math xmlns="http://www.w3.org/1998/Math/MathML"><mn></mn></math><br />
Just barely, but yes. In this case, the positive quantity of monthly savings (times months) is greater than the one-time sale loss.<br />
<br />
As another example, consider someone losing $200 a month on the mortgage compared to renting (it's a very cheap rental market!). With a $50,000 downpayment, the actual monthly loss is $325. Let's say the person lives in the house for 5 years and realizes a profit of $15,000. In this case:<br />
<br />
<br />
<div style="text-align: center;">
<math xmlns="http://www.w3.org/1998/Math/MathML"><mn>5</mn><mo>·</mo><mn>12</mn><mo>·</mo><mn>325</mn><mo>></mo><mn>15</mn><mo>,</mo><mn>000</mn></math></div>
<br />
This is a net loss overall. The monthly loss (times months) is greater than the one-time profit realized on the sale.<br />
<br />
At this point, students would be ready to write the equation after working with several examples. Furthermore, why not have students write equations with long variable names?<br />
<br />
<div style="text-align: center;">
<math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle mathsize="12px"><mrow><mtext>months of occupancy</mtext><mfenced><mrow><mtext>monthly cost over renting</mtext><mo>-</mo><mtext>interest</mtext></mrow></mfenced><mo>+</mo><mn>0</mn><mo>.</mo><mn>94</mn><mo>·</mo><mtext>final sale price</mtext><mo>-</mo><mtext>intial saleprice</mtext><mo>=</mo><mtext>net profit</mtext></mrow></mstyle></math></div>
<br />
This is an equation they would actually understand, because they built it themselves, working with examples first, confirming what the signs of each part mean, and because it's verbose. Now they have some algebra knowledge and some real-world knowledge.<br />
<br />
Here's the <a href="http://www.nytimes.com/interactive/2014/upshot/buy-rent-calculator.html" target="_blank"><i>New York Times'</i> rent vs buy calculator</a>. And here's <a href="http://www.vox.com/2016/2/3/10898326/case-for-housing-investment" target="_blank">Vox</a> on the matter, raising the good point that buying a home can force people to "save" in paying off the principal of the loan.Russell Haneshttp://www.blogger.com/profile/13594411930757264086noreply@blogger.com0tag:blogger.com,1999:blog-8734744291040505450.post-31246379319393199642015-07-04T18:38:00.004-07:002015-10-17T10:26:05.458-07:00Study of speaker points and power-matching for 2006-7For my <a href="http://art-of-logic.blogspot.tw/2015/01/100th-post.html" target="_blank">100th blog post</a>, I did an experiment to try different tabulation methods for debate tournaments. The benefit of an experiment is that the exact strength of each team is known and the simulated tournaments introduced random deviation on performance in each round. The deviation in performance is based on <a href="http://art-of-logic.blogspot.tw/2012/07/probability-of-upsets.html" target="_blank">observed results</a>.<br />
<br />
The results of the experiment showed that, even after only six rounds, median speaker points is a more accurate measure of a team's true strength than its win-loss record. Furthermore, the results showed that high-low power-matching improved the accuracy of the win-loss record as a measure of strength (but only to the same level of accuracy as median speaker points) and high-high power-matching worsened its accuracy.<br />
<br />
<h2>
Description of the study</h2>
<br />
This experiment lead me to do an observational study of the 2006-07 college cross-examination debate season. I analyzed all the varsity, preliminary rounds listed on debateresults.com: 7,923 rounds; 730 teams. This was the last year when every tournament used the traditional 30-point speaker point scale. Each team was assigned a speaker point rank from 1 (best) to 730 based on its average speaker points. Each team was also assigned a win-loss record rank from 1 to 730 based on the binomial probability of achieving its particular number of wins and losses by chance. Thus, both teams that had extensive, mediocre records AND teams with few total rounds ended up in the middle of the win ranks.<br />
<br />
Next, I analyzed every individual round using the two opponents' point ranks and win ranks. For example, if one team had a good point rank and one a bad point rank, then of course the odds are quite high the good team would win. On the other hand, if the two teams were similarly ranked, then the odds are much closer to even. Using the point ranks, I did a logit regression to model the odds for different match-ups. And I also ran a separate logit regression for win ranks. Here are the regressions:<br />
<br />
<div class="separator" style="clear: both; text-align: center;">
<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgXMkylB7ra2a44gcPge6KaDRPyb_53jl1aes1afGF4yWIUAmRybBufZB5rwZ2kA6LNk_ZsmilYOukUrzGZSnBrJFQJj6RpJuPZ43bq6gkv-dgLwFGTAgM9P3rw0EMXXlFHukvjeKt0LEfd/s1600/logit+regressions.tiff" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgXMkylB7ra2a44gcPge6KaDRPyb_53jl1aes1afGF4yWIUAmRybBufZB5rwZ2kA6LNk_ZsmilYOukUrzGZSnBrJFQJj6RpJuPZ43bq6gkv-dgLwFGTAgM9P3rw0EMXXlFHukvjeKt0LEfd/s1600/logit+regressions.tiff" /></a></div>
<br />
The horizontal axis shows the difference in the ranks between the two opponents. The vertical axis shows the probability of the Affirmative winning. For example, when Affirmative teams were 400 ranks better (smaller number) than its opponent, they won about 90% of those rounds. These odds are based on the actual outcomes observed in the 2006-07 college debate season.<br />
<br />
The belief in the debate community is that speaker points were too subjective -- in the very next season, the format of speaker points was tinkered with and changed. The community settled on adjusting speaker points for judge variability, that is using "second order z-scores." Yet my analysis shows that, over the entire season, the average speaker points of a team is a remarkably good measure of its true strength. Making a lot of adjustments to the speaker points is unnecessary.<br />
<br />
First, note how similar the two logistic regressions are. A difference of 100 win ranks, say, is as meaningful for predicting the actual outcomes as a difference of 100 point ranks. Using the point ranks regression "predicts" 75% of rounds correctly, while using the win ranks regression "predicts" 76% correctly. Both regressions "predict" each team's win-loss record with 91% accuracy. (This discrepancy between 75% and 91% occurs because, overall, many rounds are close and therefore difficult to predict -- but for an individual team that has eight close rounds, predicting a 4-4 record is likely to be very accurate.)<br />
<br />
What is impressive to me is that, even without correcting for judge bias, the two methods are very comparable. Bear in mind it is NOT because every team receives identical win ranks and point ranks. In fact, as you will see in the next section, some teams got quite different ranks from points and from wins!<br />
<br />
<h2>
Power-matching</h2>
<br />
In the second part of my analysis, I looked at how power-matching influenced the results. I could not separate out how each round was power-matched because that information was not available through debateresults.com. But college debate rounds tend to be power-matched high-low, which is better than power-matching high-high (as my experiment showed). I eliminated teams with fewer than 12 rounds because they have such erratic results. This left 390 teams for the second analysis.<br />
<br />
The goal of power-matching is to give good teams harder schedules and bad teams weaker schedules. Does it succeed at this goal?<br />
<br />
No:<br />
<br />
<div class="separator" style="clear: both; text-align: center;">
<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEh_TWNaaakDo-TplgMF5AN4puKDB_lLivO5LLIv1SdaPlyh5hRuTBUm8E0pQiNNyLcL4xt2H0KKozUM5pqYqGuCbchDzshZj9-2b-MNMu6XALauVx1Q3LcyfWqbBflkw88Ykj190eeeTYcx/s1600/schedule+strength.tiff" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEh_TWNaaakDo-TplgMF5AN4puKDB_lLivO5LLIv1SdaPlyh5hRuTBUm8E0pQiNNyLcL4xt2H0KKozUM5pqYqGuCbchDzshZj9-2b-MNMu6XALauVx1Q3LcyfWqbBflkw88Ykj190eeeTYcx/s1600/schedule+strength.tiff" /></a></div>
<br />
I made pairwise comparisons between the best and second-best team, the second- and third-best team, and so on. It is common for two teams with nearly identical ranks to have very different schedules. The <i><b>average</b></i> difference in schedule strength is 68 ranks apart out of only 730 ranks, which is almost a tenth of the field! One team may face a schedule strength at the 50th percentile, while a nearly identical team faces a schedule strength at the 60th percentile. Bear in mind that this is the average; in some cases, two nearly identical teams faced schedule strengths 30 percentiles apart! I cannot think of clearer evidence that power-matching fails at its assigned goal.<br />
<br />
Finally, I performed a regression to see whether these differing schedule strengths is the cause of the discrepancy between win ranks and point ranks.<br />
<br />
Yes:<br />
<br />
<div class="separator" style="clear: both; text-align: center;">
<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEi9lkz46i2HxSnTCXEMiewAVHCoEhmoMhlbGzmn7Lo4J-8_Z4YkePoTzSNbiJZ2sZb3XbSWkUa5zLWsSGNg7o9oqApZnn2QSUPJ8ny7FxQ3iT21WUus3qMxz6IfcsIcnv7KS9dV89hMIoap/s1600/regression.tiff" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEi9lkz46i2HxSnTCXEMiewAVHCoEhmoMhlbGzmn7Lo4J-8_Z4YkePoTzSNbiJZ2sZb3XbSWkUa5zLWsSGNg7o9oqApZnn2QSUPJ8ny7FxQ3iT21WUus3qMxz6IfcsIcnv7KS9dV89hMIoap/s1600/regression.tiff" /></a></div>
<br />
The horizontal axis shows the difference between each team's rank and its schedule strength. The zero represents teams that have ranks equal to schedule strength. The vertical axis shows the difference between each team's win rank and point rank.<br />
<br />
Teams in the upper right corner had easier schedules than they should have (under power-matched) and better win ranks than point ranks. Teams in the lower right corner had harder schedules than they should have (over power-matched) and had worse win ranks than point ranks. Having easy schedules improved win ranks; having hard schedules worsened win ranks. The effect is substantial: r^2 is 0.49. Of course, some of the discrepancy between the ranks is caused by other factors: random judging, teams that speak poorly but make good arguments, etc. But power-matching itself is the largest source of the discrepancy.<br />
<br />
Given that the schedule strengths varied so much, this is a big, big problem. I know that tab methods have improved since 2006-7 and now factor in schedule strength; this analysis should be rerun on the current data set to see if the problem has been repaired.<br />
<br />
<h2>
Conclusions</h2>
<br />
<br />
<ol>
<li>Speaker points are just as accurate a measure of true team strength as win-loss record. This confirms the results of my experiment showing that power-matched win-loss record is at rough parity in accuracy to median speaker points.</li>
<li>Power-matching as practiced in the 2006-07 college debate season does not give equal strength teams equal schedules. (This method is probably still in use in many high school tournaments.)</li>
<li>Unequal schedule strengths are highly correlated with discrepancies in the two ranking methods, point ranks and win ranks.</li>
</ol>
<br />
<br />
One could argue for power-matching on educational grounds: it makes the tournament more educational for the competitors. However, it is clear from this analysis that power-matching is not necessary to figure out who the best teams are. In fact, it might actually be counterproductive. Using power-matched win-loss records takes out one source of variability from the ranking method -- judges who give inaccurate speaker points -- but adds an entirely new one: highly differing schedule strength!Russell Haneshttp://www.blogger.com/profile/13594411930757264086noreply@blogger.com0tag:blogger.com,1999:blog-8734744291040505450.post-80466587890532035202015-06-05T21:03:00.001-07:002018-12-28T10:14:21.967-08:00College degreeMy snide summary of marketing is, "Find people who are willing to pay more, then charge them more." Searching on a specific airline's website is an indicator that you are willing to pay more, so it costs more to buy directly from the airline than from an aggregator. Buying shampoo at the salon is an indicator you are willing to pay more. My favorite example: premium gas. It is not actually better for your car; it just costs more.<br />
<br />
How about a college degree?<br />
<br />
Certain selective colleges have managed to distinguish themselves as "worth more." Parchment has an <a href="http://www.parchment.com/c/college/college-rankings.php" target="_blank">innovative method for divining applicants' perception of schools' worth</a>. They treated each applicant's decision as votes. For example, a student who got into Columbia, Duke, and Stanford and chose Stanford votes for Stanford and against Columbia and Duke. Parchment compiled all these votes using an Elo method to determine which colleges have distinguished themselves in applicants' minds.<br />
<br />
How the schools managed to distinguish themselves is a great question. Many did it through their age - our oldest colleges are often the most esteemed. Others did it through the reputation of their graduate schools. Sports catapulted other schools onto the scene. However, selectivity in admissions is the key variable. Maybe it is because <i>U.S. News and World Report</i>'s college ranking method weights selectivity so highly, but even without the <i>U.S. News</i> rankings, selectivity would definitely affect people's perceptions. (Side note: the <a href="http://www.nytimes.com/2015/02/08/education/edlife/how-to-raise-a-universitys-profile-pricing-and-packaging.html" target="_blank">rankings seriously distort college's behavior</a>.) People assume hard-to-obtain goods are worth more.<br />
<br />
<h2>
Are these schools, in fact, worth more?</h2>
<br />
In terms of the content of the courses, there is probably little difference. For the most part, a course in differential equations at Yale covers about the same topics at about the same pace as one at Ohio State. It is important to understand that most college courses are not special snowflakes but (<i>cough</i>) commodities. Of course, college professors do invent new courses, and there are programs unique to an individual school. But many courses are commodities. One may get a better or worse teacher, but because schools don't place much weight on teaching in professors' evaluations, teacher quality and school reputation don't have much correlation.<br />
<br />
Of course, course content and teaching is not the only variable that matters when talking about institution educational quality. Two colleges might teach similar courses but at differing levels of effectiveness. Good institutions have professors who keep standards for student work high; good institutions give robust support to weaker students; and good institutions develop new programs. Furthermore, due to the enormous endowments highly selective colleges have, they have a lot more money to spend per student - although much of the extra funding goes to facilities like dorms, athletic buildings, and student recreation centers that have little impact on the quality of instruction and to research facilities that may have only a small impact on <i>undergraduate</i> instruction. However, institutional quality hardly seems to justify the hysteria.<br />
<br />
One could argue that there are intangible benefits to going to a high-reputation school like being surrounded by motivated, smart students and professors. While this has makes intuitive sense, the best evidence does not really support this argument. The C.L.A., the <a href="http://wilsonquarterly.com/stories/bad-education/" target="_blank"><span style="background-color: white;">Collegiate Learning Assessment</span>, shows little pattern</a> between college attended and student learning. Some learn a lot at lower reputation schools; some learn little at high-reputation schools. One can discuss Shakespeare with other smart, eighteen- and nineteen-year-olds, but the discussion could be more enlightening if it includes a working mom who's back in college, a soldier who's back from war, ... you get my point. The student body argument cuts both ways; diversity is important, too. The C.L.A. results show that neither way is intrinsically superior. <a href="http://www.vox.com/2015/4/23/8471271/us-news-rankings-education" target="_blank">How much or how little students learn has everything to do with them</a> and little to do with the college itself.<br />
<div>
<br /></div>
<div>
A giant meta-analysis entitled <i>How College Affects Students</i> wrote:</div>
<br />
<blockquote class="tr_bq">
"The great majority of postsecondary institutions appear to have surprisingly similar net impacts on student growth. If there is one thing that characterizes the research on between-college effects on the acquisition of subject matter knowledge and academic skills, it is that in the most internally valid studies, even the statistically significant effects tend to be quite small and often trivial in magnitude."</blockquote>
<br />
Quoted from the <a href="http://www.nytimes.com/2015/07/24/upshot/the-fundamental-way-that-universities-are-an-illusion.html" target="_blank">New York Times</a>. And the New York Times continues:<br />
<br />
<blockquote class="tr_bq">
The whole apparatus of selective college admissions is designed to deliberately confuse things that exist with things that don't. Many of the most prestigious colleges are an order of magnitude wealthier and more selective than the typical university. These are the primary factors driving their annual rankings at or near the top of the U.S. News list of "best" colleges. The implication is that the differences in the quality of education they provide are of a similar size. There is no evidence to suggest that this is remotely true. When college leaders talk about academic standards, they often mean admissions standards, not standards for what happens in classrooms themselves.</blockquote>
<br />
Of course, that's about <b>learning</b>. Let's talk about <b>earning</b>.<br />
<br />
<h2>
Advantages of reputation</h2>
<br />
This leaves reputation alone as the way in which high-reputation colleges are worth more. Reputation means whether the degree will open the door to good entry-level jobs in a field and get a person off to a great start. And the evidence is that the path to many elite jobs runs through high-reputation colleges almost exclusively. Why are many elite employers so enamored of a few colleges?<br />
<br />
Let's admit that the undergraduate degree itself does not convey much information about what a person learned. We may assume that a computer science major covered certain basics in the course of earning his or her degree. But that's about it. The degree provides low-quality information about how deeply that person learned in college. (In fact, it is basically impossible to fail out of a high-reputation college - they don't want to ruin their statistics.) So why do businesses care about the undergraduate institution? The simple answer must be that the key information is about college <b>admission</b>. Businesses must believe that high-reputation colleges do a good job selecting the smartest and hardest-working students.<br />
<br />
In some fields like law, the college (and law school) a person attended are always crucially important to hiring decisions. In other fields like computer science, the potential employers care far more about work samples and portfolios. While it is hard to make generalizations, for most fields, the reality is more like law. For many entry-level jobs, employers would be hard-pressed to come up with suitable work samples recent college graduates could submit, thus employers default to college reputation. Especially for the entry-level jobs that lead to elite jobs, employers recruit heavily - almost exclusively - from high-reputation schools, many going so far as to have <a href="http://www.theatlantic.com/business/archive/2015/05/recruitment-resumes-interviews-how-the-hiring-process-favors-elites/394166/" target="_blank">dedicated H.R. teams for each school</a> or <a href="http://www.slate.com/blogs/business_insider/2015/04/02/stanford_graduates_get_fought_over_by_tech_companies_like_snapchat_and_have.html" target="_blank">special recruiting events</a>. There are substantial employment advantages to going to an elite college in the person's initial job search that could have life-long effects. Once someone is shut out of this kind of entry-level job, it is hard to gain the experience to ever be considered for the culminating elite job.<br />
<br />
The reputation of a college helps with starting a person out on the career path. A good start could have long-term financial benefits, so this might actually justify the reputation of some colleges as worth more. But my question is a different one. If what businesses are really getting is admission information, is this useful information? Are businesses right to think colleges are doing a good job selecting students?<br />
<br />
<h2>
Admission decisions</h2>
<br />
On the one hand, one can say colleges are selecting those students who are smart and hard-working - good traits for employers to seek. Let's stipulate that employers want to maximize both as much as possible; they want new employees with loads of content knowledge who can think flexibly. I am not going to engage with any question about the social implications of affirmative action or other admission policy, important though those questions are. I am merely addressing the question: Would employers be right to assume that the better the reputation of the school, the smarter and harder working its graduates?<br />
<br />
After reading Mitchell Steven's book, <i><a href="http://www.amazon.com/Creating-Class-College-Admissions-Education/dp/0674034945/ref=sr_1_1?ie=UTF8&qid=1433559597&sr=8-1&keywords=creating+a+class&pebp=1433559599428&perid=1WW2CHQBWYNMFT9176PM" target="_blank">Creating a Class</a></i>, I realized that the defining fact for college admission officers is the lack of information. Despite S.A.T. and A.P. scores and other objective information, a lot of learning that students do is invisible. Can the student learn on their own, or do his or her scores hide heavy tutoring? Softer skills - like managing intellectual disagreements and debates, grit, research skills, and integrity - are hidden. Letters of recommendation only go so far to fill in the information gap. Smart, hard-working students at schools with overworked teachers and college counselors are at a disadvantage because they may not get high-quality letters. As a result, admission officers may revert to proxies, such as the reputation of the high school. (If employers are relying on the reputation of the college as a proxy, and colleges are relying on the reputation of the high school as a proxy...) This is <a href="http://fivethirtyeight.com/features/what-were-missing-in-measuring-whos-ready-for-college/" target="_blank">what Shaun Harper found</a>: great students at weak schools are overlooked.<br />
<br />
To be fair to admission officers, students at weaker high school might never write an analytical essay, while students at great high school write one or more a week. The high school program does matter, but my point is that there are some students who would be capable but are not given the opportunity because of their high school's weak curriculum. While standardized tests are not great equalizers, without them, admission to selective colleges would be even more skewed to students who go to the best high schools. S.A.T. scores and A.P. scores give colleges some assurance that a student is exceptional despite attending a weak high school - but not enough to level the field. Colleges are not scooping up many hidden gems because they simply lack the information to do so. On top of this, of the smart, hard-working first-generation college students and minority students who do get in, many do not end up <a href="http://www.theatlantic.com/business/archive/2013/01/the-real-college-crisis-isnt-high-costs-its-low-information/266802/" target="_blank">matriculating</a>. So, these <a href="http://www.theatlantic.com/education/archive/2015/01/smart-low-income-students-who-shun-good-colleges/384694/" target="_blank">students also lack information</a>. The bottom line is that college admission is <a href="http://fivethirtyeight.com/features/what-were-missing-in-measuring-whos-ready-for-college/" target="_blank">not only about intellectual and personal capabilities but also about social capital</a>.<br />
<br />
Steven Pinker, the celebrity linguist at Harvard, points out facts about <a href="http://www.newrepublic.com/article/119321/harvard-ivy-league-should-judge-students-standardized-tests" target="_blank">college admissions at selective schools that should unnerve everyone</a>. Selective schools use holistic selection including academics, extracurriculars, and character. This disadvantages very smart but poor students who cannot afford to be well-rounded. Furthermore, it means that the student body, once at Harvard or other selective schools, spends a lot of its time in the same extracurriculars that helped them get in, and not as much on academics as one might expect. As Dr. Pinker heard a Harvard admission officer point out, their goal is not to train future academians but future leaders. (Is the fact that so many Harvardians go into finance -- the lucrative but well-beaten path -- an indication of the admission office's failure?) It is hard to believe that the extracurriculars are really a great proxy of leadership. Not to pick on any one activity here, but would an employer actually care that a person is an outstanding rower? singer?<br />
<br />
And the other shocking issue is students from China. Most high schools there do not have college counselors, so a third-party system of packagers help get students into colleges. And the <a href="http://www.theatlantic.com/education/archive/2015/05/american-universities-are-addicted-to-chinese-students/394517/" target="_blank">degree of fraud is truly shocking</a>: 90% fake recommendations, 70% fake essays, and 50% fake high school transcripts. Check out the huge <a href="http://www.reuters.com/investigates/special-report/college-sat-one/" target="_blank">five-part expose in Reuters about cheating on the international S.A.T.</a> test dates. Despite this, <a href="http://www.nytimes.com/2011/11/06/education/edlife/the-china-conundrum.html" target="_blank">U.S. colleges continue to admit Chinese students in mass</a> without demanding changes to the system. They could require <i>gao kao</i> scores. They could <a href="http://www.theatlantic.com/education/archive/2015/01/what-students-in-china-have-taught-me-about-us-college-admissions/384212/" target="_blank">demand video interviews to prove English skills</a>. Given that they do not make such demands, and given that colleges know the fraud problem, then do you have much faith in any part of the admission process? Colleges admission work is not so precise and thorough to justify business faith in college graduates absent other data. In light of this, college admissions officers' rhetoric that they are skilled at picking the best and brightest should make us incredulous -- and the effect of it on students is especially insidious. The data are just not that trustworthy to justify such boasts. (I would also add in the <a href="https://www.theatlantic.com/education/archive/2018/12/tm-landry-and-myth-meritocracy-education/578149/" target="_blank">T. M. Landry scam</a> -- which had to be at least very, very suspicious to college admissions officers, yet no one even went through the cursory steps of checking up on their data.)<br />
<br />
This is not a plea to go to a fully objective system where only standardized test scores count. One only needs to look at the <i>gao kao</i> to see the dangers. I think it is fine for colleges to have subjective opinions about potential students, just like it is fine for students to have subjective opinions about which colleges they like the best! This is why I argued in a <a href="http://art-of-logic.blogspot.com/2014/07/college-admissions.html" target="_blank">previous post for a matching system</a>. Instead, my plea is for two things: college admissions should drop the rhetoric of infallibility. Just admit that the college is looking for students who clear a certain benchmark and who fit. Second, businesses should recognize that college admission is a fuzzy science at best. Sure, one might value candidates from highly selective colleges more than those from semi-selective colleges, but making distinctions between Harvard grads and Vassar grads is folly.<br />
<br />
Businesses have created a self-fulfilling prophecy. By esteeming some undergraduate institutions far more than others, they have reinforced the reputation of those schools and created an admissions rush for those schools. The weak link in the system is that college admission cannot make the sort of fine distinctions it is presumed to. One way to break the cycle would be to prohibit employers from campus recruiting events and from asking about a candidate's undergraduate institution, but I doubt that would catch on. However, it is interesting to think about how employers would be forced to deal with evaluating 22 year olds if they only knew that he or she had an undergraduate degree in a chemistry but could not ask about the institution. Would they ask more questions about what the candidate had actually learned?<br />
<br />
These problems all stem from the relative paucity of information about college outcomes. At the top end, the lack of information creates a mad scramble for a few schools of sterling reputation. In the middle, many students at flagship states schools and solid private colleges have their excellence overlooked. At the bottom end, many students who are capable of getting into more selective schools do not bother. Nor do they realize how much their decisions matter financially, or even how to seek out financial aid successfully. Enter the Obama administration's proposal to create college rankings. Will that help combat the information desert that currently exists?<br />
<div>
<br /></div>
All prospective students, from top to bottom, care about two things: the quality of the education and the affordability. (Let's assume that college reputation is the current concern only because quality is so hard to assess currently. It's a very rare student who would choose something meaningless but prestigious. People always think other people do, however. Everyone likes to think he is the last idealist...) Would the proposed system address those issues?<br />
<br />
<h2>
Obama's college ratings</h2>
<br />
Obama has made a push for college ratings. They will largely eschew measures of quality, as it is so difficult to measure, and focus on <a href="http://www.wsj.com/articles/obama-spells-out-college-ranking-framework-1418965261" target="_blank">graduation rates, affordability, and job prospects</a>. One problem is that the schools that serve minority students, first-generation college students, and working students will by definition have lower graduation rates and unfortunately weaker job prospects. (While individual students might be improving their own prospects substantially, students at these schools as a group have weaker prospects than those for students attending more selective schools - a college degree knocks down some but not all barriers.) These schools may be doing a <a href="http://www.usnews.com/news/articles/2014/12/19/obama-administration-seeks-public-input-on-college-ratings-draft-proposal" target="_blank">good job serving their students but get punished in the ratings</a>, creating perverse incentives to not admit higher-risk students. It is worth including a social mobility score (i.e., SES diversity) in the rankings, which can help ensure colleges are compared to like-schools.<br />
<br />
Graduation rates are relatively simple to compare. Instead of reporting the percentage of students who are done after six years, colleges should report median years until graduation (maybe also the 75th and 90th percentile years until graduation). Schools could be lumped into categories based on social mobility scores (perhaps six categories or so - all the most selective schools would go into one category, by the way) and compared against peer schools. Students could see whether one school is dramatically worse than its peers - maybe indicating that the school puts too little effort into counseling. Or the more mathematically accurate way would be to use a regression. Based on a college's student population demographics, schools could be ranked on the difference between what is the expected from the regression vs. the actual graduation rates.<br />
<br />
What about affordability? First of all, the actual price, not the sticker price, ought to be used, so scholarships and other discounts ought to be factored in, plus the length of time it actually takes to complete the degree, and books. The other complication is boarding. Commuter schools need to be separated into a separate category. However, it is well worth the effort: giving simple prices to students would be a huge help to many first-generation college students! The hard part is that what people really care about is not the total cost of the degree but the cost compared to the expected earnings - so now we are talking about a combined metric. How about time to repay student loans at median earnings? This factors in the actual price of the degree and expected earnings, combining them into a number people can easily process: how long one will spend repaying loans, if the total cost is entirely borrowed. Twenty years repaying loans will be a sobering number for a lot of prospective students.<br />
<br />
How is this data on earnings to be collected? Presumably, the federal government could track this through taxes (I would not trust the colleges too), although there are privacy issues with this tracking. The bigger statistical headache is people who are not working because of illness or injury, marriage, or graduate school. Skipping over these people could distort the earnings data considerably for some schools! This leads us to the other, biggest headache: different majors. Perhaps earnings data should be <a href="http://benschmidt.org/jobs/" target="_blank">broken out by school by major or maybe by professional field</a> people eventually go into: (1) math, computer science, natural science, and engineering; (2) business; (3) education, social work, and counseling; (4) humanities, journalism, and arts; (5) medicine; and (6) law. The school ratings might list years to repay full cost for graduates working in each of those fields. Job satisfaction and ability to find jobs in their desired field could be given a score too. There could be separate but similar questions for students who go to graduate school about whether they are happy with the graduate school they got into.<br />
<br />
<h2>
Social mobility / mission</h2>
<br />
Of course, the social mobility score is necessary to rate schools properly in different categories. And the federal government spends so much money on subsidizing loans, many loans should be going to schools that help students move up in society. It is worth it to report it explicitly. And it is worth reporting explicitly what fields graduates go into. Frankly, it is embarrassing how many <a href="http://www.newrepublic.com/article/121644/elite-universities-are-turning-our-kids-corporate-stooges" target="_blank">Ivy League students go work on Wall Street</a>. (Disclaimer: I went to an Ivy League undergraduate school.) If these students represent the best and the brightest, I would hope to see more in academic research, political leadership, social activism, education, and so on. It is not that surprising, but maybe seeing that fact given an explicit score, on a government webpage, will make some colleges recruit a little harder for people with an activist and not acquisitionist mindset. And it might make some qualified applicants who have no interest in consulting or finance think twice about going to an Ivy League school.<br />
<br />
Of course, the federal government spends so much money on student loan subsidies that it could just decide to <a href="http://www.slate.com/blogs/moneybox/2014/12/09/the_cost_of_making_our_public_colleges_tuition_free_0.html" target="_blank">make every public university free</a>. I think this might have a fascinating effect on the whole system judging from how university systems work in other countries. If the U.S. government changed direction 180 degrees and cut money for loans and grants and simply made public universities free, many highly qualified applicants - especially those from the middle class - would start to pick public universities over selective private schools. I do not believe that Ivy League schools would be hurt much, but other private schools would. They would see the quality of applicants and matriculants especially decline and their reputations suffer, while public universities would see theirs soar. In many countries where public universities are free, private schools have the weaker reputation. In the U.S., the Ivy League schools have so much money and prestige that their position is more or less secure, but flagship public universities and second-tier private schools might swap places in the reputation hierarchy.<br />
<br />
An <a href="http://www.vox.com/2015/9/8/9261531/professor-quitting-job" target="_blank">interesting take from Oliver Lee</a> is to starve the system of money and let the most predatory schools collapse.<br />
<br />
<h2>
Conclusion</h2>
<br />
More or less, colleges have turned their selectivity into their competitive advantage: being hard to get in means their graduates must be desirable employees, and because employers seem to agree, the cycle is only reinforced as the next generation of students apply to elite schools in even greater numbers.<br />
<br />
But basing reputation only selectivity is special kind of insanity. We do it only because education quality is hard to assess. There needs to be external verification to make the system fairer for students at every college, so that smart, hard-working students at any institution can get their due. While standardized tests are not perfect, they do help make college admission a bit fairer. Perhaps a dose of the same kind of medicine would help college graduates. I doubt college graduates will ever face a version of A.P. tests, but there is another option: <a href="http://www.nytimes.com/2011/11/20/business/digital-badges-may-highlight-job-seekers-skills.html" target="_blank">digital learning badges</a>. The idea is simple: any organization can serve as an external validator, certifying discrete skills that can be stacked into broader competencies. The source of the learning - selective college, community college, MOOC, self-taught, on-the-job learning - is irrelevant to the validator. Anyone can review the badge holder's work. If badges were to catch on, of course, graduates of selective schools would do well at acquiring them. But many students from less selective schools would do well, too. <a href="http://www.economist.com/news/briefing/21605899-staid-higher-education-business-about-experience-welcome-earthquake-digital" target="_blank">Maybe even people taking MOOCs would do well</a>. Badges would have a profoundly democratizing, leveling force in college education because they provide a reliable source of data on what a person actually knows and has learned.<br />
<br />
<h2>
Postscript</h2>
<br />
In Dr. Pinker's <a href="http://www.newrepublic.com/article/119321/harvard-ivy-league-should-judge-students-standardized-tests" target="_blank">article</a>, I ran across this perfect description of what a good education should accomplish. My only reservation about badges is that it too many people might seek specific competencies and not a broad education as described below.<br />
<br />
<blockquote class="tr_bq">
It seems to me that educated people should know something about the 13-billion-year prehistory of our species and the basic laws governing the physical and living world, including our bodies and brains. They should grasp the timeline of human history from the dawn of agriculture to the present. They should be exposed to the diversity of human cultures, and the major systems of belief and value with which they have made sense of their lives. They should know about the formative events in human history, including the blunders we can hope not to repeat. They should understand the principles behind democratic governance and the rule of law. They should know how to appreciate works of fiction and art as sources of aesthetic pleasure and as impetuses to reflect on the human condition.<br />
<br />
On top of this knowledge, a liberal education should make certain habits of rationality second nature. Educated people should be able to express complex ideas in clear writing and speech. They should appreciate that objective knowledge is a precious commodity, and know how to distinguish vetted fact from superstition, rumor, and unexamined conventional wisdom. They should know how to reason logically and statistically, avoiding the fallacies and biases to which the untutored human mind is vulnerable. They should think causally rather than magically, and know what it takes to distinguish causation from correlation and coincidence. They should be acutely aware of human fallibility, most notably their own, and appreciate that people who disagree with them are not stupid or evil. Accordingly, they should appreciate the value of trying to change minds by persuasion rather than intimidation or demagoguery.</blockquote>
<br />
More about admissions <a href="http://www.theatlantic.com/education/archive/2016/02/whats-wrong-with-college-admissions/462063/" target="_blank">here</a> and <a href="http://www.theatlantic.com/education/archive/2014/01/why-are-american-colleges-obsessed-with-leadership/283253/" target="_blank">here</a>.Russell Haneshttp://www.blogger.com/profile/13594411930757264086noreply@blogger.com0tag:blogger.com,1999:blog-8734744291040505450.post-54979296478483173662015-05-26T02:25:00.002-07:002015-05-26T02:25:56.065-07:00Two recommendations<a href="https://www.plickers.com/" target="_blank">Plickers</a> is an easy-to-use website/app to do multiple choice review problems in class. All you need is an internet-connected computer, a projector to show the students the questions, and a smartphone with the app. The students hold up answer cards, and you scan their answers with your phone's camera. It works very smoothly!<br />
<br />
Harvey Mudd College's math department puts up <a href="https://www.math.hmc.edu/funfacts/" target="_blank">math fun facts</a>. It is full of really neat stuff! This recommendation was passed on to me by Marc Rios.Russell Haneshttp://www.blogger.com/profile/13594411930757264086noreply@blogger.com0tag:blogger.com,1999:blog-8734744291040505450.post-32882245898886801502015-05-21T18:08:00.003-07:002016-12-06T15:06:35.171-08:00Smartest Kids in the WorldI just finished reading <i><a href="http://www.amazon.com/Smartest-Kids-World-They-That/dp/145165443X/ref=sr_1_1?ie=UTF8&qid=1432255624&sr=8-1&keywords=smartest+kids+in+the+world" target="_blank">The Smartest Kids in the World</a></i> by Amanda Ripley. It's a good book, but the first appendix on how to see if a school is rigorous is absolutely stellar. Here's my quick bullet point summary:<br />
<br />
<br />
<ul>
<li>money and class size are not so important</li>
<li>a lot of technology spending is useless</li>
<li>parents' PTA volunteering not so important; parents reading to kids at home IS important -- Does the school encourage that?</li>
<li>test data doesn't show critical thinking; one should ask the principal how else the school gauges critical thinking</li>
<li>go visit classrooms; don't watch the teacher (charismatic or quiet doesn't matter); watch the students</li>
<li>an "orderly" classroom is not important</li>
<li>all the students should be paying attention and working hard; boredom and inactivity is a bad sign; if the kids really pay attention to you the observer, that's a bad sign</li>
<li>if students are breezing through exercises, they aren't being challenged</li>
<li>students should be uncomfortable sometimes (difficult thinking work required), but not despairing; helped when they need it, by the teacher or by classmates</li>
<li>not a lot of down time; there's a real sense of urgency in classrooms and between classes</li>
<li>ask the students: 1) What are you doing right now? Why? 2) Do you learn a lot every day? 3) Do your classmates behave? 4) Do you stay busy or waste time in this class? 5) If you don't understand something, what do you do? Students in rigorous schools will have good answers to each question. Many of these were key predictor questions from the Gates Foundation survey.</li>
<li>ask the principal whether he or she gets to see sample lessons before hiring teachers and gets to observe teachers often</li>
<li>ask teachers whether they have the time to watch each other</li>
</ul>
<br />
It's a fantastic list! Here's an <a href="http://www.nytimes.com/2016/12/06/upshot/what-america-can-learn-about-smart-schools-in-other-countries.html" target="_blank">updated version</a> from the same author:<br />
<br /><blockquote class="tr_bq">
Generally speaking, the smartest countries tend to be those that have acted to make teaching more prestigious and selective; directed more resources to their neediest children; enrolled most children in high-quality preschools; helped schools establish cultures of constant improvement; and applied rigorous, consistent standards across all classrooms.<br />Of all those lessons learned, the United States has employed only one at scale: A majority of states recently adopted more consistent and challenging learning goals, known as the Common Core State Standards, for reading and math. These standards were in place for only a year in many states, so Mr. Schleicher did not expect them to boost America’s PISA scores just yet. (In addition, America’s PISA sample included students living in states that have declined to adopt the new standards altogether.)<br />But Mr. Schleicher urges Americans to work on the other lessons learned — and to keep the faith in their new standards. "I'm confident the Common Core is going to have a long-term impact," he said. "Patience may be the biggest challenge."</blockquote>
Russell Haneshttp://www.blogger.com/profile/13594411930757264086noreply@blogger.com0tag:blogger.com,1999:blog-8734744291040505450.post-52913916771723329352015-05-16T05:28:00.000-07:002015-07-04T04:50:47.778-07:00The "How to" of DebateI decided to make the e-version of my introductory debate textbook free. It's an appropriate guide for middle schoolers or high schoolers.<br />
<br />
To download <i>The "How to" of Debate</i> in kindle format, for free, click <a href="https://drive.google.com/file/d/0B_ruCWmORVX2aFRTWTZheVdCT2c/view?usp=sharing" target="_blank">here</a>. (By the way, the easiest way I know to get an ebook onto any kindle device is to download it to your computer, then email it to your kindle's special email address. Look on Amazon, in your account info, for "manage content and devices." Then go to Settings, and the email address for your kindle device should be under "Personal Document Settings." Make sure your kindle device is enabled to receive emails from your personal email address, then you are ready to go! Just email it to yourself, and a few minutes later, it will sync onto your kindle device. This is much easier than trying to figure out where your device stores kindle files.)<br />
<br />
For the paperback version of <i>The "How to" of Debate</i>, click <a href="http://www.lulu.com/spotlight/coach_hanes" target="_blank">here</a> (still $15.95).Russell Haneshttp://www.blogger.com/profile/13594411930757264086noreply@blogger.com0tag:blogger.com,1999:blog-8734744291040505450.post-2957222252676649122015-05-12T18:08:00.000-07:002015-05-12T18:19:06.985-07:00Why are there no more dinosaurs?This is one of my favorite geometry problems, involving volume and proportional reasoning.<br />
<br />
The answer is: there was about 1.6 times as much oxygen in the air.<br />
<br />
<div style="-x-system-font: none; display: block; font-family: Helvetica,Arial,Sans-serif; font-size-adjust: none; font-size: 14px; font-stretch: normal; font-style: normal; font-variant: normal; font-weight: normal; line-height: normal; margin: 12px auto 6px auto;">
<a href="https://www.scribd.com/doc/265135248/Why-Are-There-No-More-Dinosaurs" style="text-decoration: underline;" title="View Why Are There No More Dinosaurs on Scribd">Why Are There No More Dinosaurs</a></div>
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Russell Haneshttp://www.blogger.com/profile/13594411930757264086noreply@blogger.com0tag:blogger.com,1999:blog-8734744291040505450.post-55220179148694509892015-04-10T02:57:00.000-07:002019-03-23T15:00:10.448-07:00Presidential primariesThere are a lot of ways we could alter with the U.S. government to improve it:<br />
<br />
<ul>
<li><a href="http://art-of-logic.blogspot.tw/2012/02/proportional-representation.html" target="_blank">proportionally elect</a> the U.S. House;</li>
<li><a href="http://www.slate.com/articles/news_and_politics/books/2015/04/ian_millhiser_s_expos_of_the_supreme_court_injustices_reviewed.html" target="_blank">end the constitutional review powers</a> of the U.S. Supreme Court;</li>
<li>give the U.S. House and Senate different, separate jobs (one obvious split is to give the House domestic powers and the Senate foreign affairs powers; another split is to give the House budget-only powers and the Senate lawmaking powers);</li>
<li>stop electing the President and go to a parliamentary-style selection of a prime minister;</li>
<li>create a separate branch of government out of the Federal Elections Commission and actually give it real teeth to enforce election laws nationally;</li>
<li>put all federal elections (House, Senate, and President) on a four-year cycle, doing away with the midterm slump.</li>
</ul>
<br />
But an easy-to-make reform I have thought about is to improve the presidential primary processes. One problem is that states want to be first, or failing that, as early as possible. This is for each state to maximize its own influence, but this creates an "arms race" among the states. There needs to be a national, coordinated solution that gives each state a fairly equal chance to each state to have a maximum impact.<br />
<br />
One possibility is to draw states at random. Two states go every week for a 25-week process - about as long as the current six- to seven-month-long primary system. This is fair, but the only problem is that California or other big states could come early. The smaller contests really ought to come first. The small contests allow for a wide field and enable less-well-funded candidates to gain exposure. Some unheard of candidates might do well and attract support and funding and be ready to move on to bigger contests. But candidates who could not finish in the top half of smaller contests run out of chances and are eliminated. Allowing large contests at the beginning would be a prohibitive barrier for all but the most well-known, well-funded candidates.<br />
<br />
My idea is to organize primaries into ten slots, each separated by three weeks. This 30-week process would start in January and finish in July, just before August conventions. The sensible thing would be to order the primaries into ever-larger blocks, so that the smallest contests are first and the largest contests come last. Here's one schedule I made up: 5, 6, 9, 13, 20, 31, 49, 78, 125, and 202. There could be a drawing of states every presidential election, and each state could be assigned in order to the earliest slot that is still available. For the first nine slots, the numbers are caps. If a state would push the number over the cap, it must go into a later slot. The last slot does not have a cap, so any state that cannot go in the first nine slots goes in the final slot.<br />
<br />
Big states can only go at the end by definition. California can only go in slot 8, 9, or 10. However, California would rather get a good lottery number and go in slot 8 (when it would dominate the candidates' attention for three weeks) than in slot 10 (when it would be only 55 out of about 202 votes and be a much smaller part of the candidates' attention). Small states with good lottery numbers that year will go early and will dominate the conversation. It is bad luck for small states that get a bad number; they will be ignored in a big vote slot. It is clear that the large states have less variation in "dominance" than the small states do. But how much less? Are small states better off, on average, under this arrangement? This calls for a simulation. I ran 200 trials. Here are the results.<br />
<br />
<div class="separator" style="clear: both; text-align: center;">
<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgnKxtcSOOnLuKe7PPYwsqCDbkVnAPF9YbgxaFNgPKOUC-BUz4mNIwmmScqHXotLb2t68D5atBq8ijks9rjijqqddAhRDJjmSTY2e-6Aj2dBElhUpDSPZ9Iu4EkEg3xlCAQViKVMatLaZtc/s1600/results.tiff" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" height="604" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgnKxtcSOOnLuKe7PPYwsqCDbkVnAPF9YbgxaFNgPKOUC-BUz4mNIwmmScqHXotLb2t68D5atBq8ijks9rjijqqddAhRDJjmSTY2e-6Aj2dBElhUpDSPZ9Iu4EkEg3xlCAQViKVMatLaZtc/s1600/results.tiff" width="640" /></a></div>
<br />
The average dominance is just under 20%, meaning that each state represents, on average, 20% of the Electoral College votes available in the given slot. But notice how even the small states have, at times, 100% dominance of the slot. Notice how the small states, mid-size states, and even some of the larger states have averages that are right around 20%. It is only the very biggest states -- Florida, New York, Texas, and California -- for which average dominance of their slots is above 20%. One could play around with the numbers a bit. For example, dropping slot 7 to a 48 would depress Florida's and New York's slightly too high chances a little (no longer could they share the slot if a 20 EV state got there first, so their odds would be slightly lower for this outcome). But my first attempt represents quite a substantial flattening out; each state has a reasonable chance of influencing the selection of the presidential candidates.<br />
<br />
Otherwise, the problems just <a href="http://www.nytimes.com/interactive/2015/09/22/upshot/how-states-jockey-for-position-in-presidential-primaries.html" target="_blank">continue</a>.<br />
<br />
<b>UPDATE, March 23, 2019:</b> This <a href="https://fivethirtyeight.com/features/what-if-early-democratic-primary-states-looked-more-like-the-party/" target="_blank">article</a> in fivethirtyeight takes a very different approach to re-ordering the primaries: they look at how similar a state's electorate was to the national Democratic electorate as a whole, then put the most similar states first. Of course, this would require (probably) that Democratic and Republican primaries go in a different order. There's a downside in that you can't get cross-over primary voters. But fivethirtyeight's analysis exposes definite problem with my proposal--none of the small states are especially representative of the nation as a whole.<br />
<br />
I have two responses, but neither of them is completely satisfying. First: we can hope that clusters of small states can be, on average, more representative. Iowa and New Hampshire might be too white, and South Carolina more African American, than the nation as a whole, but the average of the three together is closer to the national average. True, but not perfectly close. The average of these three states in particular is still far less representative than Illinois of the national Democratic electorate. And if we want to try to randomize the selection of small states, then there are many combinations that are even less representative on average. Fundamentally, a "small states first" rule must involve some trade-off with a "most representative first" rule.<br />
<br />
Second: maybe we're not so concerned that the initial states are representative. After all, I am making the case that the early states purpose is to keep costs low (by being a small state with cheap media markets) so the barrier to running for President is negligible AND then to narrow down the field by eliminating non-viable candidates. The low-performing candidates drop out, not because of money, but because they can't win votes; the high-performing candidates gain new enthusiasm and fundraising when they win early states. The real question is whether we think low-performing candidates can't win votes because they're just bad candidates--or because the early states' demographics tilt the playing field against them. The reality is probably a mix of the two effects, but I lean toward the "bad candidates" explanation. Yet I can't rule out the biasing effect either. There's no doubt that early states lean toward rural populations.<br />
<br />
Perhaps the best solution is to pair or triple states up so as to "average" out to national demographics: e.g., Massachusetts and Mississippi. The randomly draw out the 25 pairs (or sixteen triples and one pair), using the same sort of ordering method I discuss above. I'm not sure which combinations would be made, so I'm not sure how few electoral votes the smallest pair would have, or how many electoral votes the largest pair would have. But perhaps it would work.Russell Haneshttp://www.blogger.com/profile/13594411930757264086noreply@blogger.com0tag:blogger.com,1999:blog-8734744291040505450.post-9381023983591251082015-01-24T21:44:00.000-08:002015-01-24T21:44:19.778-08:00What a statistical analysis tells youWarren Sharp provided an intriguing <a href="http://www.slate.com/articles/sports/sports_nut/2015/01/ballghazi_the_new_england_patriots_lose_an_insanely_low_number_of_fumbles.html" target="_blank">analysis</a> on the ratio of plays to fumbles for all N.F.L. teams. The short version of the result is, no matter which specific statistic one looks at, the New England Patriots are clear and exceptional outliers. The Patriots don't fumble the ball nearly as often as other teams do. The Patriots fumbles are especially low compared to other outdoor teams.<br />
<br />
A specific probability figure is quoted: for the last five years of data, assuming offensive plays to fumbles follows the Normal distribution, the probability of the Patriots amassed such a record by chance would occur "once in 16,233.77 instances." In other words, it's very, very unlikely. So, does this constitute proof the Patriots cheated?<br />
<br />
There are two assumptions that are important to understand: that plays per fumble follows a Normal distribution (a bell curve), and that the Patriots were an average team.<br />
<br />
The first assumption is a fairly standard one, but there's not really enough evidence presented in the article to know whether or not it's true. The graphs presented do look like bell curve, but I would like to see a lot more data. In fact, many distributions look quite similar to the Normal distribution but are different enough to make a big difference in calculating the probability of unusual events. In other words, one in 16,233.77 might be significantly higher or lower than it should be if the distribution is not Normal.<br />
<br />
The second assumption is of a different sort. It is part of the hypothesis being tested. "If the Patriots are an average team, how likely would they have this unusual statistic just by chance?" An average team could get a whole lot of lucky breaks, but as the analysis showed, it would be very unusual. If, on the other hand, the Patriots are an above-average team, then they would be much likelier to have an unusual fumble statistic. Perhaps they are so good at avoiding fumbles that there's only a 1 in 20 chance of them accumulating such an unusual statistic -- the statistic is so unusual that even a good team still needs to get several lucky breaks to accumulate it. There still might be an element of luck, but at a more believable level.<br />
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As Mr. Sharp clearly acknowledges:<br />
<br /><blockquote class="tr_bq">
Could the Patriots be so good that they just defy the numbers? As my friend theorized: Perhaps they’ve invented a revolutionary in-house way to protect the ball, or perhaps they’ve intentionally stocked their skill positions with players who don’t have a propensity to fumble. Or perhaps, still, they call plays that intentionally result in a lower percentage of fumbles. Or maybe it’s just that they play with deflated footballs on offense. It could be any combination of the above.</blockquote>
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This is exactly right. One in 16,233.77 should be understood to be the probability an average team would have this fumble statistic by chance. It indicates the Patriots were either an above-average team in ball protection or deflating balls or both. The statistic really just helps us rule out chance. We know that it really isn't just a matter of good luck. But it tells us nothing about the mixture of causes.</div>
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The best analogy I can think of is a grand jury versus a petit jury. The statistic alerts us that something unusual has gone on. We have evidence that says, "Proceed with an investigation." But the statistic doesn't enable us to tell what flavor of unusual it is, whether it is simply great playing or it is cheating. Only a more detailed analysis and investigation will tell.</div>
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On the other hand, I can easily imagine other teams deflate balls and will never be caught by this sort of statistical analysis. How? If a team has below-average ball protection and the team starts to cheat by deflating balls, its efforts will bring it back to the average. Its results will not look unusual at all. This kind of statistical analysis will only pick up on cheating that pushes a team far above the norm.</div>
Russell Haneshttp://www.blogger.com/profile/13594411930757264086noreply@blogger.com0tag:blogger.com,1999:blog-8734744291040505450.post-51720879624501559212015-01-04T06:37:00.000-08:002017-04-30T17:46:38.715-07:00100th Post!!My hundredth post! When I started 5 and a half years ago, I never imagined I would get here. It turns out that I have written a post, on average, every 20 days. I thought for this special occasion, I would go back to one of my original reasons for starting this blog: my dislike for the traditional methods of power matching in debate tournaments. My opinion was -- and still is -- that power matching doesn't give each debate team a fair experience at the tournament. Many debate teams make it to elimination rounds <a href="http://art-of-logic.blogspot.tw/2009/03/debate-tournament-math.html" target="_blank">without facing good opponents</a>. My solution was to create a <a href="http://art-of-logic.blogspot.tw/2009/08/another-way-to-visualize-strength-of.html" target="_blank">strength-of-schedule pairing</a> that power-matched but also attempted to even out schedule strength. That was five years ago. Since that time, I have come to believe that it's <a href="http://art-of-logic.blogspot.tw/2012/07/meta-debate-tournament-tabulation-post.html" target="_blank">better to abandon power matching</a> rather than try to improve it. The alternative is random prelims. Random prelims works for the N.S.D.A. Nationals (formerly the N.F.L.) and can even be <a href="http://art-of-logic.blogspot.tw/2011/08/modest-proposal-to-ensure-geographic.html" target="_blank">improved with geographic mixing</a>.<br />
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I decided to test it out with an experiment. How do different pairing methods compare at producing the actual ranking of the teams? Obviously, one only has actual rankings in an experiment. To start, I generated 200 random teams, giving each one a true strength. The true strengths were in a Normal distribution with an average of 27 points and standard deviation of 1 point. This is realistic, based on <a href="http://art-of-logic.blogspot.tw/2012/07/probability-of-upsets.html" target="_blank">previous empirical analysis</a> I've done. Next, I paired the teams against each other using one of four pairing methods. Each team's performance could deviate from its true strength by a random number that followed a Normal distribution, average of 0, standard deviation of 1 point. In other words, most teams would perform within +/- 1 point of their true strength about 68% of the time. This may seem like a lot but is realistic from the same empirical analysis. This deviation in performance accounts for off-rounds, surprise strategies, and judging variability (e.g., point trolls), too.<br />
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Based on the two team's strengths and factoring in their random deviations from their true strengths, I decreed a winner. Then I set up the next round using the stated pairing method. After all six rounds, I calculated each team's win/loss record, total speaker points, and median speaker points (more on this in a moment). I ran the same tournament four times, one for each pairing method: (1) simple random, (2) random within win/loss bracket, (3) high-high power matched, and (4) high-low power matched. I used the same round 1 pairing for all four methods to give them all even starting conditions. For each one of the methods, I used the results at the end to calculate a traditional ranking (win/loss, then total speaker points, then median speaker points) from 1 to 200 and also a "median points" ranking (first, median speaker points, then total speaker points, then win/loss record) from 1 to 200 -- and compared them to the true rankings. The results kind of blew my mind and switched my perspective around.<br />
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A few caveats for the nit-pickers: yes, I ignored low-point wins. Those aren't too frequent and, as you will see, including them would only make my case stronger. And yes, I ignored side constraints and I pretended like the teams were from 200 different schools. Again, using those constraints would only strengthen my case. Without further ado, here are the results:<br />
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<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEiX_xBgGjCzS3oxKPvwsyXfFLR_rFpy1h3Wg7lMfjaX7ZPQXgSUZL6E6QUyysT3PQXMFn10ZrKP8oqGUJxBc0u4sH5d41kbpgwQIW-ZF7Gn_HHhDLm2yhSKTMO6O1b7FSRLUJKzPPxNX69K/s1600/img1.tiff" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" height="115" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEiX_xBgGjCzS3oxKPvwsyXfFLR_rFpy1h3Wg7lMfjaX7ZPQXgSUZL6E6QUyysT3PQXMFn10ZrKP8oqGUJxBc0u4sH5d41kbpgwQIW-ZF7Gn_HHhDLm2yhSKTMO6O1b7FSRLUJKzPPxNX69K/s1600/img1.tiff" width="400" /></a></div>
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This is the r-squared, the coefficient of determination you might have learned about in Intro to Stats, of the traditional and median points rankings to the actual ranking for each pairing method I tested out. A high r-squared is good; it means the listed ranking closely corresponds to the truth.<br />
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A couple of things to draw your attention to: (a) the median points rankings do not change much for any pairing method; (b) the median points rankings are higher than or almost equal to the traditional rankings for every pairing method; and (c) the traditional rankings are closest to true rankings for the high-low pairing, then the random within brackets pairing, then the simple random pairing, and lastly the high-high pairings.<br />
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It is actually worth looking at that last one:<br />
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<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEifYKUM5TRuP-UHzTBsGLIA-jTniLQ0m2r6EmzKxyGxZifnBseXSl5CQvOOJYegjNGccAARobVtAVL013MaR4dz2FyKlfCtx4fmzASmeL7XvI7n4_T1Ewv5fNvtXnvDXttE2yir9jgnwudT/s1600/img2.tiff" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" height="308" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEifYKUM5TRuP-UHzTBsGLIA-jTniLQ0m2r6EmzKxyGxZifnBseXSl5CQvOOJYegjNGccAARobVtAVL013MaR4dz2FyKlfCtx4fmzASmeL7XvI7n4_T1Ewv5fNvtXnvDXttE2yir9jgnwudT/s1600/img2.tiff" width="400" /></a></div>
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Notice the clear pattern? In a high-high pairing, a ton of decent teams get screwed by getting several very hard opponents and therefore have terrible records -- these are the outliers that are very low on the y-axis (indicating true strength) but on the right side of the x-axis (indicating very poor records). Notice the one team in the far bottom right: pity the poor team that had true ranking of 19 but ended up with a 1-5 record and ranked 183rd by the traditional tiebreakers. Enragingly, a lot of weak teams somehow squeak by to great records. Notice the one team in the upper left: 148th in truth, but given several easy opponents, ending up 5-1 and ranked 21st by the traditional tiebreakers. Visually, you can see how unjust the whole high-high pairing is when coupled with using win/loss record as the primary criterion for ranking, as it is in the traditional method. The median points ranking does not suffer from the same problem; even the good team that gets several tough opponents and ends up 1-5 is not penalized in the rankings, as long as that team continued to earn high points in each one of its rounds.<br />
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For comparison, here is what the best correlation looked like:<br />
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<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgxJtfpN4LcYFE3kjPhni9vB03GWxypthfTKGhIUmHQ0Y8U3ANqEGvxbqjK3tEozhWQxn6iIPH8YrZ3yRtnEfjEkRhtFZ48PGDpIc7gdCGhgywGv8z4cnoVNuUFCXazTSEN7VWf7wj3vis4/s1600/img3.tiff" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" height="310" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgxJtfpN4LcYFE3kjPhni9vB03GWxypthfTKGhIUmHQ0Y8U3ANqEGvxbqjK3tEozhWQxn6iIPH8YrZ3yRtnEfjEkRhtFZ48PGDpIc7gdCGhgywGv8z4cnoVNuUFCXazTSEN7VWf7wj3vis4/s1600/img3.tiff" width="400" /></a></div>
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To be sure, the correlation is far from perfect. But that's just about variability in the teams' in-round performances compared to their true strengths (that random deviation score I added). In other words, what you are looking at is just the off-days, surprises, and crappy judging that is unavoidable. It isn't really possible to do better than about 0.82 or 0.83 -- that's why the median rankings have about the same correlation, no matter what the pairing method.<br />
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On the other hand, the traditional rankings are <i><b>very</b></i> sensitive to the pairing method. Why? A team's record depends on both its true strength and the opponents it faces! In the high-high pairing method, many teams get unfairly hard or unfairly easy opponents. The method drives down the correlation between true strength and record by screwing some and blessing others. However, in the high-low pairing method, the assignment of opponents pushes up the correlation between true strength and record -- better teams face weaker opponents, so get a few more easy wins.<br />
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It can be a bit hard to interpret what these correlations means, so I also calculated the mean absolute deviations for each pairing method and ranking. For each team, I took its traditional rank and its true rank, found the difference, and took the absolute value. Then I averaged those to produce the mean absolute deviation (MAD). I also did the same thing for the median points rankings.<br />
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For example, for the random within bracket pairing method, the median points ranking had a MAD of 18.66. That means, on average, the median ranking was off by 18.66 places from the truth. The lower the MAD, the better.<br />
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The exact same patterns appear as in the correlations table. In general, the best we can hope for is to be within about 20 places of the truth. Given that debaters have off-rounds, and that our sample size is only six rounds, this isn't terrible: 20/200 is 10%. The true ranking is probably +/- decile from the median points ranking. Notice that the traditional rankings are sensitive to the pairing method in the exact same pattern. If one uses the traditional criteria for ranking, then the high-low pairing is best. So, was I wrong five years ago?<br />
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In both of the two tables I've given so far, the high-low pairing method plus traditional ranking was <i><b>marginally</b></i> superior to <i><b>any</b></i> pairing method plus median points ranking. But the problem is that it is not equally important to rank any team correctly. It is more important to get the top teams right. Enter the <a href="http://www.amazon.com/Whos-1-Science-Rating-Ranking/dp/0691154228/ref=sr_1_1?ie=UTF8&qid=1420378418&sr=8-1&keywords=who%27s+number+1" target="_blank">weighted rule</a>. As I did for the MAD, I took each team's traditional rank, subtracted its true rank, and took the absolute value. But before I averaged, I divided by the team's true rank. Thus, getting a good team's results wrong by a lot was worth big negative points; getting a weak team's results by a lot was worth a few negative points. The results:<br />
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The pattern is almost the same as before, except that... high-low pairings and traditional rankings is worse (higher score) than random pairings with median rankings. This means that the high-low plus traditional combination made more mistakes ranking the best teams than the random plus median combination.<br />
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<h3>
What are the take-aways?</h3>
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1. If you are doing high-high power matching, <i><b>STOP IT RIGHT NOW</b></i>. Even one round of high-high power matching is harmful. You are screwing many teams over.<br />
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2. <i>Consider using the median points ranking instead of the traditional ranking.</i><br />
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On T.R.P.C., it means putting the "drop two high - drop two low speaker points" as the <u>first</u> criterion for ranking. (For a three- or four-round tournament, the "drop high - drop low" option is equivalent to the median. For a five- or six-round tournament, the double-drop option is equivalent to the median. For a seven- or eight-round tournament, the triple-drop option is equivalent to the median.) You can make win/loss record the second or third criterion.<br />
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All the data from my experiment show that the median ranking is simply more accurate, no matter how you pair the tournament. The win/loss record is too variable.<br />
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3. <i>Consider not doing high-low power matching either.</i><br />
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It is enormously time intensive to run a power-matched tournament. In some cases, power-matching adds 2-3 hours for a six-round tournament: 30-45 minutes after rounds 2, 3, 4, and 5 -- although one or two or those lag times might occur during a food break that had to happen anyway. But 2-3 hours might be used in other ways... say, to squeeze in an extra round. Another round would, in fact, yield more data and would improve the accuracy of the results far more than stopping frequently to power match. And, as the experiment data show, high-low pairings do not improve the accuracy any more than simply switching over to median rankings. (Furthermore, I suspect that high-low pairings plus traditional rankings' accuracy peaks at around five to six preliminary rounds; my suspicion is that for longer tournaments, the accuracy starts to go down again because the brackets start to get too small.)<br />
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High-low power matching does have something to argue for it: teams get to see more opponents of similar ability levels (to themselves). But there's a counterargument: random pairings enable teams to see a wide cross-section of opponents' skill levels, and better gauge where they fall on the spectrum. Getting your butt kicked can inspire striving, and besides, your tournament should have a novice and JV division for teams that are afraid of the best opponents in the top division.<br />
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However, if you feel like high-low power matching is something you want to preserve but you do want to speed up your tournament, then go to lag-powering. For example, round 3 would be power matched, but only off of the results of round 1. You can slip round 3 pairings under the doors while round 2 is wrapping up, cutting your turnaround time drastically. You probably won't push down your accuracy too much (see how well random within brackets plus traditional rankings compares) if you lag-power -- but especially not if you use median points rankings.<br />
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4. <i>Do everything you can to help your judges give speaker points more consistently.</i><br />
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If speaker points are more accurate than records, that means we ought to put more weight on speaker points AND strive to make them seem less arbitrary. Brief training sessions at the beginning of the tournament for less experienced judges, clearly delineated rubrics for speaker points, or scoring grids for various attributes of speaking all help!<br />
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<h3>
A changed perspective</h3>
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I used to think that <a href="http://art-of-logic.blogspot.tw/2011/02/lock-in.html" target="_blank">power matching started</a> as the best way people had, when tabbing on notecards, to improve the accuracy of tournament results. Maybe that is why it got started, but as we can see, all it does is bring accuracy to parity with median rankings. Is there any other reason tabbers might have started to use power matching?<br />
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Then it dawned on me: power matching reduces the likelihood that two teams have met before will be randomly drawn against each other in later rounds. Team A might meet team B in round 1, win, then lose round 2. Team B might do the opposite and win round 2, giving the two opponents a possibility of being randomly drawn against each other for round 3 -- but overall, power matching makes it less likely than simply randomly assigning everyone in one big pool. When you're tabbing on notecards, it speeds things up considerably if this is a rare occurrence. Maybe power matching began, not with HH or HL but with the random within brackets pairing. In other words, how we pair double elimination tournaments (undefeateds and down-ones in two separate brackets, randomly assigned in each) might have gotten translated to all preliminary rounds at all tournaments.<br />
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Just a suspicion. It does make sense: high-low (or the awful high-high) brackets are hard to do on notecards, but random within brackets is easy to do.Russell Haneshttp://www.blogger.com/profile/13594411930757264086noreply@blogger.com0