Friday, November 19, 2021

Judge intervention

"[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,

What is judge intervention?

Let's start out first by explaining what judge intervention is NOT:

- Judge intervention is not when a judge prefers your opponents' argument to yours. This is, ya know, "judging."

- Judge intervention is not when a judge ridicules your argument. This is rude, but that's about all it is.

- 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.

- 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.

- 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.

- 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.

- 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.

- 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.

- 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.

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.

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.

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:

Team A: "X is a fact" [no evidence provided]

Team B: "X is not a fact" [no evidence provided]

Judge: "… fudge you all"

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:

Team A: "The sky is green" [no evidence provided]

Team B: "…"

Judge: "Come on, team B!"

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 Archer, "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.

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:

Claim: your argument

Evidence: your supporting facts or expert opinion

Warrant: the logical connection between evidence and claim

Relevance: the meaning of your claim to the debate

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…

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.

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.

A judge might believe everything about your argument but simply not get why you believe it's relevant to the debate.

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.

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.

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.

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.

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.

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.

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.

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.

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.

Wednesday, November 3, 2021

Repairing the Senate

It 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.

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.

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.

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.

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.

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.

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.

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.

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.

Sunday, March 24, 2019

Scheduled elimination tournament calculator

Single-elimination 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 majority 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.

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.

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?

Double-elimination 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?

My proposed solution is the scheduled-elimination tournament. The plan is quite simple:
  1. Do not eliminate teams that are undefeated.
  2. You must eliminate teams that are twice-defeated.
  3. Decide which once-defeated teams to keep based on speaker points or preliminary seed.
  4. Always keep an even number of teams.
  5. 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!)
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 eligible 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.

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.

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.

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:

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 two teams that are once-defeated (after rounds 2 and 3), this method eliminates having the partial elimination round where twelve teams sit around pointlessly, and it has made managing the judging pool much, much 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.

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:

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.)

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.

I think I would add one other condition to a scheduled-elimination tournament, for a total of six. Condition #6 is: "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.

I've made the applet available for you to use here: 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.

* Fun addendum: 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.

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, 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!

Thursday, March 21, 2019

Daylight Savings Time

Why 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.

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:

The solid line in the center is both solar and clock noon.

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.

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?

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.

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.

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.

To sum up, if people were to decide this rationally based on latitude alone:

Equator - standard time all year
Mid-latitude - standard time in winter, one or two hour later shift in summer
Arctic circle - standard time all year

Wednesday, December 12, 2018

Tabulation software

Hi all,

I've been thinking about how to run tournaments for many years and publishing articles on it. My published ideas have ranged from geographic mixing, logit scores, and new methods for strength-of-schedule pairing and constrained side equalization assignment.

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.

Tuesday, August 7, 2018

Approval voting and primaries

California 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 article for a description of the problem.

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:

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).

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).

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.

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.

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.

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 graph of presidential approval ratings. 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.

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.

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.

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:

My candidate - 51%
Opposition candidate I hate - 49%
Opposition candidate I would prefer - 49%

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:

My candidate - 49%
Opposition candidate I hate - 51%
Opposition candidate I would prefer - 49%

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.)

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.

Friday, July 27, 2018

Random matching in debate tournaments

Every debater knows the predicted number of teams with each record when power-matching is used:

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.

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.

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.

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.

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.

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.

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:

If the upset rate is a more realistic, empirically justified 20%, then the outcomes are much flattened and nearly equally distributed:

Here's the sheet for anyone who'd like to play around with it.