teaching different ethical philosophies

The U.S. Constitution was in many ways modeled on the Roman republic, and perhaps our founders' goal, like Rome's goal, was to create a government that blended monarchical, aristocratic, and democratic elements. In our federal government, the Presidency is supposed to represent the monarchical, the Senate the aristocratic, and the House of Representatives the democratic elements.

It occurred to me recently that whether this bit of historical speculation is true, the three branches of the U.S. federal government provide a real-world example of the three main kinds of ethical philosophies in action. Congress generally works on some kind of utilitarian basis, although examples abound to the contrary. However, the general logic of institution is to weigh competing interests and find compromises that benefit the greatest number (and thus get majority support). The Presidency, as an institution, must be grounded in a virtue-based ethical philosophy. The Presidency was set up to deal with crises needing immediate action and unitary leadership: economic panics, wars, natural disasters, etc. Exigent and unique circumstances impede the President from using a deliberative, majoritarian process and also from using a process where he or she strictly follows a predetermined set of rules of ethical actions. We're left to hope that the President acts in good faith.

This leaves the judicial branch. The Supreme Court and the appellate courts operate on a kind of deontological basis. Granted, they're not Kantians. But the role of Constitutional interpretation involves a very similar kind of reasoning: the justices start with a first principle (the Constitution, rather than the categorical imperative); they apply this principle to real-world dilemmas by a hierarchy of values (whether the commerce clause or states' rights is more important) and distinctions (whether there is a difference between a tax penalty for not buying insurance and other taxes). The question of a limiting principle would make immediate sense to Kant, who seems to have struggled with limits on truth-telling, for example. It makes sense that the judicial branch would be filled with a kind of deontologist (Constitutional deontologists?), given that the primary purposes of the courts are justice (due process and due punishment) and, more broadly, justice (whether the laws themselves are just).

Using the branches of government as a model for kinds of ethical philosophies gives students something to latch onto. It gives the students a rough empirical basis for imagining the different thought processes and considerations that occur within each ethical philosophy: "Oh, just like Congress weighs the needs of Texas against those of all Americans." It especially helps them understand deonotology as an absolutist, first-principle-based philosophy, even though the first principle is different. The most important benefit of using the branches of government as a model is that students realize that an ethical philosophy is a framework, not a script. Just as Congress disagrees, so do utilitarians.

Weighted wins 2

I've been interested in using weighted wins as a statistic for a while. The idea is that by considering the strength of an opponent, an algorithm could handicap the results: a win against a good opponent counts for more than a win against a middling opponent. Of course, the algorithm has to base the calculation of how good an opponent is on how well it did against its opponents, so the algorithm must be based on the whole set of results (I looked at a debate tournament and an N.F.L. season). The process can continue infinitely, although usually, after a couple times, things settle down and the handicapping doesn't change much upon further iterations.

One assumption that this depends on is that a team has an invariant strength. Clearly, this is suspect for debate (differing strengths on the affirmative and negative sides) and the other N.F.L. (the defense and offense are, literally, two different teams). Is it possible to use the same idea but adapt it to recognize the split-strengths?

I input total offensive yards from each 2011 N.F.L. game. A lot of yards against a weak defense is good; a lot of yard against a strong offense is better. By using only this information -- offensive yards for each team vs. each opponent -- a few matrix operations yielded a weighted offensive yards statistic and a defensive strength score for each team's offense and defense, respectively:

For example, against the "average" defense, the Saints would have earned 460 yards. The Steelers defense would have cut that to 82%, to 377 yards. Or so say these statistics. They never actually played.

How well did these statistics work? Well, as predictions, terribly. But, compared to reputable sports statisticians, fairly well. This is a comparison of my rank versus football outsiders rank (before the playoffs began) [offense on left, defense on right]:

On offensive, the difference was on average 3 ranks. On defense, the difference was on average 5.3 ranks. So, the rankings I generated from nothing other than actual yards in regular season games compared moderately closely to the ranks based on a complex calculation they call the DVOA (Defense-adjusted Value Over Average).

The same idea would work for debate tournaments: affirmative strength and negative strength could be treated as two separate variables for each team.

The free market is not the free market

What I find most difficult about teaching utilitarianism to students is that they conflate it with a cost-benefit analysis. It is an understandable mistake; in each, one aggregates many different kinds of effects, puts them into one unit, and measures the total outcome. Students have trouble understanding happiness as a unit of measure. Dollars seem so much more real. I like to discuss with them how some kinds of effects are put in dollar terms: for example, the value of people's enjoyment of a neighborhood park. Either we ignore that benefit, or we come up with somewhat contrived measures, such as the increase in property values around the park as a reflection of how much money it is worth. Isn't happiness generally what is being measured?

The other notion that seems clear in their minds before the discussion begins is that CBA entails certain outcomes. Most students do not believe that parks, regulations, or investment would survive a CBA. They take CBA to be a kind of corporate logic: cut wages, cut investment, do anything to boost sales, and so on. Given the political and economic environment today, this is a reasonable association to have, that a CBA is about the short term, narrow interests, and the bottom line. But students need to be coaxed into thinking about whether a CBA can focused on the long term and inclusive of broad effects. And then they can also be guided into a discussion about whether a metric other than dollars can be used before it is worth it to introduce utilitarianism. As with most ideas, I find that it is better to confront preconceptions first and introduce the new idea after we have aired out prior notions. The teacher has to dislodge the profit-seeking logic of corporations before moving onto the "hedonic calculus" of governments.

In the same category of ideas that are difficult for students to understand separately from current context is the free market. Ask a student to describe the free market; you will get a description of the current economic environment: corporations that dominate the economic landscape, and to a lesser extent, the political landscape; globalization; and perhaps a mention of consumer choice or absent consumer protections. Here is a good question to start: What role does the government have in creating, nurturing, and protecting corporations? I believe most students think about the free market as an absence of government regulation but assume that corporations are "natural" and will exist and function just fine without any government intervention. So, I try to pick at this notion and ask them how they think corporations would do if:

1) government stopped enforcing contracts

2) government no longer recognized corporate charters, i.e., corporations no longer provided limited liability to managers and shareholders

3) government stopped enforcing patents and trademarks

4) government stopped providing basic social services, like roads, education, investment in basic research

My goal is not to make an ideological point with them; I am not trying to argue for corporations as good or bad. I am simply trying to get them to recognize that corporations are not natural; they are legal, thus government, creations. In the absence of 1-4, it seems quite likely to imagine that a truly free market -- a truly laissez faire government policy -- could only exist on a much smaller scale, mostly small, family-owned businesses. As a factual matter, the U.S. economy is not a truly free market, not because of the big individual welfare programs (education, health care, unemployment, retirement, food stamps, and public housing), but because of the legal and other policies designed to support corporations.

Do students ever think about this in a U.S. history class? It seems vitally important to understand, but I doubt high school students think about these issues unless they take a civics class in high school (a dwindling number I am sure) or debate.

A Wikipedia theory

A tip of the hat to XKCD. The theory is simple: On any Wikipedia page, click on the first link that is not in italics or in parentheses; repeat; you'll eventually end up on the philosophy page.

My students tested this out (n = 160 trials). They found that they did always end up on the philosophy page, with a mean of 16 links required (and s = 4.6). Neat.

Should all laws sunset?

A recent article on Germany's system of periodic legal review got me thinking. Specially-tasked panels in the government review old laws and recommend updates to the legislature; some old laws are recommended for repeal. There is an obvious efficiency advantage to updating old laws, but there is also a democratic value to it as well. Why do laws bind future generations indefinitely? The problem is even worse when you consider laws passed by slim majorities. As a thought experiment, I like to ask my students to consider this proposition: All laws should sunset.

Here is the scenario I give them: the size of the majority that passes the law will determine its longevity. I give them this function as an example: years duration = 0.0005 x^2 + 0.0012 x + 1, where x is the margin of victory minus 1 (the coefficients are scaled to the U.S. House of Representatives). A one-vote margin of victory would entail a year's duration. A more standard party-line vote, say 242-193, would result in a two-year duration. Around a 60% majority, say 255-180, would result in a four-year duration. A unanimous passage would result in a 96-year duration. This example seems reasonable, so it forms the basis for our discussion.

Three interesting game theory questions always come up.

1. This gives a meaningful distinction to a vote to abstain, from a yes or no vote. The vote to abstain does not impede the law's passage, but it does limit its duration.
2. This gives the ruling party in Congress a real incentive to craft bipartisan legislation, if they want the law to endure beyond one term of the House. This could backfire, of course, and make the country even more difficult to govern. Not least of the reasons why it might backfire is the notion that Congress will have a very full docket re-passing about-to-expire laws. The tax code comes to mind as a frequently recurring matter, because it will never pass with large majorities.
3. What about repealing laws? Say a law has 76 years left. Does Congress have to muster a supermajority (411-24) to repeal it (an all-or-nothing repeal rule)? Or would the repeal rule be that a simple majority could "injunction" it for a year, but then the law would come back in force? For the purposes of the discussion, I usually go with the latter idea -- it more cleanly hews to the idea that laws should not be binding in perpetuity.

Students have a fun time discussing this idea. Invariably, we discuss how difficult it might be for everyone to comply (the lack of predictability), but I try to steer the discussion to this core idea at the heart of the thought experiment: Ought some rights exist in perpetuity? Is it democratic to have a fixed Bill of Rights?

Here's some further reading.

proportional representation

The gerrymandering of U.S. congressional districts is a problem. First, it is simply at odds with democratic principles to have our representative choose US. Gerrymandering can lead to extraordinarily safe districts and can slightly tilt the balance of the whole state delegation. We get less turnover (fewer competitive races) AND skewed results.

Second, there's the appearance of corruption, unless the redistricting process is handled transparently by a nonpartisan committee (and these are few and far between). Even when a nonpartisan committee does try to do the redistricting fairly, it's hard to do: districts are supposed to be geographically compact (a smaller perimeter/sqrt[area] is better); minorities are supposed to be given a voice (so create some minority-majority districts); and some districts are supposed to be competitive (so, near 50-50 splits). But here's the key problem: a district can be represented (a representative speaks for the overwhelming majority in that district) OR competitive but not BOTH at the same time. I have a simple solution: Elect U.S. congresspeople in at-large races in each state, like senators.

There's nothing in the U.S. Constitution to prohibit it: it's up to states how to elect their representatives: "The Times, Places and Manner of holding Elections for Senators and Representatives, shall be prescribed in each State by the Legislature thereof..." (Art. 1, Section 4)

This change would allow states to use a proportional allocation method. There are all sorts of methods, but the simplest one to imagine starts with each party putting forward a list, in order, of its potential delegation. If the Democratic party wins 4 seats, the first four people on the list become U.S. representatives. (Obviously, being toward the end of the list is an honorary thing, since it's very unlikely one party would win all the seats in a state.)

Again, there are all sorts of ways to let people vote in these kinds of elections. One way is that a voter could receive a ballot that gave him one of two options in voting: a straight party line vote, and picking and choosing from the various parties. Say John is voting in Colorado's election (7 representatives). He could vote down the Democratic line, for their 7 candidates, or he could vote for any 7 candidates he liked, regardless of party. I think for simplicity and to avoid strategic voting, it's best to make the voting unranked; this would be approval voting. (The mathematics of proportional representation tallying are fascinating.)

Proportional representation gives third parties a better chance to win at least one seat. It allows ideologically unified but geographically spread minorities to build a voting block. And there are no districts to draw.

Well, not quite.

While it would be reasonable for Colorado to treat the state as one delegation, it's hard to imagine California (53), Texas (36), Florida (27), New York (27), Illinois (18), Pennsylvania (18), or Ohio (16) doing it. I think electing around a dozen at-large representatives is best: it gives third/minority parties a good chance, but isn't overwhelming to the candidates and voters. These large states would need to be subdivided. The key criteria would be creating geographically and economically cohesive units, transparency, and stability (with luck, the zones could exist without modifications for two or three census cycles).

Perhaps the most obvious way is to divide along county lines. Here's a possible zoning map for California:

Zone 1 is the Bay area counties: population 6.1 million, 9 representatives. Zone 2 is L.A. county: pop. 9.8 m, 14 reps. Zone 3 is San Diego/Empire: pop. 8.4 m, 12 reps. Zone 4 is N. California: pop. 7 m, 10 reps. Zone 5 is S. California: pop. 5.6 m, 8 reps.

It's possible to imagine other ways to partition it, but the voters/reps ratios are fairly consistent across the different zones. How did I do on geographic compactness? Using the formula perimeter/sqrt[area], most of the zones are decent:

Zone 1 is the most compact, with about 4000 sq. miles in 260 miles of perimeter. I calculated a compactness factor of about 4.2. To put it in perspective, that's only 1.2 times worse than a circle. Zone 5 is the worst, about 58,000 sq. miles in 1400 miles of perimeter (it has to go around L.A. and Fresno counties). I calculated a compactness factor of about 5.7. That's about 1.6 times worse than a circle. That's worse than an equilateral triangle. In the grand scheme of things, it's not terrible. Certainly, not as bad as this:

or this:

It's hard to know which is my most favorite ridiculous district. Districts 3, 10, 11, 15, and 18 are misshapen lumps. Districts 27, 29, 32, 39, and 40 are odd. Is it just me, or does 42 look like Italy? But the most bizarre must surely be 38.

Texas might divide itself into three zones (western; eastern: Dallas, FW, Austin; and coastal). New York: upstate and city, perhaps. Illinois: Chicago and the rest. Pennsylvania: Pittsburgh, middle, and Philadelphia. Ohio: perhaps northern and southern.

A modest proposal to ensure geographic mixing at Nationals

I wrote an article for the Rostrum (which I'll link to once it comes out in September) [note: they declined to publish it. Here's a link to the article I wrote] about using geographic and strength criteria to mix teams in preliminary rounds at NFL Nationals. In other words, I advocate the use of a system that ensures that each team will debate a broad cross-section of different opponents, from different parts of the country and at different skill/experience levels, as measured by NFL debate points. I won't repeat the arguments here about why I think this is a worthwhile goal, except for this one thought: Geographic mixing makes it likely that the less experienced teams -- who probably have not travelled far afield -- will debate opponents at Nationals they have never seen before. Even with geographic mixing, there is still a chance that national circuit teams might face an opponent in preliminary rounds at Nationals they have debated many times during the invitational season. That is why there is also a need for skill/experience level mixing. Both are necessary to make it likely every team will see "new" opponents at Nationals.

I will focus on two technical concerns about my proposal in this blog post.

Concern 1: Can two criteria really be maximized at the same time?

Yes and no. In a strict sense, no: only one variable can truly be maximized at a time. That is to say, you can have a round where the average geographic distance between opponents is maximized, or you can have a round where the average difference of skill/experience between opponents is maximized, but you can not have both at the same time. However, in a looser, more practical sense, the answer is yes: you can have a round where opponents are well-mixed geographically (even though not maximally mixed) AND well-mixed skill/experience-wise (even though not maximally mixed). Let me show you with the sample data I used in the Rostrum article.

Here are 26 fictitious teams, spread throughout the country in geographic clusters, and at different skill/experience levels (normally distributed from 0 to 1 in my sample data). I imagined that the NFL points could be scaled so the weakest team to qualify was given a rating of 0 and the most experienced a 1, but they do not need to be scaled at all for this method to work. The median distance between every possible pairing in the whole set is 2138 miles. The median difference in experience is 0.28 units.

If one tries to maximize geographic spread, the round 1 pairings that are selected would look like this:


The median distance between two opponents in each pairing is 3333 miles, and the shortest distance is 2452 miles. In other words, every match chosen is above the average of 2138 miles. This is maximized; it is a Pareto optimal solution, meaning that any change to improve a pairing by swapping opponents would have to make another pairing worse. The net result can not be improved. In the first round, teams in the middle of the country would debate coastal teams. As the tournament proceeds, each team would get opponents from every geographic region of the country.

If one tries to maximize the differences of skill/experience levels, the round 1 pairing would look like this:


The median difference between opponents is 0.45 units, and the least difference is 0.42 units. Every match chosen is above the average of 0.28 units. Again, this is a Pareto optimal solution. In the first round, mid-level teams would debate either inexperienced or highly experienced teams. No inexperienced team would be matched against a highly experienced team -- this would force two mid-level teams to debate. However, in further rounds, each team would get opponents at every different level.

What happens if you try to maximize both? The resulting pairings (which were published in the Rostrum) would look like this:


The median distance is 3092 miles, and the shortest distance is 2003 miles (with only 15% of matches below the average of 2138 miles). The median difference is 0.45 units, and the least difference is 0.23 units (with 23% of matches below the average of 0.28 units). Although these pairings do not maximally mix for geography, they do pretty well. And likewise for difference in skill/experience level. This represents a lower boundary of how well this method could work. If we use a larger data set, such as the 200+ teams at Nationals, then it becomes easier to find pairings that maximize both criteria.

Concern 2: Would this method create the same pairing year after year?

It seems like it might: an optimal solution for one year seems like it might be the same, or very similar, the next year. No one wants to see the same opponent in preliminary rounds two (or more) years in a row at Nationals.

However, this kind of optimization is chaotic, meaning it is extremely sensitive to small changes.