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. Therefore, 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. This is a kind of Markov chain technique.

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 yards 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.

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. And another article on the liberal bias to policymaking, specifically because it is difficult to repeal laws.