War, what is it good for?

A partial list:

• Winning independence
• Ending slavery
• Stopping invasions throughout the world
• Protecting enormous numbers of people from their would-be murderers
• Making the world safe for liberty and democracy
  

Soldiers who have had to go through things that I cannot imagine going through, to do things that I cannot imagine doing, to sacrifice their physical health, their mental health, or even their lives, have fought these wars because they believed in the causes that they were fighting for. Americans owe them a tremendous amount of gratitude, as do many others around the world.

The Dependency Hypothesis

People respond to incentives. That is the insight that many libertarian-types have taken and run with, seemingly analyzing everything in terms of economic rationality and the logic of the market. (This leads to eminently mockable turns of phrase, such as "Assuming choices to engage in risky sex are made rationally".)

It may be revealing, then, to look at the cases where these libertarian-types embrace some other view of human behavior. One view that shows up time and again (see recent posts by Becker, Posner, Whitman, and Wilkinson) is the generalized dependency hypothesis. This is the hypothesis that people who receive benefits from government programs like Medicaid and welfare develop generalized deficits in areas like initiative, energy, willpower, and independent decision-making, and that these generalized deficits make them less effective at dealing with situations where independent, willful action would be beneficial, such as preparing for Katrina.

It is important to clarify what this hypothesis is not saying. There's a different hypothesis about dependency that is right up the free market alley. That is the view that government programs create incentives that induce people to depend on them, rather than using them as a temporary safety net. Unreformed welfare, for instance, gave people enough money to live without working, and it increased the effective tax rate that people going from welfare to work would face (including the removed welfare benefits), so the hypothesis that people develop a dependency on welfare could be based only on the claim that people respond to incentives.

A second kind of dependence is slightly more general, dealing with a domain of life rather than a particular government program. Some government retirement savings programs, to take an example, don't require the individual to make any decisions or to become informed about how to invest. This can lead to dependency in the domain of financial investment, in that people who have been relying on the government program will not be prepared to make their own informed decisions about investments in other programs. This type of dependency requires an account of human psychology that is only slightly more complex than "people respond to incentives", to wit, "people learn from experience."

The generalized dependency hypothesis is far more ambitious empirical claim than either of these more limited claims. It is supposed to be able to account for people's decisions of all kinds (or people's inability to make independent decisions of all kinds). It applies even to rare or novel situations, like fleeing from an approaching hurricane. In order to have such generality, this hypothesis requires a much more complex view of human psychology, one with such general capacities as "initiative" or "energy", to use Becker's terms, or "will power", to use Whitman's. It is also less clear how government programs would reliably produce such dependency.

What is my view on these three kinds of dependency, dependence on a program, dependency in a domain, and generalized dependency? I am not really sure. That's why I've asked Becker and Wilkinson if they could point me to any empirical studies of generalized dependency, or any thoughtful, empirically-informed books on the subject. And that's why I'm making the same request to you, my loyal reader / transient visitor / confused googler. Are there people who have rigorously studied this generalized kind of dependency, investigating the mechanisms at work, its causes and effects, when it occurred and when it did not? Have they written anything good? I would like to read more, no matter what the ideology of the author (as long as it is someone thoughtful, not an ideologue).

I am a blogger, so I do, of course, have some views on the topic. I think that there is a lot more variability than dependency hypothesizers allow. The three kinds of dependency seem so different that it is probably unhelpful to refer to them all with the same word (that is why I focused my request on generalized dependency). The role of the government in breeding a "culture of dependency" probably varies a lot across the three kinds of dependency and across different government programs.

Dependence on particular government programs is probably relatively common, though some overstate its prevalence in cases like welfare, and it is not always such a terrible thing (perhaps "reliance" would be a more neutral term than "dependence"). It is also not limited to government programs. People come to rely on all sorts of arrangements that were intended to be temporary. Good program design can help avoid this problem, but it is often a difficulty that must be dealt with.

Dependency in a domain really should not be called "dependency" at all, I think. Often, being unable to make independent decisions in a domain is a perfectly reasonable, fine position to be in. There is just too much to learn, in too many different domains, to be able to make independent decisions everywhere. Many government regulations are designed to reduce this information burden and to give people a guide to, say, which doctors they can trust to be competent. In many cases, the government takes the role of informing people to facilitate better decisions, as by mandating nutrition information labels on food and making them include comparisons to government-devised Recommended Daily Allowances. The kind of process that Whitman warns against, where one government policy weakens their decision-making ability on another subject and makes further government regulation seem appropriate, can occur with this kind of "dependency", but that does not mean that the government should stay out of the way. For one thing, we can be careful about this kind of government expansion, and promote more government programs that keep people informed and involved. Also, this kind of expansion is not necessarily bad, as long as it doesn't stretch out too far. Finally, the benefits of the program can easily outweigh this effect when it is negative. Making beneficial programs like 401(k)'s opt-out instead of opt-in could make people less inclined to become informed about them, but the reason that this change is attractive is that many people remain uninformed about them under the current system and thus fail to take advantage of programs that would be beneficial to them.

Generalized dependency is the one that I feel like I know the least about. There are some related areas of study in psychology, like learned helplessness and the effects of expectations, which suggests that there might be some empirically viable content to the concept of generalized dependency. However, in most cases people who promote the generalized dependency hypothesis use "folk" concepts and do not seem to have much contact with relevant social science research. Whitman is an exception, but the conclusions that he draws from Roy Baumeister's research on the "self-control muscle" go far beyond the existing research. Whatever the psychological process, it is not clear that the government has enough of an influence on people's lives to create widespread, generalized dependency (except for people who are incarcerated). Possibly some government programs increase this kind of dependency (perhaps indirectly), but it is also possible that some decrease it, and that many have no effect on it. Which government programs are most likely to create this kind of dependency or to alleviate it, and how? What else, other than the government, influences the generalized dependency of a culture, and how?

These are the important questions that I have the most trouble answering, which is why I'd like to go read something that explores them. I'd prefer to read a book or a published study, since I expect that blog discussion would be relatively cursory and not tied very closely to empirical work (and anyone capable of better in a blog comment would most likely be able to recommend a study or book that was even better).

So hit me with recommendations if you can.

Rational Voting: The (Ir)relevance of Interference in Close Elections

An election is supposed to be simple. Voters cast their votes, those votes get counted, and the candidate with the most votes wins. As we all know, that's not how things work out in real life. There's fraud, intimidation, overly stringent restrictions that keep voters from having their votes counted, underly stringent restrictions that allow people who aren't eligible to vote to cast votes nonetheless, imperfect vote-counting, suspect voting machinery... And if the election is close enough so that any of these factors might have made a difference, then it will probably go to court, where a few people in robes can effectively hand the election to one candidate or the other.

This is bad for a variety of reasons. It can affect the outcome of elections. The lack of transparency undermines democratic values. Questions about legitimacy can lead to outrage and partisan divisiveness. It can make citizens feel disempowered, as the judges or the fraudsters seem to be determining the result.

This last effect intersects with a common blogosphere topic: why vote? The probability that a single vote will change the outcome of an election is tiny. Contra Frank, the question is not why so many people are voting against their economic self-interest, but why anyone would vote out of economic self-interest. Anyone's economic self-interest would be much better served by staying home and using that time productively. Levitt and Dubner (of Freakonomics fame) have an article in the NY Times Magazine giving their take on why people vote if the incentives don't seem to be there. After going through the standard argument for why an election is unlikely to be decided by a single vote - your vote - and providing some historical data on Congressional elections (or should I say "election") where the margin was a single vote, Levitt and Dubner go on to claim:

But there is a more important point: the closer an election is, the more likely that its outcome will be taken out of the voters' hands - most vividly exemplified, of course, by the 2000 presidential race.

But is this true? In the Crooked Timber thread I linked to before (and before), John Quiggan argues that your impact on the outcome does not change if close elections are decided by a "tortuous litigative and bureaucratic procedure":

In a close election, no vote is decisive, but every change in the (election-night) margin changes the odds. 1000 extra votes for Gore in Florida would have made a big difference, so every vote cast in Florida made (roughly) 0.001 of that big difference.

So does the intervention of judges and so forth reduce your chances of affecting the outcome of the election? Who's right, Quiggan or Levitt + Dubner?

I gave an answer in the comments at Freakonomics: Levitt and Dubner are wrong. I'd like to defend it here with somewhat more precise reasoning.

Let's say that there are two candidates, and let x be the number of votes that are cast for the candidate you prefer minus the number of votes cast for the other candidate. We define two functions in terms of x, both based on the best guesses that you can make before the election, when you are trying to decide whether to vote:

Let p(x) be the probability that your candidate will get x votes more than the other candidate from all of the voters besides you (so p(x) excludes your vote).

Let f(x) be the probability that your candidate will win the election, given that he received x votes more than the other candidate.

What is the probability that your candidate will win? Well, for each possible pattern of voting (which is represented by a particular value of x), we want to figure out how likely it is that this will be the voting pattern (that's p(x)), and then figure out how likely your candidate will win if this is the voting pattern (that's f(x)). We multiply these together and add up the values for all possible voting patterns and the result is the sum over all integers x of p(x)f(x).

What is the probability that your vote will make the difference in the election? Well, for each possible pattern of voting for all of the other voters (which is represented by a particular value of x), we want to figure out how likely it is that your candidate will win if this is the voting pattern and you do not vote (that's f(x)), and subtract that from how likely it is that your candidate will win if that is the voting pattern and you do vote (that's f(x+1), since your candidate is getting one more vote), and as before we multiply by the likelihood that this will be the voting pattern and sum over all possible voting patterns. The result is the sum over all integers of p(x)[f(x+1)-f(x)].

There is one assumption that we are making here, and that is that all votes are equal. Your vote is not less likely to be counted than anyone else's vote. If you're doing something reckless like casting a provisional ballot then this equation vastly overstates your chances of impacting the election. If you're more conscientious than the average voter at using the voting equipment, though, the probability that your vote will make a difference in the outcome of the election is slightly larger than what you'd get from this formula.

In an ideal election, you candidate would win if x>0 and he'd lose if x≤-1. That is, f(x)=1 for all x>0 and f(x)=0 for all x≤-1. Since f(x)=f(x+1) for all values of x but two, the infinite sum over all values of x of p(x)[f(x+1)-f(x)] reduces to p(-1)[f(0)-f(-1)]+p(0)[f(1)-f(0)], which equals p(-1)[f(0)]+p(0)[1-f(0)]. Assuming that p(-1)=p(0) (that is, a one-vote loss for your candidate is just as likely as tie, not an unreasonable assumption given that your predictions of other voters' behavior can hardly make much of such fine-grained distinctions), this simplifies to p(0). So the probability that your vote will make the difference in the election is equal to the probability that the election would result in a tie without your vote, a rather intuitive result.

But what happens when things get messy? What if a candidate could win the election despite garnering fewer votes, because of the crazy electoral system? What if f(x) is not a neat step function, but some complicated, smeared out function (possibly biased, maybe even non-monotonic!)? My claim is that your impact on the election is just about the same, as long as there exist integers a and b, with b>a, such that

1. f(x) is approximately 0 when x ≤ a
2. f(x) is approximately 1 when x ≥ b
3. p(x) is approximately constant for all x where a≤x≤b

In other words, even if the election procedure is messy for close elections (where the differential between a and b is small), it is reliable once either candidate gets a large enough lead. And, the range of voting patterns where the unpredictability happens is narrow enough so that it is hard to say beforehand which of the voting patterns within that range are most likely.

More precisely, we can write these conditions in terms of three errors, e1, e2, and e3, all of which are approximately 0:

1. f(a) = e1
2. f(b) = 1-e2
3. p(min)/p = 1-e3, where p is the maximum value of p(x) for a≤x≤b and p(min) the minimum

Then the probability that your vote will change the outcome of the election is no less than p(1-e1-e2)(1-e3). If p is approximately p(0) and e1, e2, and e3 are small, then this is about the same as p(0). Usually, p will be larger than p(0), since p is the maximum of p(x) for a≤x≤b.

This formula can be derived by evaluating the infinite sum over all x of p(x)[f(x+1)-f(x)]. Since this value is always positive, the sum over all x is greater than or equal to the sum from a to b-1 of p(x)[f(x+1)-f(x)], which is greater than or equal to the sum from a to b-1 of p(min)[f(x+1)-f(x)], which equals p(min)[f(b)-f(a)], which equals p(1-e3)[1-e2-e1].

Why can we say that the errors, e1, e2, and e3, are close to 0? We can make e1 and e2 small with values of a and b that are relatively close to 0 as long as the problems with the election procedure only arise in close elections. In an election with a million voters, we can assume that, as long as one candidate has at least a few thousand votes in his favor, it is very unlikely that the other candidate will be able to steal the election away. Since we get our information about how other voters are likely to vote from polls with margins of error of plus/minus a couple of percentage points (which would give us a 95% confidence interval with a length of 50,000 in our election with a million voters), our knowledge is not fine-grained enough to distinguish the likelihood of values of x that are within a few thousand of each other, as a and b are. So p(x) will be approximately constant in that range, and p(min)/p will be close to 1.

Even if these conditions do not hold very well, your chances of impacting the election will still be close to p. If there is a lot of variation in p(x) between a and b, then (p)(1-e1-e2)(1-e3) is likely to significantly underestimate the true value of your impact, since we are using the minimum value of p(x) on that domain. Unless the procedure for determining the winning candidate was really wacky, it seems unlikely that your probable impact on the election would ever drop below something like three-fourths of p(0).

Given the uncertainty in everything else that you might want to measure (the benefit of making your candidate win, the cost of voting), the probability of a tie among the rest of the voters seems like a very good (and intuitive) estimate of the probability that your vote will be decisive in favor of your candidate. The precise procedure by which the election will be decided is much less important in influencing the rationality of voting than the other factors that determine your incentives. And there is no reason to feel disempowered when the outcome of the election is determined by judges, or bad voting machines, or ... . Angry, maybe, or outraged, or disgusted, or betrayed, or ashamed, or bemused, or frustrated, or vengeful. But not disempowered. As long as your vote was cast, it had just about as much of an expected impact as always. Not that its impact is very large.

UPDATE (11/11/05): Here are some more intuitive ways to think of this result, two from correspondents and one from me:

- In both ideal elections and real elections where judges can get involved, a few thousand votes will swing the election from one candidate to the other. The average impact of those few thousand voters is the same in both cases, and, since we can't predict vote totals precisely enough to distinguish possibilities that are within a few thousand votes of each other, the more fine-grained differences between the two cases are irrelevant. The expected impact of a single voter is the same in both cases.

- Any loss in marginal vote power attributable to "stolen elections" is counterbalanced by the gain in marginal vote power from (a) being able to push a potentially stolen election into the sure-win range and (b) being able to push a sure-loss into the potentially stolen range.

- What judges do is spread out the probability that your vote is the pivotal one, rather than concentrating it on one marginal guy.

Keeping Score in the Culture War

Our country is in the midst of a culture war, we always hear, with the Christians facing off against the Godless. But what metrics do we have to keep track of who's winning and who's losing? How do we keep score, and how do we even identify meaningful battles?

Well here's one battle that matters and comes with its own convenient metric: Rick Warren v. Peter Singer. Pastor versus utilitarian. May the best man win.

Singer: I’m not living as luxurious a life as I could afford to, but I admit that I indulge my own desires more than I should. I give about 20% of what I earn to NGO’s, mostly to organizations helping the poor to live a better life. I don’t claim that this is as much as I should give. Since I started giving, about thirty years ago, I’ve gradually increased the amount I give, and I’m continuing to do so.

Warren: Kay and I became reverse tithers. When we got married 30 years ago, we began tithing 10%. Each year we would raise our tithe 1% to stretch our faith: 11% the first year, 12% the second year, 13% the third year. Every time I give, it breaks the grip of materialism in my life. Every time I give, it makes me more like Jesus. Every time I give, my heart grows bigger. And so now, we give away 90% and we live on 10%.

This round, the points go to Team Jesus.

(HT Ezra)