Comments on: Rational voting

By: jr

jr — Wed, 29 Sep 2004 04:18:33 +0000

Your argument assumes that people routinely assign a dollar value to their time and effort in ordinary life activities. They don’t. Except for those few of us who bill time at our jobs, does anyone ever even think of valuing a purchase at its cost plus a dollar amount for the time spent shopping? Or the cost of a meal as the check plus some value for the two hours spent consuming it? The few minutes spent voting (not an unpleasant activity) have no calculable dollar cost. If it cost even a trivial amount to vote (say $5) one would expect to see the voting rate drop precipitously.

By: Jason

Jason — Tue, 28 Sep 2004 15:32:05 +0000

The caret’s disappeared in the formatting. It may make the calculations a little hard to follow. A lot of the numbers squished together are supposed to be “to the power of,” in particular the final answer was 10 to the -26

By: Jason

Jason — Tue, 28 Sep 2004 15:25:30 +0000

Yes, I’m assuming there is a proportion p of the population that will vote one way, and a proportion the other. Personal observations, Polls, Election Markets etc. (pick your poison) offer up something like estimates of p, and these estimates are unlikely to be too far removed from p. If you view polling for example as an (unbiased) sample of how the population will vote, then if the estimate of p is say consistently .6, then the probability under say a uniform prior that p is below .5 is ummm, this will take a fair dredging of my knowledge here (my earlier comment was just based on the fact that this was a “rare event” and thus likely to be exponentially small). Let’s see, uniform prior = beta(1,1). Suppose we sample 3000 people and get 0.6, so 1800 positives, and 3000 total. Thus posterior = beta(1801,1201). Now, head to beta tables … Bah! Can’t find any tables … OK, let’s look at LR’s and bound the probability … LR is proportional to p^{1801 (1-p)}1201. Thus, the ratio of the probability of being 0.6 to that of being 0.5 is (0.6/0.5)^{1801 (0.4/0.5)}1201. Taking logs and seeing if my calculator is OK with this, 1801 ln 0.6 + 1201 ln 0.4 – 3002 ln 0.5 = 60 (give or take), so the probability of being smaller than 0.5 in the posterior distribution is certainly smaller than e^{-60, or 1 in 10}26. Also, CA is a democrat state, so a scandal about Arnie is unlikely to change the outcome, unless it was a scandal like he’s going to give all his money out to Californians, but only if they vote Bush. It’s hard to think of a scandal that could swing CA to the knife edge, while keeping the rest of the country on a knife edge too. I don’t think my second point weakens my case (actually I don’t really think I have a case, my first point is that if everyone were rational there would still be people voting, my second is that your 1/n estimate is way off). Your 1000 people block voting is not the same as 1 person voting. Yes, if I can get 10% of the population to sign a contract pledging to block vote then we could swing almost any election. This is essentially what special interest groups try to do (and use peer pressure to enforce the vote).

By: JamesW

JamesW — Tue, 28 Sep 2004 13:45:06 +0000

So it’s just about rational to turn out on polling day but not to invest a lot of quality TV time in finding out whether the candidates are honest and competent. Seems to fit the data.

By: John Quiggin

John Quiggin — Tue, 28 Sep 2004 06:37:25 +0000

Jason, could you spell out your argument? Are you assuming that the vote is given by a binomial distribution with some fixed p, not equal to 0.5? If so, don’t you concede the possibility that some shock (say, a scandal about Schwarzenegger) might shift p close to 0.5. Given a reasonable Bayesian prior over p that includes some weight in a neighborhood of 0.5, I don’t think you can get far away from a 1/N chance of a tied vote. Your second point actually weakens your case. 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.

By: Jim Birch

Jim Birch — Tue, 28 Sep 2004 06:16:32 +0000

One major problem with expected utility problems like this is that they assume rationality is identical with self-interest. A selfless act can be totally rational. If you’re truly not at all altruistic and moderately smart then I expect that shooting strangers and removing wallets from the bodies would be a better income stream than voting.

By: Jason

Jason — Tue, 28 Sep 2004 02:53:57 +0000

2 things, First, people differ. Different types will generate an equilibrium where some people vote and others don’t. That said, enough people vote irrationally that the rational agent model isn’t a good one. Second, I don’t see any reason why I should expect my chance of affecting the outcome to be on the order of 1/n. The probability of a binomial distribution being a significant distance from the mean is exponentially small, not harmonically small. I live in CA (although as a non-resident). If I had to estimate the probability of a single voter turning CA from one party to the other, It would be in the trillions to one (actually, it would be higher than this, but largely because of some rare events that might cause most of the population of CA to die, eg. nuclear war, huge earthquake, etc.). On top of that, does anyone truly believe that if the presidential election came down to 1 vote in 1 state, that it would be that vote that would actually change the outcome rather than an tortuous litigative and bureaucratic procedure?

By: Jack

Jack — Mon, 27 Sep 2004 21:16:42 +0000

Would a student presenting the calculation above in a term paper in Rational Choice Theory would they be expected to adjust both the probability of making a difference and the size and strucure of other rewards for voting? It seems (as perhaps intended) to me that it would be easy to treat this calculation as being normative and draw a very wrong conclusion. If I understand Chris’s suggestion properly taking the explanatory view it becomes clear that the calculus presented is incomplete because it suggests actions that people do not take.

By: Jay

Jay — Mon, 27 Sep 2004 19:19:39 +0000

I think there is an intrinsic value to human beings in expressing themselves. This blog, to wit, and my post. Voting is a form of self-expression, and thus has value, in and of itself. Of course, not everyone values self-expression, or the particular form of self-expression that is voting, the same. And the number of individuals for which it exceeds the cost of voting is going to vary with the issues on the table. Thus Karl Rove gets the right all fired up about gay marriage and bible banning. Most of these people know they aren’t going to stop gay marriage ultimately, they aren’t going to stop abortion, they aren’t going to establish Christianity as the state religion. But they want to stand up and make themselves heard, and voting is a way for them to do that. This also holds for me, living in CA. My own vote for John Kerry will not make the slightest bit of difference. CA is a foregone conclusion for Kerry. If I want to change my life, buying a ticket for the CA lottery, which is over $35 million at the moment is more rational than voting. Except I want to be counted. I want to be heard. I want to express myself. So any model that ignores this expressive value of a vote will underpredict the number of voters.

By: avoter

avoter — Mon, 27 Sep 2004 18:53:30 +0000

If you’re a consultant that earns $200/hr I guess the rational thing would be to work 30 minutes, vote, then bill the client for an hour. I’ll make $200.01.

By: Sebastian Holsclaw

Sebastian Holsclaw — Mon, 27 Sep 2004 18:51:49 +0000

This is one of the paradigm cases of what David Post called “The Reverse Tinkerbell Effect” over at The Volokh Conspiracy (scroll down to the “Tinkerbell Effect” posts. It describes phenonmena where “The more people who believe it, the less true it is.” Like many such phenomena it works both ways. The more people who believe voting is crucial, the less likely it is that your vote is crucial. As more and more people believe that their vote isn’t likely to make a difference, it becomes more likely that an individual vote makes a difference.

By: John Kelsey

John Kelsey — Mon, 27 Sep 2004 18:16:21 +0000

It seems like most of the benefit of voting is outside the realm of having a tiny fraction of a say in deciding who wins. From feeling good about your citizenship to getting the little “I Voted” sticker they give you around here for voting, you get some external benefit. And of course, that’s necessary, because based on your chances of affecting the election’s ultimate outcome, there’s really almost no benefit to voting. (I can look at the fact that there is substantial turnout to the elections, and thus decide that my vote will have a negligible effect.) —John

By: Guy

Guy — Mon, 27 Sep 2004 18:15:14 +0000

If you’re a consultant that earns $200/hr, then $10 is indeed a ridiculous(ly low) cost for your vote. :) More seriously, the model is robust to the choice of voting costs. As long as the benefits of having “my choice” win are sufficiently high relative to those costs, elections will have a non-zero turnout. I think this result should hold up even if we introduce cost heterogeneity into the population.

By: AVoter

AVoter — Mon, 27 Sep 2004 18:05:20 +0000

Naive question: Why do we get to determine arbitrary values for voting based on direct material gain while leaving the costs wide open. Ten dollars is a ridiculous cost for my vote. I can walk to the polls and be done in half an hour. Using electricity to watch a soap opera with zero material value would be much more expensive.

By: Zizka

Zizka — Mon, 27 Sep 2004 17:09:06 +0000

Few of the discussions I read about rationality make me conclude that rationality is really a very good thing atall, either analytically or normatively. Amarya Sen (in “Rationality and Freedom”?)recently replaced three common definitions of rationality with his own. I liked his definition fine, but it had lost all the supposed clarity, definiteness and power that made the other, wrong-headed definitions interesting.