Friday, April 4, 2008

Gelman and Kaplan on Rational Voting

Sometimes in economics, you read an argument that puts a new twist on an old theory, and you immediately think, "Of course! How did I not see that before? It's so obvious!" That's what happened when I read Andrew Gelman and Noah Kaplan's article, "Voting as a rational decision", on Vox EU. Standard rational choice theory has long been unable to adequately explain the (relatively) high rates of voter turnout. In national elections, the probability that your vote will decide the election is so small that the decision to vote seems irrational. As Gelman and Kaplan point out, even if you estimate that having your preferred candidate win will result in a very large benefit to you, the extremely low probability that your vote will be decisive still makes voting irrational. However, Gelman and Kaplan point out what should have been obvious:

"If your vote is decisive, it will make a difference for tens of millions of people. If you think your preferred candidate could bring the equivalent of a $100 improvement in the quality of life to the average person in your country--not an implausible hope, given the size of national budgets and the impact of decisions in foreign policy, health, the environment, and other areas--you’re now buying a billion-dollar lottery ticket. With this payoff, a 1 in 10 million chance of being decisive isn't bad odds.

And many people do see it that way. Surveys show that voters choose based on who they think will do better for their country as a whole, rather than their personal betterment."

In fact, the surveys showing that voters choose based on national interest more than self-interest have been around so long that I remember reading about them back when I was in grad school! (Or was it undergrad?) I think Gelman and Kaplan's theory actually reinforces the argument Bryan Caplan made in his truly excellent book, The Myth of the Rational Voter: Why Democracies Choose Bad Policies. If voters are choosing based on which candidate they believe will benefit the nation as a whole rather than which candidate will benefit them individually, we would expect their choices to be even less rational. Voters are presumably better at deciding whether a policy will benefit them individually than they are at deciding whether the policy will benefit the nation as a whole. Voters have a much better understanding of their own preferences than of the entire nation's preferences. Voters' beliefs about what the nation as a whole wants are heavily influenced by media accounts (which, it's fair to say, are not terribly accurate), as well as anecdotes. If an altruistic voter would personally prefer Policy A to Policy B, but mistakenly believes that more people prefer Policy B to Policy A, then he will vote for the candidate proposing Policy B. So even if voters fully understood how policies would affect the nation as a whole -- an assumption Caplan pretty much eviscerated anyway -- it's unlikely that they could accurately match the policies with the nation's preferences. It may be easy to object to the theory that voter turnout is rational because most voters are altruistic by noting that most people are decidedly not altruistic. But Gelman and Kaplan explain how their model actually filters out voters who choose based purely on self-interest, and attracts altruistic voters:
"[I]f turnout declines, then the probability of a tied election increases, which in turn implies that, on the margin, it then becomes rational for some people to vote. The feedback with voter turnout is why voting is not a simple free-rider or prisoner’s dilemma problem: the more people who free ride (by not voting), the higher the expected benefit to you of voting, and so extremely low turnout is not an equilibrium."
This equilibrium -- with high turnout of mostly altruistic voters -- is the most interesting result in my mind. I haven't fully run through all the possible objections to this equilibrium, but intuitively, it seems correct.