In swing states (or for close non-presidential elections), though, it’s a different story Aaron, Nate, and I have estimated the probability of your vote being decisive in a swing state as being in the range 1 in a million to 1 in 10 million. Low, but not zero, and Aaron, Noah, and I argue that it can be make sense to vote because of the social benefits that a voter might feel arise from his or her preferred candidate winning.Phil Arena:
First, being pivotal to the outcome of your state is not the same as being pivotal to the outcome of a presidential election.Kindred Winecoff:
Even still Arena is giving Gelman's argument more credit than it deserves. In fact, Gelman doesn't have an argument. He simply pretends as if there was a utility function out there such that it would make sense for people to vote at 1/10,000,000 odds (those are only the swing state voters, not the median or modal or otherwise typical voter). So far as I know no such utility function has ever been modeled or tested against peoples' actual subjective utilities, and Arena points out numerous analogous situations in which folks generally behave differently -- getting in a car crash, getting shot while on campus, etc. -- despite similar or better (worse?) odds.Actually, David Myatt has a paper showing that, in a plausible model of voting, one's probability of pivotality is 1/N, where N is the number of voters, and that for some standard utility-based models of altruism, that should be enough to get you to vote (because you are providing a benefit to N people). Warning: the paper is not as easy to read as a blog post. As I understand it, David is not arguing that this kind of instrumental rationality does explain why people vote; he is arguing that it could explain it, and that therefore two critics of rational choice theory from the 1990s are mistaken.
I remember the 90s!
Relatedly, at ESA Tucson I saw Ulrike Malmendier present a field experiment - not currently available online - on why people vote, arguing that it is related to (1) social pressure and (2) the cost of lying. This seems a more hopeful approach than constructing game-theoretic arguments alone - though, NB, the paper combined data with theory to estimate parameters of a model, rather than just directly estimating vote probabilities.