Just How Much Your Vote Matters

by Conor Clarke

The National Bureau of Economic Research sent out a new paper this morning, by Nate Silver and Andrew Gelman (of the great fivethirtyeight.com) and Aaron Edlin of Berkeley. The paper asks a simple question: "What is the probability your vote will make a difference?" And the abstract has a pretty simple answer:

One of the motivations for voting is that one vote can make a difference. In a presidential election, the probability that your vote is decisive is equal to the probability that your state is necessary for an electoral college win, times the probability the vote in your state is tied in that event. […In 2008,] The states where a single vote was most likely to matter are New Mexico, Virginia, New Hampshire, and Colorado, where your vote had an approximate 1 in 10 million chance of determining the national election outcome. On average, a voter in America had a 1 in 60 million chance of being decisive in the presidential election.

The basic takeaway here will be familiar to most people familiar with public choice economics: If your decision to vote is motivated by the sense that "one vote can make a difference," you are being substantially less rational than someone who never leaves the house for fear of being killed by a meteor. Voting is irrational.

But let's not get carried away. Voting can still send a potentially valuable signal — to elected officials and to each other — that we care about civic engagement and democratic accountability. That civic expression can still make us feel good. And there are still strong moral reasons to do it. Sure, the cost of your individual decision to stay home on election day might be insignificantly small, just as the cost of an individual decision to litter or touch a delicate painting in a museum might be close to nonexistent. But I wouldn't want to live in a world in which no one voted and everyone littered, for the fairly simple reason that there's a difference big between what's individually "rational" and socially beneficial.

UPDATE: I should have been clearer in the original post. The paper in question doesn't make the argument that voting is irrational. (Indeed, Andrew Gelman emailed to make clear that he thinks it can be rational.) The point about irrationality was my gloss, although I certainly stand by it.