by Conor Clarke

Reader Marshall Eubanks, of America Free TV, emails about my earlier post on the irrationality of voting, and makes the argument that I overlook the expected value of one's vote. (Andrew Gelman, the lead author of the paper in question, also emailed to make a similar point.)

This is pretty standard statistics. Suppose that [Nate Silver et al] are correct, and the probability that your vote matters is one in 60 million for all recent national elections. (Such probabilities are in general unknowable; let's just assume this for a reasonable estimate.) What is the expected value ? It's the probability times the possible cost or gain if your vote is made or not made. The Iraq war shows that $ 1 trillion dollars may be a reasonable estimate for that. (I.e., if Gore had won instead of Bush, we might have saved $1 trillion on the war alone. Similar arguments can be made for McCain vs Obama.)

$1 trillion times 1/ 60 million is $ 16,666. In a close state, the probability of being decisive is (according to the article) more like 1/10 million, for an expected value of roughly $100,000. By this standard, voting has a much higher expected value than most lottery tickets (where the expected value is almost always significantly below the cost of the ticket).

Well, a couple of points about this standard. (Aside from the fact that something like the Iraq War would be hard to predict on election day.) First, the cost of casting an informed vote -- one that distinguishes rationally between a variety of complicated public policy positions and sifts through a lot of campaign lying -- is much, much higher than the cost of buying a lottery ticket. Casting an informed vote requires hundreds of hours of attention, often to highly trivial and/or highly tedious subjects.

Second, the monetary value of avoiding the Iraq war is not $1 trillion for an individual voter. That benefit is spread across the present and future taxpaying population! Even if the expected social value of your swing-state vote is $100,000, the individual value would be that divided by several hundred million. So the individual expected benefit would probably be less than a cent. 

Of course, one might have strong moral reasons for opposing the Iraq War, and those are difficult to quantify. But that was also the point of the original post: that we don't vote for our "rational" individual benefit. We vote for plenty of good reasons, though.

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