Co-Conspirator Eric Posner challenges my argument that it might be rational to vote. He argues that there is little reason to do so because, in the unlikely event that your vote really will break a tie, that probably means that the two candidates were of virtually equal quality:
[B]reaking a tie is beneficial only if your vote is more likely correct than not—that is, you actually vote for the better candidate. Surely your vote is more likely to be correct than not? After all, you have some information, and that means you are doing better than flipping a coin. However, you need to reflect on your own ignorance with some humility. If, by hypothesis, your vote breaks a tie, then it means that (putting aside the vagaries of the electoral system) half the country prefers one candidate and the other half prefers the other. If all of these people have enough information that their votes are not random, the existence of a tie (aside from your vote) indicates that the two candidates are almost exactly equal in quality. The probability that your own puny knowledge (elsewhere in the same article Ilya discusses the problem of rational ignorance—people have weak incentives to inform themselves about the candidates and policy in general) will distinguish the infinitesimally better candidate is itself infinitesimal.
The problem with Eric's argument is the assumption that if the other people's votes are not random, that necessarily means that they are - on average - well-informed, or at least more likely to be correct than mistaken. However, lots of research, such as Bryan Caplan's recent book, and my own article that Eric links to, suggests that voters often make systematic errors where "mistaken" votes for one side are not offset by an equal number of mistakes favoring the other. Thus, if your fellow citizens are equally divided in their voting preferences and are voting nonrandomly, that doesn't necessarily mean that the two candidates are nearly identical in quality. It could be that the weaker of the two is benefiting from systematic flaws in voters' evaluation of the information they have. So my argument for voting in cases where you think there is a big difference in quality between the two candidates still holds true.
Obviously, Eric is right to counsel "humility" in assessing one's own ignorance. If your knowledge is much less than that of the average voter, that may be a consideration in favor of staying home. But if it is equal or greater, then you have a good case for casting a vote if you think there is a substantial difference in quality between the available alternatives. That is especially true once you consider the possibility that you might have underestimated the quality difference in favor of your preferred candidate, a scenario that to some degree counterbalances the chance that you have overestimated.