Voting, Altruism, and Total vs. Average Utilitarianism

Interesting debate over at the Volokh Conspiracy, where Ilya Somin has explained his theory of rational voting and is now defending it against Jim Lindgren. Here’s Somin’s original post and Lindgren’s first response.

Somin’s argument, in a nutshell, is that despite the incredibly small chance that your one vote will actually affect the outcome of an election, it’s nevertheless rational to vote if you’re even just a little bit altruistic. The reason is that you have to multiply the very tiny probability of your vote making a difference by the very large number of people who will be affected (beneficially in your opinion) by your favored candidate taking office.

Lindgren has challenged some of the mathematics behind Somin’s argument. Although Lindgren’s criticisms are cogent, I suspect Somin can probably rehabilitate his model. A somewhat more complex mathematical specification can probably produce qualitatively similar results.

My concern with Somin’s model, which I noted in the comments for one of Somin’s reply posts, is that it turns on the size of the population. The larger is the population of people who will benefit from your preferred candidate winning, the greater is your incentive to vote. Other things equal, that should mean a larger percentage of people should vote as the population increases – but that’s not what we’ve seen historically.

What I realized a short while later is that other things won’t be equal, since a larger population presumably means a smaller chance that your vote will make a difference. The countervailing effects of rising population could cancel out, so maybe my objection doesn’t matter empirically. However, it does matter philosophically. By treating the altruistic benefits of voting as a function of the sheer number of other people who will benefit rather than the percent, Somin has implicitly assumed that people are essentially total utilitarians rather than average utilitarians. Total utilitarianism has problems, the most important of which is the implication that we would rather have a very large population of people with lives just barely worth living than a smaller population of very happy people (as long as the total happiness of the latter was smaller). Average utilitarianism also has problems, such as the implication that we might want to kill people painlessly if doing so left a remaining population with higher average happiness.

But perhaps this philosophical issue doesn’t matter in the voting context, since total and average utilitarianism only differ when the population size is not fixed. Then again, at least some policies do affect the size and composition of the population; abortion springs to mind.