## Monday, November 06, 2006

### 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.

Anonymous said...

I'm not going to vote this time round. I don't want to take the time to become an "informed" voter. I suppose I could vote "no" on all the propositions. Then again, I could vote "yes" on all of them. Or, I could yes on some and no on others. Or, I could skip the confusing ones. Or, I could vote yes or no on the confusing ones depending on how I felt at the moment. I could vote all the incumbents out, or I could vote to retain some or all of the them. I could go on and on with what I could do, or not do. I could vote a straight party ticket or I could mix and match. I could vote for abortion or gay marriage or I could choose to forget the whole thing. Do I sound apathetic to you, or merely pathetic?

Gil said...

I think I agree with Loren Lomasky that many people vote for expressive, rather than instrumental, reasons.

Patri Friedman said...

If he assumes that the benefit scales w/ the number of people but the chance of effecting does not...well, that's completely bogus to the point of being intellectually dishonest. OTOH, it would not surprise me if the math worked out that way. That is, the std. dev of a distribution goes up with root(N), so if the chance of the election being tied without you is proportional to the stddev it could be that the ratio of benefit to chance goes up with N. If I wasn't about to go to sleep I'd work it out.

Glen Whitman said...

"If he assumes that the benefit scales w/ the number of people but the chance of effecting does not...well, that's completely bogus to the point of being intellectually dishonest."

I don't think he makes an assumption either way. He appears to be working with a fixed population (300 million) and a fixed likelihood of your vote making a difference (1 in 100 million).

Patri Friedman said...

Hmm, it looks like my intuition is wrong. If the election is a dead heat (each person votes w/ 50/50 probability), then with 300,000,000 voters, the chance of you being the swing vote is about 4.5 * 10^-5, which is substantially higher than 1 in 100,000,000, and what I would hav expected. However, it is incredibly sensitive to p. If p = 0.501, the chance of a swing vote = 1.2 * 10^-261 - in other words, vanishingly small.

So the 1 in 100,000,000 number is based on a bogus assumption.

Brandon Berg said...

Regarding your point about average versus total utility, I think that both should be taken into consideration. Assuming that we have no control over the size of the population, it's unambiguously better to increase the average utility of a population of ten million by some given amount than it is to increase the average utility of a population of ten by the same amount.

Anomaly UK said...

Is it not also the case that if you vote, then people like you are more likely to vote too?
(Actually I think it probably isn't, but I can't work out why not)
The question in more detail