Co-blogger Jim Lindgren has a thoughtful response to my analysis of the rationality of voting. To briefly recap, I argue that voting is rational if 1) voters value the utility of their fellow citizens as well as their own, and 2) they perceive a big enough difference between the "right" candidate and his or her opponent. In reply, Jim makes the point that I may overestimate the extent to which people value the utility of others relative to their own. I assumed, in my analysis, that they value benefits to fellow citizens on average, 1/1000 as much as they value benefits to themselves. Jim argues, however, that:

Ilya's equation assumes that, if a voter could guarantee a victory for his preferred candidate, a typical voter would be willing to pay only $5,000 for one person's benefit (presumably his own), but that the same voter would be willing to pay about $1.5 billion dollars to benefit others ($5,000 x 300 million people / 1000). In other words, Ilya assumes that a rational voter when voting values the total utility of other Americans 300,000 times more than he values his own total non-altruistic utility ($1.5 billion to $5,000). Moreover, even leaving aside the comparative valuation, it can’t be that (because of altruism) the utility to each person voting of having one’s preferred candidate certain to win would be $1.5 billion dollars. To say that these are extraordinarily implausible assumptions is an understatement.

I have two responses to Jim's point, one technical, the other intuitive. Let's take the intuitive point first: Jim's analysis assumes that the relationship between the amount of money you are willing to give up to benefit others and the amount of benefit they receive from the sacrifice is purely linear. That is, if you are willing to give up $1 so that your neighbor will get $1000, you are also willing to give up $1.5 billion in order to give your fellow Americans $1.5 trillion. To my mind, the second doesn't necessarily follow from the first. Jim has shown that my analysis becomes implausible in cases where the voter/citizen is called upon to make very large sacrifices. When we're talking about voting, we're generally talking about a very small sacrifice.

Second, the technical point. Jim has (understandably) conflated the distinction between dollar income and utility. My analysis assumes that people value the utility of others at 1/1000 of their own, which is not the same thing as valuing the added dollar income of others at 1/1000 of the rate at which you value adding dollars to your income. When we're talking about making a sacrifice of $35,000 out of a $50,000 annual income (to use Jim's example), we're talking about a vastly greater loss of utility to the donor than when we're talking about sacrificing $10. And the difference between the two may well be much greater than $35,000/10. The $10 sacrifice is essentially trivial, while the $35,000 may wreck the donor's life for months or years to to come.

The slightly altruistic donor/voter of my model might well reason that this massive sacrifice on his part outweighs the utility gain to the rest of the population from having the right candidate win, so long as he discounts the latter by a factor of 1000. It's worth noting, however, that there are in fact people who sacrifice the equivalent of 70% of one year's income to try to ensure that their preferred candidate will win an election. Many campaign volunteers do precisely that. I suspect that there would be more such people if they could be assured that their sacrifice would guarantee victory, rather than just increase the likelihood somewhat at the margin.

In a large and diverse electorate, the 1/1000 figure is best viewed as a rough average rather than as a precise estimate of every individual voter's degree of altruism. In reality, some people are much less altruistic than this and others more so.