I can see that Ilya Somin and I will probably go a couple more rounds in our discussion of rational voting.

Nonetheless, I confess that I was surprised by Ilya's response in a post below.

**Here is Ilya's first point:**

But Ilya, surely you understand that it is YOUR EQUATION that is linear. If you run the numbers through your own equation, you get EXACTLY the results I reported. You assume that each and every voter on average would value a guarantee of his own preference for president at $5,000 for one person's benefit and altruistically internalizes 1.5 billion dollars of the benefit of others.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:

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.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.

Dividing the $1.5 billion altruistic utility that your equation and example say that each voter on average acts on in choosing to vote by 100 million to generate a benefit of $15 does not make your equation any less linear, a fact that you surely know. If the relationship is not "purely linear" (or even remotely linear), then your equation is dead wrong because your equation is purely linear.

Really, you can forget about whether the supposed $1.5 billion converts to income in a linear fashion, since my critique does not actually depend on whether you are now partially undercutting your earlier claim that the utility you posit has direct dollar equivalents.

As my own speculative example hinted at, I doubt that most voters valuing a win for their preferred candidate at $5,000 (your assumed utility value) would altruistically value and internalize into their own decisionmaking the utility of victory for others at more than $5,000-50,000, certainly nothing even close to the $1.5 billion value for altruism you posit as being present on average.

Remember, you need such a huge altruistic value for total utility or your hypothesized rationality doesn't appear. Would someone rationally incur a $10 loss to gain a 0.005 cent to 0.05 cent gain in utility, as my more reasonable assumption of total utility would generate? Even if your model had assumed nonlinearity or nonequivalence in money (neither of which you actually assumed in your article), there still would be a massive gap between the 1.5 billion in total internalized utility that you assume on average and the $5,000 to $50,000 total internalized utility that I would assume on average.

I guess I've persuaded you that your equation is wrong, because in your response you appear not to think that each and every voter on average values the winner at 1.5 billion dollars, which is the number that your equation and your hypothetical example yields.

Related Posts (on one page):

- Still More on Rational Voting - 2nd Reply to Jim Lindgren:
- Rational Voting: Second Lindgren Post (Responding to Somin).--