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Boy is S.M. at The Economist's "Democracy in America" blog having to engage in contortions to defend the rationality of voting.

Launching off from Katherine Mangu-Ward's really excellent summary of the case against voting, S.M. invokes Gelman's argument that large N elections both reduce the probability of decisiveness and increase the potential benefits from winning.
The mathematics are convoluted, but the message is simple: even with a one in 10m chance of casting the decisive vote, the stakes are high. In fact, the lower the odds are of influencing the vote, the higher the stakes. This is because everything scales linearly and more people will bear the brunt—or enjoy the benefits—of a country led by candidate X rather than candidate Y. So your vote in Ohio, Wisconsin or another tipping-point state is worth $60,000 to your fellow citizens. That’s a pretty good return on the investment of the hour or so it takes to vote.
Except that the very fact of your decisiveness in the election proves that half of all voters disagree about whether you're making the world a better or a worse place! You can only be decisive by making or breaking a tie. That happens when half the voters think you're rather wrong. And, unless you are in an epistemically privileged situation relative to other voters (and why would you think you are!), you can't know whether you're on the right side or the wrong side. Gelman's a great statistician, but I've never liked his argument here.

Worse, S.M. pulls a pretty shonky Kantian move.
This misses the point of the Kantian argument for voting. The idea is not that one person’s decision to forgo voting would crash the system—how would that possibly happen?—but that it is immoral to act on a maxim that we cannot imagine everyone else acting on. So if I consider adopting Ms Mangu-Ward’s proposed maxim—I will abstain from voting because the costs of voting outweigh the benefits—I will first need to see if the maxim passes a test implicit in Kant’s categorical imperative. I ought not act in accordance with the maxim if it fails the test.

So let’s see: can I universalise the non-voting maxim? Can I imagine living in a world in which every eligible voter opts for a nap or a game of Temple Run in lieu of going to the polls? No. The logic of American democracy does not support such a universalised principle. No one votes, no one is elected, a moment of constitutional failure brings an emergency convention in which unelected delegates draft a new constitution calling for an alternate system of specifying leaders that doesn’t involve the public. The franchise, and America as we know it, disappears. Since the logic of the system cannot be sustained were everyone to adopt the nap-over-voting maxim, I am morally bound not to act on it.
Here's the universalisable version. Two weeks before the election, flip a coin. If it comes up heads, flip it again. If it comes up heads, flip it again. If it comes up heads a third time (a 12.5% chance), study hard about the policy options, decide which candidate is best, and then go vote. If everybody does that, there's a non-trivial chance of being decisive (maybe we'd need four heads in a row to be more sure) and so you've an instrumental reason to get out and vote - and to vote more sensibly. At current levels of turnout, it's clear that everybody else is failing to play the universalisable Kantian "vote at low probability" rule, so a good rule of thumb is then "Don't vote unless turnout looks low enough; if turnout is low, run the coin flips."

The simplest and most plausible way of squaring voting with rationality is simply to recognize that people like doing it for its own sake. We don't try to come up with stories about how onanism increases reproductive fitness; it's done for its own sake. Same with voting. Unfortunately, that breaks most of the normative desirability of median voter outcomes.