Wednesday, October 19, 2005

Rational Voting

Andrew Gelman cleanly and clearly convinces me that voting is rational:
For example, consider a two-candidate election with n voters. Suppose the election is anticipated to be close, and each candidate is expected to get between 47 and 53 percent of the vote (and thus the vote differential is expected to be in the range ±6%). The probability that a single vote is decisive is then about 1/(0.12n).6 So for a selfish voter, the expected utility gain from potentially swinging the outcome of the election is about B_self/(0.12n), which even for a moderately large election (e.g., n = 1 million) is minor: even if the outcome of the election is worth $10,000 to a particular voter, the expected utility gain is less than 10 cents. This point has been widely recognized (see the references at the beginning of this paper). Given that the act of voting has a nonzero cost, voter turnout is thus usually attributed to some mix of irrationality, confusion, and the direct gratifications of voting (including the performance of a civic duty); that is, a negative net cost c of the act of voting. However, these motivations do not explain observed variations in voter turnout between elections. In addition, voting is an act with large-scale consequences beyond any immediate satisfaction it gives to the voter. At the very least, many voters seem to consider their voting actions with more seriousness than other low-cost consumption decisions.

[...]

For example, consider the same hypothetical election as above, in which the n voters represent a jurisdiction with population N. Further suppose that 1/3 of the population are voters; that is, n/N = 1/3. If you, as a potential voter, think that the net benefit to your fellow citizens of candidate A winning the election is the equivalent of B_soc = $10 per citizen, then you are effectively giving them a total of $10N/(0.12n) = $10N/(0.12(N/3)) = $250 in expected value by voting. Voting in such a circumstance is a perfectly reasonable thing to do, regardless of population size: a small effort yields a substantial expected social gain, equivalent in some ways to giving $250 to a national charity. For example, if your discounting factor for benefits to others is a = 0.1, then your net utility gain from voting is positive as long as your cost of voting c is less than $25. In many elections with issues such as national security, global climate change, and nuclear weapons proliferation, a rational citizen could think that the superiority of his or her candidate might deliver an expected value per citizen far in excess of $10, and thus an expected return on voting far in excess of $250.
Of course the only way it isn't rational is if you only care about yourself. By and large, people also care about others.

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