It really is not a mystery why people vote, after all. Given the importance of who wins, even a tiny probability of being decisive is enough, if the voter is altruistic.

I came across "Estimating the Probability of Events That Have Never Occurred: When Is Your Vote Decisive?" by Andrew GELMANG, Gary KING, and W. John BOSCARDIN,

*Journal of the American Statistical Association*, March 1998, Vol. 93, No. 441,p. 1. Professor King of Harvard certainly does interesting work. On page 5 it says:

... the 1952-1988 elections. For six of the elections, the probability is fairly independent of state size (slightly higher for the smallest states) and is near 1 in 10 million. For the other three elections (1964, 1972, and 1984, corresponding to the landslide victories of Johnson, Nixon, and Reagan), the probability is much smaller, on the order of 1 in hundreds of millions for all of the states. This strong dependence of the estimated probability on the size of the victory margin invalidates most of the existing theoretical models.

1 in 10 million is really a huge number, in this context at least (not in most, I guess). If the difference between Bush and Kerry is worth 10 billion dollars, a trivial amount on the international scale, then a vote is worth $1000.

Even in a landslide year, a vote is worth perhaps $2, if $10 billion is at stake. But in those years, people think the amount at stake is bigger too. We can work the calculation out the other way using that thought. Suppose it costs $20 to vote. The marginal voter thought that $200 million was the difference between Clinton and G.H. Bush. He thought perhaps $10 billion was the difference between Goldwater and Johnson. These amounts seem way too small, not too large.

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