CarlShulman comments on Voting is like donating thousands of dollars to charity - Less Wrong
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I rarely make decisions involving such low probabilities, so I don't really know how to handle risk-aversion in these cases. If I'm making a choice based on a one-in-ten-million chance, I expect that even if I make many such choices in my life, I'll never get the payoff. This is quite different than handling one-in-a-hundred chances, which are small but large enough that I can expect the law of large numbers to average things out in the long term. So even if I usually subscribe to a policy of maximizing expected utility, it could still make sense to depart from that policy on issues like voting.
BTW, in my state, Maryland, Obama has a 18-point margin in the polls. That could easily be six standard deviations away from the realm where I even have a chance of making a difference.
Voting for electoral impact doesn't make sense from a causal decision theory selfish point of view: you won't consider a $1 trillion gain to the U.S. to be a billion times as great as $1,000 for you. This argument presumes that you have a "risk-neutral charity budget."