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PhilGoetz comments on Aumann voting; or, How to vote when you're ignorant - Less Wrong
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Voting to "cancel out an idiot" is possibly acceptable as a first-order approximation, but sorely lacking beyond that.
Even assuming single-issue voting on a question that is completely linear, if you believe that the correct point is at point X% of the way from A to B, where Y% of the idiots vote towards A and (100-Y)% towards B, a second-order approximation of rationality would mean randomly voting toward one side or the other in proportion to the difference between X and Y such that if X and Y are equal you flip a coin.
That approach would be good if there were a large number of people using this strategy, or if you voted many times on the same issue.
In this case, moving to Chicago is an option.