From: Anthony Duff <[EMAIL PROTECTED]> Subject: Re: [EM] approval strategy
My favourite approval strategy to recommend generally is "vote for your strategic plurality candidate and every candidate you like better." (suggested to me by Marc LeBlanc)
Besides Kevin's suggestion (approve everybody that you like better than the average of the two front runners) and this one of Anthony's, here's one that has been called "Strategy A" by Rob LeGrand:
First approve all candidates that you like better than the one, say X, that is most likely to win. Then if some candidate that you like less than X is more likely to win than any candidate that you like more than X, then approve all of the candidates that you like as much as X, too.
Another strategy (due to Joe Weinstein) is to find a candidate Y such that there is a 50% chance or better that the winner will be as good as Y, and a 50% chance or better that the winner will be as bad as Y. Approve all of the candidates you like better than Y. Approve Y also if it is as likely that the winner will be worse than Y as it is that the winner will be better than Y.
In a zero information election this strategy reduces to "approve median and above."
If you change "as likely" to "more likely" in the strategy, then the zero information case reduces to "approve above median."
The basic idea of these last few strategies is that the strategic voter wants to maximize the conditional probability that his ballot would tip the balance in favor of the best member of a tied set, given the condition of an approval tie without his ballot.
Since most tied sets will be ties among only two candidates, the most important thing is to set your approval cutoff between the two front runners. Beyond this everything is frosting on the cake.
Of course, it may happen that both front runners are so bad that you cannot support either in good conscience. In that case you should move your cutoff up to the level of someone that you can feel good about. Then get one of those bumper stickers that says, "Don't blame me; I voted for [fill in your decent candidate]."
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