Stephane Rouillon wrote:
I agree, provided "the ones I like" means the ones I consider better than average.1) I would cut all candidates into two equal groups the ones I like, the ones I do not.Without poll information, I believe it is the vote that would optimize my voting power...
No, here I disagree with you. In the good-information case, you don't need to worry about whether a candidate is better or worse than average ("liked" or "not liked"); only ordinal rankings are needed.2) If I can get some poll information I judge reliable enough: out of my desired candidates, I would vote for the one I prefer the most and would approve too all my desired candidates that obtain a better position according to the poll. Example: sincere preferences A>B>C>D | E>F>G>H No poll: vote ABCD. The poll: D>H>B>A>C>G>F>E. I would vote ABD. Is it the same you say?
In the example you cite, I would not vote ABD, but rather ABCD. It makes no sense to vote for D and not for C. If there are many voters who think like you, then your support for C may allow C to beat D. There isn't really a reason in approval to vote for one candidate and not approve a candidate you like more.
Moreover, your strategy could easily end up making you not vote for either leading candidate. Take the case of A>>B>C sincere preferences, and C>B>A in the polls. Your strategy suggests voting for A and not for B, which is clearly not optimal since the race appears to be between B and C.
Once again, I suggest that you should vote for every candidate you like more than the front-runner, and also vote the front-runner if you like him/her more than the second place candidate. Say your preferences are A>B>C>D>E>F, and the polls show C>E>D>B>F>A. You should vote for A and B because you prefer them to the front-runner C, and you should vote for C because you prefer C to E (the second place candidate). So your vote is ABC.
-Adam
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