Choice of Approval strategies depends largely on what you prefer to estimate.
I suggested a strategy that I called Expected Differences, which, for deciding whether to vote for candidate X, requires judging the probability that X will be in a tie or near-tie with someone better, or someone worse, and the expected utility difference between that better or worse candidate and X.
Forest suggested Better/Worse, which merely requires an estimate of whether the winner is likely to be better or worse than X.
But how about another simplification of Expected Differences:
Just ask whether the threat from worse candidates than X is greater than the promise of better candidates than X.
That sounds like Better/Worse, but, instead of asking whether someone better is more likely to win than someone worse, it asks whether the expected worseness is greater than the expected betterness. Arguably one has a feel of whether fear of worse is greater than promise of better, more than one has an estimate of whether worse is more likely than better.
Threat/Promise, along with Better-Than-Expectation, is probably the next simplest thing than just asking yourself if you feel like voting for X.
Like Better/Worse, Threat/Promise is very similar to Forest´s Greater-Than-Expectation strategy, which asks if X is better than the expected outcome. In other words, Greater-Than-Expectation says to vote for X if you´d rather have X in office than hold the election.
It´s a small step from saying to vote for X if the expected worseness from someone worse winning is greater than the expected betterness of someone better winning to saying to vote for someone if s/he is better than the election´s expectation.
Usually you´ll know whom you want to vote for and whom you don´t want to vote for, but, when you don´t, that´s when strategies such as these and the others we´ve discussed will be useful.
If there´s a strong feeling about two candidates being the likely frontrunners, then maybe one would feel like using one of the Best Frontrunner (BF) strategies that have been discussed here.
Having recently posted a list of those BF strategies, and suggestions for choosing among them, I shouldn´t repeat that here. BF is important since it´s what voters say they´re using now, though they´re using it without reliable information.
Strategy A sounds very different from BF(1st), but it amount to the same thing. BF(1st) is basically a rewording and renaming of Strategy A. It seems to me that BF(1st)´s wording is simpler and more obvious and that its name more descriptive.
If there´s no information and no estimates other than the candidates´utilities, then use the 0-info strategy of voting for the above-mean candidates.
And lastly, if the candidates are in 2 sets such that the merit differences within the 2 sets are negligible compared to the merit difference between the two sets, then of course vote for the better set candidates and not for anyone else. That isn´t really a different strategy, since all the strategies lead to it. But when its premise is true it makes voting much simpler. I claim that its premise is true in our political system.
Even if you don´t agree with me about the last sentence of the paragraph before this one, it would be difficult to deny that our elections are 0-info. So the two paragraphs before this one are my suggestions for Approval voting in the elections in the U.S., with the current political system, because the conditions match the premises of those two paragraphs.
I know I´ve recently said this too, but, in Plurality the 0-info strategy is to vote for your favorite.
And, in Plurality, if there are 2 sets of candidates such that the merit differences within the two sets are negligible compared to the merit difference between the sets, then vote for whichever better-set candidate is most likely to take victory from a worse-set candidate.
Mike Ossipoff
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