Forest:
You were the first proponent of the Approval strategy that I call Better-Than-Expectation. It's certainly one of the best, maybe the best unless the voter has a strong opinion about 2 frontrunners, or about whether, for a particular candidate, the threat of someone worse winning is worse than the promise of someone better winning.
But you spoke of it in terms of the voter calculating his/her expectation by multiplying each candidate's win-probablity by that candidate's utility. Of course few voters would do that. The easier use of Better-Than-Expectation is to just estimate what the value of the election is, compared to the merit of the various candidates. For some 2 candidates Smith & Jones, the value of the election is perceived to be between that of Smith and Jones.
Or, as I was saying before, for a particular candidate that you're consisdering voting for, vote for him/her if s/he's so good that you'd rather have him/her in office than hold the election.
We've discussed a number of Approval strategies that can be used when the information isn't 0-info, and when the candidates aren't in 2 sets such that the merit differences within the 2 sets are negligible compared to the merit difference between the 2 sets--but those two conditions are covered by the strategy methods that we've discussed. Better-Than-Expectation is one of those general-applicability strategies.
Of course, under that latter condition, it would be enough to just say "Vote for the better-set candidates, and not for anyone else". That condition allows that shortcut, and makes Approval voting especially simple.
Though Better-Than-Expectation is one of the best, there are a few others that have been discussed here:
Best Frontrunner:
If you consider a particular two candidates, F1 & F2 to be likely to be the top-two votegetters, and expect the election to be a contest between those two, then vote for whichever of those two you prefer to the other.
In postings a few months ago I discussed some enhancements of Best-Frontrunner, and I've posted about those strategies more recently too. For instance, if one wants to consider the possibility that a candidate other than those two could be one of the toip-two, then one might vote for candidates whose merit is between those of F1 & F2. Previous postings, a few months ago and more recent, describe those Best-Frontrunner enhancements. Strategy A is the same as one of those, though the wording sounds different. Sometimes strategy A would be the one to use, sometimes a different one would be the one to use.
Those previous postings tell when to use those various Best-Frontrunner enhancements.
Threat/Promise:
Vote for a candidate, X, if, should you not vote for him/her, the threat of someone worse winning is greater than the promise of someone better winning.
By threat, I mean the difference between X's merit and the expectation contribution of the worse candidates. By promise, I mean the difference between X's merit and the expectation-contribution of the better candidates.
Again, one would estimate which of those differences is greater without actually calculating the expectations.
Of course, Threat/Promise is very close to Better-Than-Expectation. Slightly different question.
Better/Worse:
Vote for a candidate if, should you not vote for him/her, it's more likely that someone worse will win than that someone better will win.
Similar to Threat/Promise. It seems to me that Threat/Promise's question is more natural, more likely that a person would have a feel for. Easier to judge fear and promise than to estimate probabilities.
Those are the main Approval strategies that have been proposed. They're all good for different situations, when different questions or answers are felt by the voter.
I should add that often, maybe usually, the voter will know whom s/he wants or doesn't want to vote for, and won't need the abovementioned methods. The strategy methods described above are for when it isn't otherwise obvious whom you want to vote for.
Mike Ossipoff
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