Kurt--
You wrote:
1) Are there cases where you would consider a candidate outside the Schwartz set to be the proper winner?
I reply:
Sometimes, when there are pairwise ties, Ranked-Pairs, or MAM, can choose outside the Schwartz set. But that; won't happen in a public election, where pairwise ties are vanishingly unlikely.
Whether the possibility of choosing outside the Schwartz set is a problem in committee voting is a matter of opinion. It's an aesthetic issue, not a strategy problem.
Though RP has that aesthetic disadvantage with respect to SSD or BeatpathWinner, it's also true that RP has an aesthetic advantage with respect to those methods: With RP, a nullified defeat can't participate in the nullification of anothler defeat. It makes sense for it to be like that.
So there are these not-really-important aesthetic differences between RP and SSD or BeatpathWinner.
I think those aesthetic differences are insignificant, and one should just recommend or propose whichever one is most likely to be accepted. For public elections, for a Condorcewt version, I like SSD, because I've encountered better reaction to it than to BeatpathWinner, CSSD or RP, and because SSD doesn't mention cycles or need them for justification. If people a really simple Condorcet version, then it's PC. I've talked to people on newsgroups who rejected anything more complicated.
You continued:
2) Are there cases where you would consider a candidate outside the Smith set to be the proper winner?
I reply:
I expect that everyone here agrees that it's better if Condorcet methods choose from the Smith set. All but PC will always do that.
Of course maybe someone could want PC's defining standard, and might want the candidate with the least maximum pairwise vote against him/her.
You continued:
I'm curious about that in terms of criteria/strategy, but I'm also curious about it in a larger way - because I think I remember Mike saying that if we could be assured of sincere ballots, he'd prefer the Borda winner - even if there were a different Condorcet Winner.
I reply:
Well, that's if we're talking about rank-counts. Without that requirement, then CR would be ideal if voters didn't care about optimizing their outcome, but only cared about voting sincerely, to do their part to maximize SU.
Some people point out that it can be a little problematic for all the voters to rates incerely on the same scale, to mean the same thing for all of them.. Methods that choose the CW don't have that problem, and I've recently posted about how well the CW maximizes SU.
So I don't know--Condorcet or CR to best maximize SU, when voters are completely sincere?
It's a moot point, since voters are inclined to strategize. In actual electorates, I'd expect Condorcet to ordinarily do the best job of maximizing SU. But some months ago someone pointed out how sometimes CR could do better, even with some people strategizing and some rating in proportion to utility.
You continued:
I disagree with that stance because I believe that it is simply more appropriate to accord equal power to each voter, rather than allow a passionate minority power over a less passionate majority.
I reply:
Sure, but what if voters aren't interested in power? What if the majority don't want majority rule, but want maximum SU?
You continued:
3) In a two candidate race, if 51% mildly preferred A to B, and 49% passionately preferred B to A, who should win?
I reply:
With existing electorates, under existing conditions, the majority should win, because otherwise there will be strategy problems.
In a different, Utopian, world, that would depend on whether there's a majority who don't want majority rule.
You continued:
I am also curious how "common" multi-member Schwartz (or Smith) sets are.
In all of the rank-balloting polls I've participated in or conducted, there hasn't been one circular tie. I doubt that I've even heard of a rank-vote that had a circular tie.
Sure, considering the Schwartz set to be a tie, for poll-reporting purposes is perfectly reasonable.
Mike Ossipoff
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