I am curious about the answers to the following questions regarding Condorcet. Forgive me if these are simplistic, I am kind of looking for a summary of what the consensus is here:
1) Are there cases where you would consider a candidate outside the Schwartz set to be the proper winner?
2) Are there cases where you would consider a candidate outside the Smith set to be the proper winner?
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 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. Who's to say the minority is not ignorant as well as passionate? I guess an alternate way of asking the larger question is:
3) In a two candidate race, if 51% mildly preferred A to B, and 49% passionately preferred B to A, who should win?
I was surprised to find out that some of you might say "B". If that is true, then I find the discussion emphasis on Condorcet tiebreakers kind of odd. (For those of you who would say it depends on whether it is a political vote... I might agree with that. But I am mostly thinking of political votes when I ask the question.)
I am also curious how "common" multi-member Schwartz (or Smith) sets are. This is an abstract question but I think it makes a difference to the layperson how controversial the results of a voting method would be. People tend to be concerned about circular victories, but if they could be told that they are very rare, or at least likely to be less common than our current rate of contested elections, then it could help. But I have no sense on how common the circular scenario is. Perhaps it could be compared to plurality elections finishing within a particular vote margin or something.
Finally, I am curious if anyone has presented a solid way to figure proportional support for multiple candidates in a Condorcet election. For instance, given a particular Condorcet result among five candidates, can you look at the overall "available support for all candidates" and say that Candidate A had x% of it, Candidate B had y% of it, etc? Obviously, the first place CW must have the highest percentage, etc. The last time I asked, people mused about using average vote margins between a candidate and all the people that the candidate defeated, but this ended up being problematic. This is relevant for questions like how to award delegates in Democratic primary battles, how to find out how close the 2nd place candidate was to winning, tracking how public support for a candidate/issue ebbs and flows over election cycles, etc.
I tend to carry around the definition in my head that Condorcet methods are "perfect" up through the identification of the Schwartz Set. For public polling purposes, I would probably just communicate a multi-member Schwartz Set as a tie.
Thanks, Curt
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