A while back, it was said that Smith//Condorcet had a problem peculair to it, in which it would choose the same alternative when people were voting for the worst that it chooses when people vote for their best. Before I talk about why I don't expect that to happen in typical situations, I want to first add that it doesn't seem to me that it would be a problem even if it did happen. We've talked about various standards & principles that are important to us, & to many others, like LO2E & majority rule (Sorry, Mike S.). And the further-refined desire to avoid less gross violations like clone-set subcycle fratricide. But is it really important what happens if we were to reverse all the rankings? Say there's a Smith set, & there are also alternatives that aren't in the Smith set. When we reverse all the rankings, the former members of the Smith set become the set of alternatives such that every alternative in the set is beaten by every alternative outside the set. Smith//Condorcet wouldn't choose its winner from tht set. But say that there are no alternatives outside the Smith set (is that likely in a public political election?). Or that we're talking about plain Condorcet rather than Smith//Condorcet: For Condorcet to pick the same alternative whether or not the rankings are all reversed, that requires that the alternative whose greatest pairwise defeat is the least is also the alternnative whose greatest pairwise win is the least. How likely is that in a real election? Is it something to justify saying that a method has a problem? I'm not saying it could never happen. A long time ago somoene pointed out that plain Condorcet (but not Smith//Condorcet) fails the Majority Loser Criterion. I pointed out at the time that that only happens in a bizarre & hopeless bottom-end situation where the candidate who has fewest people preferring anyone else to him is also the candidate who is the last choice of a majority. I agree that "strange" is indeed the word for a situation like that. Again, not the kind of thing that, in my opinion, justifies saying that a method has a problem. I'm interested more in what happens at the top-end, when there's a Condorcet winner, when a good outcome is possible, not in improbable, bizarre, hopeless bottom-end situations. Mike Ossipoff
