James--
You said:
The Pareto version I'm talking about is this: "If all voters prefer X to Y, and vote sincerely, then Y should not win."
I reply:
But that has the same malfunction as FHC. Though academic authors tend to be quite vague, I get the impression that Pareto is intended to be votes-only. Well, I can't claim to know what is intended when Pareto is mentioned, but the version that you quoted above shares FHC's malfunction.
Maybe there should be a Pareto Criterion similar to PMC. If everyone prefers X to Y, then they should have a sincere way of keeping Y from winning.
Sequential Pairwise is the notorious Pareto-failer. It fails the above version. It can't be said to fail the votes-only version, because Y can win because the XY comparison never gets voted on. When authors say that SP fails Pareto, it would seem that they can't mean votes-only Pareto.
But SP fails my Preference Pareto, as one would expect it to.
You could hypothetically suggest that SP could be carried out based on rankings, but that isn't how it's done.
SP fails your Preference Pareto too.
Well, those are my first impressions, but they could be wrong.
If both Preference Paretos are going to be mentioned more, they need to get separate names. I suppose they could be distinguished by lower-case abbreviations like oPC (opportunity Preference Pareto) or cPC (certainty Preference Pareto).
Mike Ossipoff
_________________________________________________________________
Don�t just search. Find. Check out the new MSN Search! http://search.msn.click-url.com/go/onm00200636ave/direct/01/
---- Election-methods mailing list - see http://electorama.com/em for list info
