James G-A, I've been looking at your Sun.Jul.25 post in this thread. You wrote:
I wanted to talk about Condorcet completed by IRV (CCIRV) a bit more
here, beef up the proposal a bit. First of all, if there is a top cycle in the pairwise result, I'd like to
eliminate the non-members of the Schwartz set (union of minimal
undominated sets) before moving on to the IRV tally.
A little further you write:
The UMID set it seems to me is the same as "Condorcet Non-loser (Gross)", or the "Schwartz (Gross)" set; which could beMy proposal for IRV-completed Condorcet is to eliminate every candidate outside the UMID set before proceeding to the IRV tally. Okay, so the UMID set is like the Schwartz set, but a little different, because it takes into account whether a candidate is beaten by a majority or a minority. If there is a set such that no candidate within the set is majority-beaten by any candidate outside the set, then it's an inconclusively-dominated set. If it doesn't contain other inconclusively-dominated sets, then it's a minimal inconclusively-dominated set. So the union of minimal inconclusively-dominated sets consists of all the candidates who belong to a minimal inconclusively-dominated set.
defined as the smallest non-empty set of candidates for which it is true that none of the members are pairwise beaten by a
majority of ballots by any non-member. Or have I missed something?
If I am right, then doesn't your definition of this method need to include something about restricting winners to members of the
Schwartz set? Because otherwise couldn't it be possible for there to be a (net)CW who is not in the "UMID" set, and who doesn't go on to win the IRV count?
Chris Benham
http://lists.electorama.com/pipermail/election-methods-electorama.com/2004-July/013450.html
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