Forest/Warren/all, One serious disadvantage that the new Simmons method (in pure form) has is that it has a nasty Local IIA problem, and fails what I might call "Independence of/from Irrelevant Candidates" which says that if there is some losing candidate X with fewer top preference votes than any other candidate and which is pairwise beaten by every other candidate, then dropping X from the ballots can't change the winner. This is a weak criterion that is easily met by IRV and arguably by all good methods.
02: X>A>B 24: A>B 25: C>A 49: B>C (maybe sincere is B>A or B) A>B>C>A. "Simmons" scores: A25, B24, C49 B has the lowest score and so wins, but if X is dropped from the ballots then B's score rises to 26 and A wins. Those two X supporters have a "semi-clone" split-vote problem. This problem can be easily patched up by first dropping from the ballots all non-members of the Schwartz set before applying this simple Simmons method (to give "Schwartz//Simmons"). Warren Smith wrote: > actually, Simmons is NOT a Condorcet method at all, > in the sense that it is entirely possible for a unique > Condorcet winner W to exist, but Simmons does not select W as the unique > winner, instead claiming that several candidates are tied for winner. > > This usually happens when W has zero top-rank votes. > > I'd pointed that out before but this makes it clearer. > > Similarly, Simmons does not really obey the Smith set property. > My suggested patch would also of course fix this problem. Chris Benham ---- election-methods mailing list - see http://electorama.com/em for list info
