[EM] RE: MMPO satisfies FBC in the general case

Simmons, Forest simmonfo at up.edu
Mon May 23 19:52:27 PDT 2005

Kevin, thanks for supplying the details of MMPO's FBC compliance.
I never doubted it since I suggested it back in March 2003, inspired by your "median winner" method for two slot ballots.
I was discouraged when Markus and Steve pointed out to me that MMPO failed Clone Winner, since Clone Winner compliance is important for avoiding the spoiler problem.
It seems like there should be some way to get around that.
As you know, the problem is that an MMPO winner with a max pairwise opposition of, say 40 percent, could be replaced by a cycle in which each member was opposed pairwise by some other cycle member on more than 60 percent of the ballots.
In a case like this it seems natural to collapse the cycle, and then when the MMPO winner turns out to be the collapsed cycle, find the MMPO winner within the (reconstituted) cycle.
Spruced Up MMPO would be too drastic.  Perhaps leaving off the first stage of the spruce up process, and proceeding directly to the "beat clone collapse" stage would do the trick.
How about Reynaud (PO)?  Does the sequential elimination  wreck the FBC?
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