[EM] RE:MMPO, contd
simmonfo at up.edu
Fri Jun 3 18:59:01 PDT 2005
Near the end of his message Mike wrote ...
It seems to me that the first step of sprucing-up was to eliminate every
candidate who isn't in a certain selection set. The set of candidates who
could win without violating BC? And then was that followed immediately by
the collapsing of beat-clone-sets? A two-part procedure?Anyway, I guess I'll
keep looking. But Forest, could you post the full complete definition when
you get a chance to?
The "certain selection set" evolved over time from Smith, to Uncovered, to Banks, to Duda, to "Minimal Covering Set," and yes, that step was followed by clone collapsing, but I abandoned the spruce up quest for two reasons:
1. It satisfied Smith, which I came to believe was too restrictive. [And we suspect that Smith is incompatible with the FBC.]
2. Spruced up random ballot turned out to be non monotonic, due to the restriction to the Uncovered Set (or its more restrictive subsets). And I suspect that clone collapsing by itself could also impair monotonicity; I'm not sure.
So the method never came to a definitive form.
The nearest it came to a definitive form was in a posting that I wrote in reply to somebody that wanted to do a Wiki page on it. I'll try to find that if you want me to. Ted Stern was following the discussion pretty closely back then; perhaps he can find it.
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