Cycle Definition of BeatpathWinner

[MIKE OSSIPOFF]

Markus wrote:

you wrote (21 Sep 2002):
>A defeat is nullified if it's in a cycle that doesn't
>include a weaker defeat. A candidate wins if he doesn't
>have an unnullified defeat. This is a briefer definition
>of BeatpathWinner. It has as obvious & natural motivation
>& justification as CSSD, but it's much briefer than either
>the BeatpathWinner wording or the CSSD wording.

The definition above is incorrect.

Example:

A:B=52:48
A:C=53:47
A:D=49:51
B:C=56:44
B:D=45:55
C:D=54:46

Candidate A is the unique winner. However, also candidate D
has no unnullified defeat.

I reply:

Apparently so. I was sure that I had a demonstratation that anyone
who wins in BeatpathWinner wins in NIN, and that anyone who doesn't
win in BeatpathWinner doesn't win in NIN.

In that example, BeatpathWinner chooses A, RP chooses D, and
NIN choosess A & D.

OF course 2 winners in an election with no pairwise ties or equal
defeats isn't good, even if they're the winners by BeatpathWinner/CSSD
and RP.

Too bad, because NIN combined extreme brevity with obvious justification.

But now the best public-use definition for BeatpathWinner/CSSD is still
the CSSD definition, because of its obvious motivation & justification.

Mike Ossipoff




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