[EM] Majority winner set

[MIKE OSSIPOFF]

Markus wrote:

Beat path GMC is defined in terms of voted preferences.
Beat path GMC is met e.g. by Schulze(wv)

I reply:

Ok, that was what I'd thought, but the other day you posted a
definiton in terms of people preferring one candidate to another,
and the natural interpretation of that is felt preferences,
sincere preferences. But I recognize that BPGMC is in terms of
voted preferences, and therefore I agree that BeatpathWinner meets
BPGMC.

And so does Plurality.

I'm not just picking on BPGMC. The usual definitions of the
Condorcet Criterion have the same problem. When CC is defined in
terms of sincere preferences, as it often is, then no method meets it.
When it's defined in terms of voted preferences, then Plurality meets
it.

So here's how I define the Condorcet Criterion:

If there's a sincere CW, and if everyone votes sincerely, then
the sincere CW should win.

Sincere Voting:

A voter votes sincrely if he doesn't vote a preference that isn't
a sincere preference or leave unvoted a sincere preference that the
balloting system would have allowed him to vote in addition to the
preferences that he actually did vote.

(By "preference", I mean "pairwise preference")

[end of definition]

A similar fix could fix BPGMC, as well as Condorcet Loser,
Mutual Majority Criterion, etc., which share that problem.

Mike Ossipoff





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