[EM] Majority winner set

[Markus Schulze]

Dear Mike,

you wrote (24 Nov 2000):
> 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.

FPP violates Condorcet and beat path GMC.

Example:

   40 voters vote A > B > C.
   35 voters vote B > C > A.
   25 voters vote C > B > A.

   Due to the Condorcet criterion, candidate B must be
   elected. Due to beat path GMC, candidate B must be
   elected. But the FPP winner is candidate A.

   In the example above, I didn't make any presumptions
   about whether the voters vote sincerely or strategically.
   In the example above, I didn't make any presumptions
   about the sincere opinions of the voters. Did I?

Markus Schulze