[EM] Majority winner set

[Bart Ingles]

Bart Ingles wrote:
> 
> Markus Schulze wrote:
> >
> > 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?
> 
> Uh, yes, you presume the voters will vote sincerely in FPP, in order for
> A to win.

My mistake, I can't say that you presume sincere voting for FPP, since
you don't specify whether the rankings are sincere.  On the other hand,
the example is not sufficient to show A as the FPP winner.