[EM] Condorcet Criterion for plurality.

[Bart Ingles]

Markus Schulze wrote:
> 
> Dear Bart,
> 
> you wrote (25 Nov 2000):
> > Markus wrote (25 Nov 2000):
> > > 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?
> >
> > The example is not sufficient to show A as the FPP winner.
> 
> Why?

You said you weren't making any presumptions about whether the voters
were voting sincerely, so there is no telling how they will vote under
different systems.  Even if they were ranking sincerely here, that is no
guarantee that they would vote sincerely under FPP.

Even in the absence of polling information, the positions of the
candidates on a policy continuum might be enough to make it obvious
which of them is a potential Condorcet winner -- in which case the
voters might think it safer to vote for the Condorcet winner.  Depending
on the candidate's utilities to the voters, of course, which throws
another variable into the equation.

If you were saying that the above _was_ FPP, i.e. the rankings were
solicited but it was known in advance that they would never be counted,
then I suppose you can say that A is the FPP winner, but in that case
the rankings are not directly comparable to rankings collected under any
other system.

Bart


> You wrote (11 Dec 2000):
> > You are also making an unstated assumption that voters have no
> > knowledge of the other voters' preferences, or at least of the
> > candidates' relative positions in the political spectrum.
> 
> Please explain!
> 
> You wrote (11 Dec 2000):
> > Anything can be defined as anything, but defining Plurality
> > on preferential ballots doesn't make it the same Plurality as
> > is used in the U.S. and U.K.  To use two different meanings of
> > the same term interchangeably is a logical fallacy (equivocation).
> 
> Please explain!