Dear Mike,
you wrote (9 May 2000):
> Markus wrote (9 May 2000):
> > Very frequently it is presumed that if Approval Voting is used
> > then the voters (if they are sophisticated) vote in such a way
> > that a Condorcet winner (if one exists) will always be elected.
>
> I doubt that anyone makes that claim. Riker showed, however, that
> if voters have complete information about eachother's preferences
> (and maybe about eachother's actual voting), the sincere CW will
> always win, regardless of what the method is. Of course that's as
> true for Approval as for any method.
Where is the difference between these two claims?
******
You wrote (9 May 2000):
> Markus wrote (9 May 2000):
> > If this presumption is true then even Approval Voting doesn't
> > guarantee that a like-minded group isn't punished for going to
> > the polls and voting in a sophisticated manner. The proof of
> > this fact is very similar to Moulin's proof that Condorcet and
> > participation are incompatible.
>
> I don't know how that conclusion follows, and anyway, I don't
> agree with the premise.
Do you mean Riker's premise or the other mentioned premise?
Moulin proved that it is possible to construct an example such
that independently on who is elected it is always possible to
add a like-minded group such that a candidate to whom the actual
winner is prefered by this like-minded group becomes a Condorcet
winner. If it is true that a Condorcet winner (if one exists) is
always the unique sophisticated winner then (if the voters are
sophisticated) this like-minded group is punished for going to
the polls because this group prefers the original winner to the
new winner.
Markus Schulze
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