[EM] Participation & SARC

[Markus Schulze]

Dear Mike,

you wrote (10 May 2000):
> Markus wrote (10 May 2000):
> > Mike 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 said the voters were sophisticated, but you didn't say they
> were perfectly informed. But if that's added then what you said
> matches what I'd heard.

By definition, a "sophisticated" voter
(1) is perfectly informed about the sincere opinions of the other
    voters and
(2) takes the sincere opinions, the possible strategies and the
    possible counterstrategies of the other voters into consideration
    when he decides how to vote so that his own utility expectation
    is maximized.

******

You wrote (10 May 2000):
> Markus wrote (10 May 2000):
> > Mike 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.
> >
> > 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.
>
> Interesting. I hadn't heard about Moulin's statement.  So when
> complete information is available to the voters, an added group
> of voters who have the same preferences & vote the same way
> can worsen their outcome, no matter what the method is.
>
> Maybe that could be considered the strongest adverse-results
> criterion, met by no methods.
>
> Of course SARC would be unmeetable too if it were about worsening
> one's outcome, rather than just defeating one's favorite or
> electing one's last choice.

If you want to say that Approval Voting guarantees that if the
voters are sophisticated then a like-minded group cannot change
the winner from their favorite to a different candidate or from
a different candidate to their least prefered candidate then I
have to answer: I see no justification for this claim. Could
you please give a heuristic or a proof of this claim?

Markus Schulze
schulze at sol.physik.tu-berlin.de
schulze at math.tu-berlin.de
markusschulze at planet-interkom.de