[EM] Participation & SARC
nkklrp at hotmail.com
Wed May 10 17:53:23 PDT 2000
>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 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.
>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?
I didn't agree with the other premise until I understood that
it's about perfectly-informed voters.
>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
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.
Maybe limiting the adverse outcome to defeating one's favorite
or electing one's last choice sounds contrived to let Approval
through, but I believe there were already some adverse results
criteria that spoke of that kind of adverse results. Besides,
those are surely the most undesirable kinds of adverse results.
Anyway, I know Approval doesn't meet the strongest adverse results
criteria that could be written, then, but no method does.
But, under the reasonable conditions where the best strategy in
Approval never includes skipping, voters in Approval can never
worsen their outcome compared to what it would be if they
Approval of course meets Participation.
If the criterion stipulates sincere voting, and if sincere voting
is defined as voting without reversing any preferences, then
Approval meets Participation. If, on the other hand, Participation
instead says that a same-voting group of voters should never
cause the election of someone whom they vote lower than the
candidate who'd have won if they hadn't showed up, then Approval
meets that version too.
In fact, if sincere voting is the stipulation, and is defined
as not voting a less-liked candidate equal to or over a more-liked
one, then the only sincere way to vote in Approval would be
to vote only for your favorite (or favorites if several candidates
whom you prefer equally are your favorites). Of course voting that
way can't worsen your outcome, compared to not voting. So Approval
meets Participation, however defined. Well no doubt it's already
agreed that all the point systems meet Participation, and that
would include Approval.
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