[EM] SARC definition improvement

[Markus Schulze]

Dear Mike,

you wrote (10 Sep 2000):
> Markus wrote (10 Sep 2000):
> > In the website http://home.pacbell.net/paielli/voting you introduce
> > 7 criteria. 2 of the 7 criteria are violated by Condorcet methods.
> >
> > 4 of the 5 remaining criteria are motivated by the opinion that
> > if a majority of the voters strictly prefers candidate A to candidate
> > B then rather candidate A than candidate B should be elected resp.
> > then there should be a way of voting with certain properties that
> > will ensure that B cannot win.
> >
> > The problem is that these 4 criteria (SFC, GSFC, WDSC, SDSC) are so
> > similar that a reader either considers all 4 to be important or all
> > 4 to be unimportant.
> >
> > A reader who thinks that the fact that a majority of the voters
> > strictly prefers A to B has no important meaning will simply reject
> > all 4 criteria simultaneously.
>
> Sure, but you'd be surprised how many people value majority rule.

And you would be surprised how many people value majority rule
without valueing the Condorcet criterion.

******

You wrote (10 Sep 2000):
> Markus wrote (10 Sep 2000):
> > Steve once wrote that he doesn't consider the particpation
> > criterion to be important enough because voters usually don't
> > vote sincerely but strategically. But a criterion that says
> > that a voter should not be punished for showing up and voting
> > strategically would have been to strict. Therefore Steve and
> > you relaxed this criterion and got SARC.
> >
> > The question is: From all the possible relaxations of that
> > criterion that says that a voter should not be punished for
> > showing up and voting strategically, why should we just take
> > SARC?
>
> I'd be interested in any other criteria you could write. I
> certainly don't claim to have written all of the possible
> defensive strategy criteria (aside from the fact that Steve
> has written some of them).
>
> We didn't get SARC by starting with that other criterion and
> then relaxing it. We wanted something like the ordinary adverse
> results criteria, but something more realistic that doesn't
> pretend that everyone votes sincerely. And I repeat that SARC
> doesn't protect the more insincere voters. It protects voters
> by protecting them from the drastically insincere strategy that
> could defeat favorites or elect last choices. The criterion's
> definition doesn't explain that, but that's how SARC complying
> methods avoid violating SARC--by not forcing the drastically
> insincere voting that would violate SARC.

Suppose that you were a very pessimistic voter. Suppose that you
believed that whenever you do something then the worst possible
will happen. Then -if PC was used- you would divide the candidates
into two groups and approve (i.e. give a "1" to) all the candidates
of the one group and disapprove (i.e. give a "2" to) all the
candidates of the other group. Since this voting behaviour
guarantees that the winner cannot be changed from an approved to
a disapproved candidate, this voting behaviour guarantees that
you cannot be punished for showing up. Therefore the same voting
behaviour that guarantees that you cannot be punished for showing
up under Approval Voting also guarantees that you cannot be
punished for showing up under PC. Therefore -although Approval
Voting meets SARC and PC violates SARC- it isn't feasible to
conclude that Approval Voting deters less from showing up than PC.
To my opinion, this demonstrates that SARC doesn't do what it
was designed for.

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