[EM] SARC definition improvement

MIKE OSSIPOFF nkklrp at hotmail.com
Tue Sep 12 18:40:23 PDT 2000

I'd said:

> > Sure, but you'd be surprised how many people value majority rule.

Markus said:

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

No, I don't think that would surprise me, since most people have
never heard of the Condorcet Criterion.

I'm not sure what your point is in the above-quoted sentence.

I don't consider the Condorcet Criterion important, because
any rank method that meets BC automatically meets the Condorcet
Criterion and probably the Smith Criterion too. We have good,
simply-defined rank-counts that meet BC. So why bother with any
rank-count that meets the Condorcet Criterion but not BC?

When I said that I don't consider the Condorcet Criterion
important, I meant that it won't usually be of any practical use
in comparing methods.

Well, the Condorcet Criterion could be mentioned as one advantage
that goes with BC. But the Condorcet Criterion's usefulness is
greatly limited by the fact that it stipulates sincere voting.
For rank methods, that means everyone sincerely ranking all of the
candidates. Right :-)

Well, I admit that I sometimes use IRV's especially extreme
violation of the Condorcet Criterion, in discussions of IRV,
so I won't say that the Condorcet Criterion is of no use at all.

>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.

I don't know if that's so. Is that the strategy to minimize the
maximum possible Savage regret in PC? I do tend to vote in the
way that you suggest, under the existing conditions, but not for
the reason that you give.

Actually, if I believed as you say, I'd rank in 1st place everyone
but my last choice--isn't that how to vote in order to prevent
the worst possible outcome?

So we don't necessarily agree on now one would vote in order to
prevent the worst possible outcome.

>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.

That may be so, but it doesn't mean that PC meets SARC.

>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.

Why stop there? With Plurality, even if you're fairly sure,
but not entirely sure, that your favorite can't win, you could
vote for your favorite anyway, and thereby avoid your vote being
an example of a SARC failure. In fact I'm in favor of that kind
of voting with Plurality.

I don't understand how your arguement is an argument against
using SARC. A method meets SARC if undominated voting can't
defeat your favorite or elect your last choice. Wouldn't it be
nice if we could count on voters not voting in a way that
could do that--but we can't always count on that. So the fact that
you can find a way of voting in Plurality or PC that wouldn't
violate SARC doesn't mean anything unless you can promise that
that's how everyone will vote.

I suppose your Approval-voting PC-voter could avoid
showing a Participation violation too. So shall we drop

But I agree that Condorcet, when it violates FBC & SARC, doesn't
do so in a way that really bothers me.

>To my opinion, this demonstrates that SARC doesn't do what it
>was designed for.

It was designed to find out with which methods undominated voting
can defeat favorites or elect last choices. It does what it's
designed for. The fact that you can devise some way of voting
in PC or Plurality that won't do that doesn't matter unless you
can promise that everyone will vote as you suggest.  Because,
otherwise, you haven't shown that the violation won't happen.

You're making the error of feeling as if a method meets a criterion
because you can find some case where it doesn't fail the criterion.

Mike Ossipoff

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