[EM] SARC definition improvement

[Markus Schulze]

Dear Mike,

you wrote (13 Sep 2000):
> Markus wrote (13 Sep 2000):
> > Mike wrote (12 Sep 2000):
> > > Markus wrote (12 Sep 2000):
> > > > Mike 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.
> > >
> > > 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.
> >
> > Your comment ("You'd be surprised how many people value majority
> > rule.") makes sense only when you presume that everybody who
> > values majority rule also values SFC, GSFC, WDSC and SDSC. My
> > comment ("You would be surprised how many people value majority
> > rule without valueing the Condorcet criterion.") says that I
> > don't agree that everybody who values majority rule also values
> > SFC, GSFC, WDSC and SDSC.
>
> Now you're saying that standards on which criteria are based
> mean nothing because maybe someone will agree with the standard
> and not like the criterion. Are you saying that you don't
> agree that SFC, GSFC, WDSC & SDSC measure for the majority rule
> standard.

You will have to rephrase this because I have absolutely no idea
what you mean.

******

You wrote (13 Sep 2000):
> Markus wrote (13 Sep 2000):
> > Mike wrote (12 Sep 2000):
> > > Bruce sent me an objection to it by individual e-mail,
> > > and I answered his objection. Then, at least some months
> > > later, Bruce repeated the exact same objection on EM, making
> > > no reference to my reply that I'd sent him. I questioned the
> > > sincerity of that intentional re-use of an answered objection
> > > without reference to the answer. That tactic by Bruce was in
> > > violation of the stated guidelines for EM.
> > >
> > > Anyway, now it looks as if it's necessary for me to answer
> > > that same objection yet again, just like I did on EM before
> > > (Markus, why didn't you posts that too), and just like I did
> > > when Bruce sent it to me individually. I suppose I could look
> > > it up in the archives and re-post my reply, but that would be
> > > even more time consuming. But I suggest that we ask ourselves
> > > why Markus re-posted Bruce's old objection, without re-posting
> > > my reply to it. By so doing, Markus is wasting your time & mine,
> > > and, it seems to me, is violating the EM guideline against
> > > recycling old arguments without replying to the answers that
> > > were already given to those arguments.
> > >
> > > Why is Markus posting this outdated message from Bruce?
> >
> > I don't agree with you that Bruce's message is "outdated." Bruce
> > wrote in great detail where he had problems understanding the
> > wordings of your "lesser-of-two-evils" criteria. It is true that
> > in a reply to Bruce you explained in great detail the wordings
> > of your "lesser-of-two-evils" criteria. But nevertheless you
> > still use the same wordings. Therefore someone who reads today's
> > wordings of your criteria will still have the same problems like
> > Bruce.
>
> Only if they imagine something that I didn't say. I didn't say
> that all 3 majorities should be able to simulataneously use their
> SDSC power to defeat all 3 candidates. I said that each one of
> those majorities should have a way of voting that will defeat
> a certain candidate, under those conditions.

On the other side in your definitions you don't say that not all
3 majorities are able to simultaneously use their SDSC power.

You wrote (13 Sep 2000):
> By the way, it isn't that I explained otherwise incomprehensible
> wordings to Bruce. I told him why his interpretation was contrary
> to the literal meaning of what I'd said. I explained to him that
> he'd invented something that I hadn't said. That isn't the same
> as admitting that the wording was ambiguous and supplementing it
> for Bruce.
>
> You can help by trying to find actual problems in the criteria.
> But saying that you or someone misunderstood it, without being
> able to point to ambiguity in the wording, that doesn't prove
> anything, because, frankly, you're motivated to find a problem.
> That's what makes you so helpful in finding actual problems.
> We want to know of any problems that you can find.
>
> But if the worst that you can say is that you misunderstood it,
> without showing ambiguity; or that a criterion of a different
> type could be written (but without writing one), what that shows
> is that you can't find a genuine problem with the criteria.

In so far as Bruce explained in great detail where he had problems
understanding your definitions, I don't understand your comment.

WSDC says: "If a majority of all the voters prefers A to B, then
they should have a way of voting that will ensure that B cannot win,
without any member of that majority voting a less-liked candidate
over a more-liked candidate."

Bruce mainly criticized two points.

First: Your definition doesn't say whether in a given example the
WDSC power can be used for only one pair of candidates A and B or
for several pairs of candidates simultaneously.

Second: Your definition doesn't say what a "way of voting" is. Is
a "way of voting" a "way of voting such that independently on how
the other voters vote" or a "way of voting such that if the other
voters vote sincerely" or whatever?

It is true that you have answered these questions. But nevertheless
you haven't changed your definitions accordingly. Therefore Bruce's
criticism is still valid.

******

You wrote (13 Sep 2000):
> Markus wrote (13 Sep 2000):
> > Mike wrote (12 Sep 2000):
> > > Actually it might be possible to write a wording of SDSC that
> > > refers to actual votes instead of sincere preferences, and
> > > is about a specific way of voting rather than speaking of
> > > people having a way of voting, a wording that means the same
> > > as my SDSC wording.
> > >
> > > But I doubt that it would be simpler. And I doubt very much
> > > that it would be as clear in its purpose. WDSC & SDSC are about
> > > a majority being able to keep someone from winning without
> > > a specified degree of insincere voting. I don't think you could
> > > say it more directly or simply than the current wordings.
> > >
> > > But I wish Markus would write the new WDSC & SDSC wordings that
> > > he suggests. Then Blake won't say that all of the defensive
> > > strategy criteria were written by me. Actuall, even now, one
> > > of them, GSFC, was written by Steve, who also wrote a wording
> > > for SDSC, but that doesn't stop Blake from making that claim.
> >
> > I suggest beat-path GMC as an alternative to SFC, GSFC, WDSC and
> > SDSC. (In so far as you consider beat-path GMC to be too strict,
> > you can also use BC.)
>
> Now that's better. Any rank method that meets BC meets SFC, GSFC,
> WDSC & SDSC. The reason to use those 4 instead of just BC is
> that those 4 majority defensive strategy criteria have obvious
> purpose & motivation: A majority being able to defeat someone
> without some specified degree of insincere voting. For people
> who don't want sincere voting to be punished (you, for instance
> don't), the purpose & desirability of those criteria is obvious.
> We don't name BC at the website because its purpose isn't obvious.
>
> Being able to defeat some greater evil without an unnecessary
> degree of insincere voting obviously reduces the lesser-of-2-
> evils problem, because that's what that problem is about. It
> also accomplishes that goal that you expressed: protecting
> sincere voters.

On the other side in so far as SFC, GSFC, WDSC and SDSC are
ill-defined it is arbitrary to ask whether your "lesser-of-
two-evils" criteria or BC are more obvious and intuitive.

******

You wrote (13 Sep 2000):
> Markus wrote (13 Sep 2000):
> > Mike wrote (12 Sep 2000):
> > > 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.
> >
> > In so far as I wrote in my last mail that Approval Voting
> > meets SARC and PC violates SARC, I don't understand your
> > comment.
>
> You know that PC violates SARC, but you feel as if PC
> as-good-as-meets SARC, because you've found a case where
> PC doesn't violate SARC.

I wrote: "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."

Therefore it is clear that I didn't claim that PC meets SARC.

Au contraire: I demonstrated that -although Approval Voting
meets SARC and PC violates SARC- Approval Voting doesn't
deter less from showing up than PC.

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