[EM] Majority winner set

[Markus Schulze]

Dear Mike,

you wrote (28 Nov 2000):
> Ok. So now you're saying that, when Schulze's method is used, voters
> report their vN-M utilities. You'd previously given the impression
> that the voters report pairwise preferences, via a ranking. Which
> is it?
>
> Yes, you'll say that someone could rank the candidates in order of
> their vN-M utilities for that voter. Fine, but the voter reports
> pairwise preferences, via a ranking, with your method, yes? You can
> call that reporting the order of his vN-M utilities, or we could just
> as well call it reporting pairwise preferences that may or may not
> be sincere.
>
> So now, unless you're really changing that, we're back to you saying
> that, actually, with your method, voters report pairwise preferences,
> via a ranking. You call it reporting pairwise preferences which may
> be insincere, and I'd say it would make more sense to say that people
> are simply casting pairwise votes with their ranking, but now that
> I know what you mean, it doesn't matter which way we say it.
>
> Good, because that's what I thought--people report pairwise preferences
> in your method, which means they cast pairwise votes.
>
> Now that we know what you mean, it's evident that it doesn't do
> anything to save BPGMC. All this mumbojumbo about vN-M utilities,
> and what it still amounts to is that your method, like all rank
> methods, is defined in terms of the rankings that people vote.
>
> Sometimes you say that your BPGMC is defined in terms of preferences
> and sometimes you say it's defined in terms of votes. Now I realize
> that when you say "preferences" you mean preferences that may be
> insincere, and so we can assume that by pairwise prefereces you mean
> pairwise votes.
>
> Fine. We're now back to this: Plurality meets your BPGMC. You
> say it doesn't, because you say that Plurality should be tested by
> applying its count rule to rankk balloting, which Plurality doesn't
> use, by calling top-rankedness a Plurality vote. You never answered
> about how you'd apply that notion to Approval, Cardinal Ratings,
> and single-winner Cumulative, and it's evident now that you aren't
> going to, because of course you know that it can't be applied to them.
>
> And all that garbage about vN-M utilities was just an attempt to
> use big words to try to cover up the fact that you can't defend your
> faulty definition of BPGMC.

The concept that criteria and election methods are defined
on the reported von Neumann-Morgenstern utilities of the
voters presumes that every voter casts (not necessarily
sincerely) his von Neumann-Morgenstern utilities and that the
used election method takes from the reported von Neumann-
Morgenstern utilities that information that this election
method needs to calculate the winner. You claim that this
concept was "faulty" because some election methods depend on
LESS than the reported von Neumann-Morgenstern utilities.
But when you re-think your statement then you will observe
that this concept is problematic only when the used election
method depends on MORE than just the reported von Neumann-
Morgenstern utilities.

Again: When you really think that the well known and widely
used concept that criteria and election methods are defined
on the reported von Neumann-Morgenstern utilities of the
voters is "inadequate," "vague," "sloppy," "dishonest," 
"absurd," "faulty," "poor," "silly," "contradictory,"
"useless," "garbage" and "mumbojumbo" then you are invited
to introduce your own concept and to explain why you think
that your own concept might be better. Nobody hinders you
from introducing your own concept.

However, I don't have the impression that your statements have
anything to do with majority winner sets or beat path GMC.

Markus Schulze