[EM] Majority winner set

[Markus Schulze]

Dear Mike,

you wrote (28 Nov 2000):
> Markus wrote (28 Nov 2000)
> > Mike wrote (28 Nov 2000):
> > > Excuse me, but I didn't notice anything about von Neumann-
> > > Morgenstern utilities in your definition of "Schulze's
> > > method", for example.
> >
> > In my definition of the Schulze method, I talk about the
> > number of voters who strictly prefer candidate X to candidate
> > Y. When you know the von Neumann-Morgenstern utilities of the
> > voters, then you also know how many voters strictly prefer
> > candidate X to candidate Y. Therefore the Schulze method
> > can also be defined in terms of von Neumann-Morgenstern
> > utilities.
>
> Look, I don't care how you find out people's sincere preferences,
> but what you're saying is that you define "Schulze's method" in terms
> of sincere preferences. It makes no sense to define a method that
> way, since the method's actual input consists of votes, not preferences,
> and those votes are what the method must act on.
>
> You've contradicted yourself about whether you define BPGMC in terms
> of preferences or votes. And now you say you define "Schulze's method"
> in terms of sincere preferences, which is entirely absurd, because
> a method can only act on votes. By all means define your criterion
> in terms of sincere preferences, with a stipulation of sincere voting,
> but a voting system must be defined in terms of votes rather than
> preferences.

It isn't clear to me why you believe that the Schulze method and
beat path GMC were defined in terms of SINCERE preferences. In so
far as I wrote that I use "the concept that criteria and election
methods are defined on the REPORTED von Neumann-Morgenstern utilities
of the voters" it is clear that I am talking about the REPORTED
von Neumann-Morgenstern utilities of the voters and not about the
SINCERE von Neumann-Morgenstern utilities of the voters.

You wrote (28 Nov 2000):
> From your demonstration of its use so far, I must say that it's an
> entirely inadequate way to define a voting system, if it's used as
> you describe. That's because you speak of using the utilities to
> determine people's sincere preferences, and defining the method in
> terms of those sincere preferences.

Again: It isn't clear to me why you believe that the Schulze method
and beat path GMC were defined in terms of SINCERE preferences.

You wrote (28 Nov 2000):
> You said that we define a voting system in terms of sincere
> preferences rather than in terms of votes. That's absurd.
> You said that the vN-M utilities are used to determine people's
> sincere preferences, but you didn't explain how the voting system
> determines those utilities.

Again: It isn't clear to me why you believe that the Schulze method
and beat path GMC were defined in terms of SINCERE preferences.

Again: When you 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
"vague," "sloppy," "dishonest," "faulty," "poor," "silly,"
"useless" and "contradictory" 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.

You wrote (28 Nov 2000):
> There's no need for me to introduce a new concept.

Then you have to live with the fact that the concept that
criteria and election methods are defined on the reported von
Neumann-Morgenstern utilities of the voters is widely used.

Markus Schulze