[EM] Majority winner set

[MIKE OSSIPOFF]

Markus said:

>you 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.


>
>You wrote (28 Nov 2000):
> > How does it save your BPGMC criterion from its faults that
> > I described?
>
>In my definition of beat path GMC, I talk about the number of
>voters who strictly prefer candidate X to candidate Y.

No, a voting systek must be defined in terms of how it acts on
people's actual votes, not on their preferences.


>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 beat path GMC can also be defined in
>terms of von Neumann-Morgenstern utilities.

No. For the reasons I stated above.


>
>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"
>and "useless" 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.

Again: I didn't say that the concept that you hinted about is
any of those things. I didn't criticize it at all. But, 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. What you forgot to explain was: How does
the voting system find out the voters' von Neumann-Morgenstern
utilities? The only input available to the voting system is the
voters' actual votes.

There's no need for me to introduce a new concept for what input to
refer to when defining voting systems. All of us define them in
terms of people's votes. The voting system specifies a way that
voters may express their preferences in the balloting, and a count
rule for choosing a winner based on those ballots. That's how
voting systems are defined, by everyone who defines a voting system.

As I said, I don't have any argument with your claim that someone
else does it differently. That's their business, and it's fine with
me. I have no idea how it would be done, but I'm not asking you
to explain it. However what you've said so far about how it's done
wouldn't work: 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.

Mike Ossipoff


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