[EM] Majority winner set
Markus Schulze
schulze at sol.physik.tu-berlin.de
Tue Nov 28 00:59:41 PST 2000
Dear Mike,
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.
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. 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.
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.
Markus Schulze
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