[EM] Majority winner set

MIKE OSSIPOFF nkklrp at hotmail.com
Tue Nov 28 20:45:34 PST 2000

Markus said:

>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.

That presumption is incorrect. What each voter casts depends on
the balloting used by the particular method in use. If the method
is Cardinal Ratings, then you can call someone's ratings his
sincere or insincere vN-M utilities. And then maybe you can bend the
meanings a lot and say that when, in Plurality, someone votes for
Gore, then he's voting a set of insincere vN-M utilities, when he gives
Gore 1 and everyone else zero. But there's no way that you can call
a ranking a set of sincere or insincere vN-M utilities.

>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.

No, it's problematic anyway. You didn't say that the voter casts
something that could be derived from his sincere or insincere vN-M
utilities. You said that he casts his sincere or insincere vN-M
utilities. With rank methods he in no way can be said to do that.
This isn't complicated.

You say it isn't problematic because, if we know the vN-M utilities
that the voter would like to represent, then from that we can
determine how he would vote a ranking, or any other type of balloting.
But that's got nothing to do with your earlier claim that the voter
votes his sincere or insincere vN-M utilities. He doesn't necessarily.
You claim is obviously incorrect.

>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"

...don't forget "crap".

>then you are invited
>to introduce your own concept

I'm not going to claim credit for a concept that isn't mine, for
specifying balloting in method definitions. However, I'm going to
introduce you to the universally accepted concept for that:
When defining a method, we tell how voters can indicate preferences
or ratings, by marking their ballot, and we specify a count rule
for determining the winner from those ballots. That's what you
yourself did when you specified that your method uses rank-ballots.

>and to explain why you think
>that your own concept might be better.

Now I'm going to explain to you why that's better: It applies to
more diverse methods, with their different balloting systems, than
does your suggestion to define methods as receiving a set of
sincere or insincere vN-M utilities from each voter, a suggestion
that is quite inapplicable to rank methods.

This isn't rocket science, Markus: The fact that you can make a ranking
by ordering the candidates according to someone's vN-M utilities for
them does not mean that the voter who votes a ranking is casting his
vN-M utilities, sincere or otherwise.

>Nobody hinders you
>from introducing your own concept.

You're too kind, but I'm willing to use the same balloting concept
for method definitions that everyone else uses when defining methods.

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

Actually, at this point, you're right. When I said that Plurality meets 
you define it, you at first claimed that it doesn't, because of
your claim that methods (or just Plurality?) should be evaluated
according to what their count rule would do if it were applied
to rank ballots. You abandoned that when I asked you to apply
it to some well-known methods. Then you started repeating that
methods are defined in terms of an input of vN-M utilities. You
say you don't have the impression that that has anything to do with
my claim that Plurality passes BPGMC? Neither do I :-)

I agree that what you've been saying has nothing to do with my
claim that Plurality meets BPGMC, and that it doesn't in any way
answer that claim.

You know what, Markus? I would expect that people are real tired of
that repetition. I'm not going to be a party to continuing to send
them that repetition. When I reply to those endlessly repeated
statements, then I'm partly at fault for their being posted, and
I prefer to not be part of the cause of that repetition being
posted. Repeat the statements again if you want to, but for me to
keep replying to them would be inconsiderate of the other people on
this list.

Mike Ossipoff

And so let me summarize and conclude it in this way: If you want
to say that someone

>Markus Schulze

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