[EM] Majority winner set

[MIKE OSSIPOFF]

Markus said:

>I have already said in a different context (23 Sep 2000)
>that I use the concept that election methods are defined
>on the reported von Neumann-Morgenstern utilities of the
>voters.

Excuse me, but I didn't notice anything about von Neumann-Morgenstern
utilities in your definition of "Schulze's method", for example.

>But in your reply (23 Sep 2000) you wrote that
>this concept was "funny," "incomplete," "undefined,"
>"vague" and "not precise." Now you write that this
>concept was also "sloppy" and "dishonest."

Maybe the reason why I said "undefined" and "vague" was because
you referred to those purported definitions in the same vague way
as you do now, and because you haven't given us a definition of
the type to which you vaguely refer.

>
>If you didn't refuse to read scientific literature

When did I say I was unwilling to read scientific literature?


>then you
>would observe that the concept that election methods are
>defined on the reported von Neumann-Morgenstern utilities
>of the voters is widely used and that e.g. Gibbard and
>Hylland use this concept for their impossibility theorems.

You say that someone else defines methods in that way, but you
don't define your own method in that way. I have to admit that
it isn't clear to me how someone else's way of defining some other
method is relevant to the issues we've been discussing. For instance,
how does it save your BPGMC criterion from its faults that I
described? I've asked you twice to show that Approval, Cardinal Ratings,
Plurality, and single-winner Cumulative pass or fail the Condorcet
Criterion , if we assume that each voter votes a
ranking and we have to apply those methods' count rules to rankings.
I've explained that your failure to do that shows that the limited
applicability of our approach makes it a poor approach of limited
& questionable usefulness. I've pointed out the silliness of judging
a method by what its count rule does with some other method's balloting,
when the method we're judging doesn't use that balloting.

>
>When you think that this concept is "vague," "sloppy" and
>"dishonest"

I'm not saying that the concept to which you refer so vaguely is
vague or sloppy or dishonest. Your reference to it is certainly
vague, and your attempt to save BPGMC by requiring the tested method's
count rule to be used with a different method's balloting system,
with which it may not be usable--that was sloppy. Or, if it wasn't
pure sloppiness, maybe it was bias in favor of the way you want to
define BPGMC--that's what I meant by "a little bit less than honest
with us."


>then you are invited to introduce your own
>concept and to explain why you think that your own concept
>might be better.
>But unless you have done this,

The concept to which you refer is a way of defining a method. All of
us here and elsewhere who have defined methods have defined them in
some way. I daresay that most of us have defined them in terms
of a way in which voters are allowed to express their preferences or
ratings of the candidates, and a count rule for counting those
expressed preferences or ratings.

Explain why that's better than what you've vaguely referred to?
Look, if you want to introduce here a way of defining methods that's
new here, then you first must define it much better than you have.

Then you must show why it's better. It isn't on me to show that it
isn't better--least of all now, when it hasn't been defined, but has
only been vaguely referred to.

For instance, after you define your idea much more clearly than you'
have defined it, then you should write definitions for Plurality,
Approval, IRV, Tideman(wv) and BeatpathWinner, using the form that
you propose for method definitions.

But I am NOT asking you to do that, because it doesn't sound like
something that would be useful. I'm saying that if you want to
discuss the issue of whether your way is better, then you must do as
I suggested in the 3 preceding paragraphs.

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

Fine, I'll take your word for that, that someone else, somewhere else,
defines voting systems in a different way that you refer to vaguely.
But I'm not asking you for a more precise specification about that.
I doubt that it would be useful. I merely state that you've referred
to it vaguely, and I'm willing to leave it at that and take your
word for it that someone defines methods in that sort of a way.

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

This has been about a problem of BPGMC.

>




>Markus Schulze
>

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