[EM] Majority winner set

[MIKE OSSIPOFF]

Markus said:
>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.

Ok. So now you're saying that, when Schulze's method is used, voters
report their vN-M utilities. You'd previously given the impression
that the voters report pairwise preferences, via a ranking. Which
is it?

Yes, you'll say that someone could rank the candidates in order of
their vN-M utilities for that voter. Fine, but the voter reports pairwise 
preferences, via a ranking, with your method, yes? You can
call that reporting the order of his vN-M utilities, or we could just
as well call it reporting pairwise preferences that may or may not
be sincere.

So now, unless you're really changing that, we're back to you saying
that, actually, with your method, voters report pairwise preferences,
via a ranking. You call it reporting pairwise preferences which may
be insincere, and I'd say it would make more sense to say that people
are simply casting pairwise votes with their ranking, but now that
I know what you mean, it doesn't matter which way we say it.

Good, because that's what I thought--people report pairwise preferences
in your method, which means they cast pairwise votes.

Now that we know what you mean, it's evident that it doesn't do
anything to save BPGMC. All this mumbojumbo about vN-M utilities,
and what it still amounts to is that your method, like all rank
methods, is defined in terms of the rankings that people vote.

Sometimes you say that your BPGMC is defined in terms of preferences
and sometimes you say it's defined in terms of votes. Now I realize
that when you say "preferences" you mean preferences that may be
insincere, and so we can assume that by pairwise prefereces you mean
pairwise votes.

Fine. We're now back to this: Plurality meets your BPGMC. You
say it doesn't, because you say that Plurality should be tested by
applying its count rule to rankk balloting, which Plurality doesn't
use, by calling top-rankedness a Plurality vote. You never answered
about how you'd apply that notion to Approval, Cardinal Ratings,
and single-winner Cumulative, and it's evident now that you aren't
going to, because of course you know that it can't be applied to them.

And all that garbage about vN-M utilities was just an attempt to
use big words to try to cover up the fact that you can't defend your
faulty definition of BPGMC.


>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.

Widely used, I couldn't say. Well known? Certainly not coherently
stated by you here. When voters vote a ranking, you can say that
they're reporting, truly or falsely, the order of their vN-M utilities.
Fine, I don't care, but it can also be said that what they're doing
is voting pairwise preferences by voting a ranking.

In other words, all your vN-M crap changes nothing: Voters are still
voting a ranking. That's how your method, and every rank method is
defined.

>
>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.
>

Widely used, I don't know. What you said here amounts to methods
being defined in terms of rankings voted by the voters. You can
say that when you vote a ranking, you're truthfully or untruthfully
reporting the order of your vN-M utilities, but the fact is that
your voting system is defined in terms of only one input: a ranking
from each voter. A voted ranking.

Mike Ossipoff





>Markus Schulze
>
>

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