[EM] Schulze's method fails Condorcet's Criterion, right?

[MIKE OSSIPOFF]

Dear Markus--

You said:

>criteria and election methods are defined on the reported
>vNM utilities of the voters.

No. They're defined that way by you, and, according to you, by
some academics.

Most of the rest of us would agree that it would be pretty silly
to define methods & criteria based on vN-M utilities reported by
the voters, for voting systems in which voters don't report vN-M
utilities, or any kind of cardinal ratings.

And it's ironic that you use the word "defined", when your
Beatpath GMC is still undefined, because you still are unable to tell
us how we should "take from the voters' reported utilities the information 
that the particular voting system needs", and which it
would get directly from the ballots in a genuine election.

You talk of how criteria are defined, but you still haven't
defined Beatpath GMC.

>In your example, candidate B
>is the Condorcet winner of the reported vNM utilities and
>the Schulze method chooses candidate B.

Now I'm almost afraid to ask what you think "Condorcet winner" means.
You said that you define Condorcet's Criterion based on actual votes,
by which (you later explained) you meant the ratings that you assume
that the voters report.

When defined in terms of actual votes, Condorcet's Criterion says
that if a candidate, when compared separately to each one of the'
other candidates, is voted over him/her by more voters than vice-versa,
then that candidate should win. When voting ratings, one votes A
over B if one rates A higher than B. Or do you & your scientists
have a different definition of that too?

I'd asked you to explain how you think we should "get from the voters'
reported utilities the information that is needed by the voting system
being tested." I asked for your uniform rule for that, without which
you don't have a definition of your criterion. But instead of
telling that, you're instead indicating that you have have an unusual
notion of what the Condorcet Criterion would mean if defined in terms
of actual votes. If you think it doesn't mean what I said in the
previous paragraph, when defined in terms of actual votes, then what
do you think it means?

Now, in my example, 60% of the voters indicate by their reported
ratings that C is their favorite. That 60% indicate that they
like C better than B, and that they like C better than A.

Which part of that don't you understand?

>Therefore your
>example doesn't demonstrate a violation of the Condorcet
>criterion.

Now I think you need to tell us what you think the Condorcet Criterion
would say if it were defined in terms of actual votes. But don't forget
to also tell us your uniform rule for determining how to mark the
tested method's method-specific ballot based on the voters' reported
ratings.


>
>In your example, you presume that candidate C is the
>Condorcet winner of the sincere vNM utilities and that as
>some voters vote strategically candidate B is the Condorcet
>winner of the reported vNM utilities. But in so far as
>criteria and election methods are defined on the reported
>vNM utilities, it is only relevant how the voters vote but
>not why they vote the way they vote.

I didn't say that it was important why they vote as they do. You
said that their reported ratings may be insincere; fine.

But in my example, 60% of the voters indicated that C is their
favorite. If we use actual votes (in the form of those voted ratings)
to determine pairwise preferences, then C pairwise beats everyone,
and is the candidate who must win in order for the method to meet
Condorcet's Criterion.

Because you wont' tell your uniform rule for marking the method-specific
ballots based on the voters' reported ratings, I've guessed and suggested 
that the uniform way would be to use 0-info strategy. If
that's it, then:

Schulze's method fails Condorcet's Criterion.

Mike Ossipoff





>
>Markus Schulze
>

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