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

[MIKE OSSIPOFF]

There's a very big gap in Markus's explanation of how his scientists
deal with balloting in method definitions for the purpose of
criterion compliance determinations.

He says that they assume, bizarrely, that the voter votes ratings,
no matter what the method is, no matter what the method's balloting
system is. And then, the method takes from those ratings the information
that the method needs, the information that it would get from its
ballots in a real election.

But "the method takes from those ranking the information..." leaves
much unsaid. How does the method decide how to interpret those
voted ratings for the purpose of making out the voter's ballot for
that particular voting system?

Apparently Markus would say that if the method is Plurality, then
we mark the Plurality ballot by writing a vote for the top rated
candidate in that voter's voted ratings. Maybe he'd say that, if
the method's a rank method, he'd make out the rank ballot by ranking
the candidates in the order of their ratings expressed by that voter.
He didn't say it with a wording that applies both to Plurality and to
rank balloting. Maybe that's possible; I haven't checked. Presumably
with Cardinal Ratings, he just uses the voted ratings. But what about
Approval or single-winner Cumulative?

So, Markus, what is your (and your scientists') uniform rule for
how we get the actual ballot marks, for the method's own ballot,
from the voter's voted ratings. I said _uniform_.

Since you've never answered that question, suggesting that you
know that your approach isn't applicable to all methods, I suggest
that we can already say that you've admitted that your approach
is inadequate.

But maybe you'll say that you'd apply your system to Approval and
single-winner Cumulative in the following way: Mark the method's
individual ballot in the way that maximizes that voter's utility
expectation in a 0-info election. That's most likely the only way
that you can try to say that your system can be applied at all to
Approval and single-winner Cumulative.

But it's no good to have different rules for applying criteria to
different methods. If it's 0-info strategy for nonrank methods, then
it should be 0-info strategy for all methods. Suppose, then, we
apply that to BeatpathWinner (aka "Schulze's method"):

Voters' voted ratings:

# of Voters        A         B        C

20                 1         .3       0
20                 .3        1        .7
60                 0         .7       1

(Though this isn't required, these ratings are in keeping with
candidates & voters on a 1-dimensional policy space, with ratings equal
to 1 - distance).

Markus would use these ratings to determine the sincere CW. 70%
of the voters vote C over everyone. As Markus would apply them,
Condorcet's Criterion and Beatpath GMC would require that C win.
(C has majority beatpaths to A & B, and neither have any beatpath
to C).

Now, what would be these voters' 0-info strategy?

Blake pointed out that, with winning votes in a 0-info election,
with 3 candidates, a voter can sometimes maximize his utility
expectation by voting Middle equal to Favorite, while liking Favorite
better than Middle--if (Middle-Worst)/(Favorite-Worst) is sufficiently
high. I determined that it has to be more than 2/3. If you aren't
inclined to take my word for that figure, that's ok, because however
high that ratio has to be, my example could obviously be written to
make the A voters vote A=B>C.

Rankings that we write, based on the voted ratings, with 0-info strategy:

20: A>B>C
20: B>C>A
60: C=B>A

B wins by BeatpathWinner. BeatpathWinner fails Condorcet's Criterion
and Beatpath GMC if we use Markus's system, and if we "take information
from the voted ratings" by writing 0-info strategy based on those
ratings (Markus, do you have another _uniform_ way to make out the
method-specific ballot based on the voter's voted ratings?)

Someone might suggest that the B voters might vote A=B. They won't
in this example, but even if they did, B would still win.

Mike Osspoff


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