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

[MIKE OSSIPOFF]

Markus asked:

>1. You forgot to define the term "sincere CW."

I didn't state a definition for "sincere CW", because we earlier
discussed that, and my definition for "sincere CW" is the same as
yours:

A sincere CW is a candidate who, when compared separately to each one
of the other candidates, is preferred to him/her by more voters than
vice-versa.

[end of definition]

>
>2. How does your definition of "sincerity" look like when the
>    used election method allows the voter to cast more than just
>    preferences? Example: When Average Rating or Median Rating or
>    Cumulative Voting is used, then how has a voter to vote to be
>    "sincere"?

My definition works fine for single-winner Cumulative. If you vote for
3 candidates, out of 7, then your vote is sincere as long as you don't
prefer someone you don't vote for to someone whom you do vote for.
Maybe there's a 4th candidate whom you like less than the 3 you vote
for, and more than the remaining 3. The fact that you didn't vote for
him isn't insincere, because if you voted for him, you'd no longer be
voting over him the 3 that you actually did vote for. So, by my
definition, with single-winner Cumulative, you don't vote insincerely
unless you like someone you don't vote for better than someone you
vote for.

As for ratings-balloting, I covered that in my message to Craig L.

If I don't cover it as well here, check that other message.

With ratings voting, my definition of course doesn't require that you
vote your  sincere ratings. It requires that the order of your ratings
be correct, however. So my definition of sincerity requires a degree of
sincerity which, for ratings-balloting, is less than complete sincerity.
It only requires order sincerity.

That's ok. A sincerity definition doesn't have to be about cardinal
sincerity. Besides, the rating-balloting methods can't pass the
criteria for which I stipulate sincere voting anyway, so it makes no
practical difference how my sincerity definition applies to them.
Thirdly, cardinal ratings are much more difficult to vote than rankings.
You know that you like Nader better than Gore, Gore better than Bush,
and Bush better than Buchannan. But rating the candidates with cardinal
numbers is more of a task. Whereas the rankings would come natural to
you, and you could immediately write them down, you wouldn't be able
to immediately write down your ratings so easily. Maybe you'd have
a difficult job determining them. And maybe one person would decide his
sincere ratings directly, while someone else would use hypothetical
lotteries, a la vNM, because that might be the only way that he feels
comfortable with the reliability of his ratings. So the ratings have
more subjectivity than the rankings.

Aside from all that, of course it might be desirable, just on principle,
to have a sincerity definition that is truly universal. For that
purpose, a simple & brief clause could be added to my definition, or
to that of Craig L. But, as a practical matter, there's no need to
add that clause.

Mike Ossipoff
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