I'm replying to this by copying it from the archives. It seems to
be format-distorted, in my copy. I hope your copy arrives better.
Markus wrote:
Dear participants,
Mike Ossipoff wrote (3 July 2001):
> Since Condorcet wasn't very specific, it's reasonable to
say that
> the Condorcet methods are those methods that solve
circular ties
> by successively dropping defeats in a way that gives
priority to
> dropping weaker defeats.
It should be added that Mike Ossipoff uses the term
"dropping" in
a different manner than Condorcet used the term
"eliminating".
Condorcet wrote in his "Essai sur l'application de
l'analyse
a la probabilite des decisions rendues a la pluralite des
voix"
(Imprimerie Royale, Paris, 1785):
> Create an opinion of those n*(n-1)/2 propositions which
win
> most of the votes. If this opinion is one of the
n*(n-1)*...*2
> possible, then consider as elected that subject to which
this
> opinion agrees with its preference. If this opinion is
one of the
> (2^(n*(n-1)/2))-n*(n-1)*...*2 impossible opinions, then
eliminate
> of this impossible opinion successively those
propositions that
> have a smaller plurality & accept the resulting opinion
of the
> remaining propositions.
Due to Condorcet, an "opinion" is a complete ranking. Due
to
Condorcet, when one "eliminates" a pairwise comparison then
one
still has an "opinion". Therefore, it is clear that when
Condorcet
used the term "eliminating" he talked about _inverting_
rather than
about _dropping_ a pairwise comparison.
I reply:
An "opinion" is a set of collective pairwise preferences. An
opinion is possible if it doesn't contradict itself by implying
directly or indirectly that A is better than B, and also that B
is better than A. In other words, an opinion is possible if it
is transitive, cycle-free.
The purpose of eliminating a proposition (collective pairwise
preference) is _not_ so that you won't have an opinion. It's so that
you'll have a "possible opinion" instead of an "impossible opinion".
When Condorcet said "eliminate", there's no reason to believe that
he meant something different from "eliminate". Eliminating a pairwise
defeat is the same as dropping it. If someone meant to say that
we should reverse a defeat, he'd say so. "Eliminate" just means
eliminate. When you eliminate something, it's no longer there. It
isn't there in reversed form.
When you have an impossible opinion, you can make it into a
possible opinion by dropping (eliminating) some of its propositions.
That's what Condorcet said to do. He spoke of the order in which
the propositions should be eliminated from the opinion.
Markus continued:
Condorcet suggested that
circular ties should be solved by successively _inverting_
defeats
in a way that gives priority to _inverting_ weaker defeats.
I reply:
Condorcet said nothing about inverting defeats. Eliminating something
means making it not be there.
Markus Schulze
Mike Ossipoff
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