[EM] Markus rewrites Condorcet

[MIKE OSSIPOFF]

Markus wrote:

Dear participants,

due to Condorcet, a "proposition" is a statement of the
form: "X is better than Y." An "opinion" is a set of
n*(n-1)/2 propositions (one for each pair of candidates).

I reply:

Did Condorcet say that there have to always be n(n-1)/2 propositions,
and that a proposition has to say one candidate is better than another?

Suppose that, initially, there's a pairwise tie. Then, if Condorcet
said what you claim, then initially there's no opinion, if an
opinion must have n(n-1)/2 propositions, and a proposition must say
that one candidate is better than another. So are you making the silly
claim that when there's a pair-tie, then initially there's no opinion
at all? In fact, then there can never be an opinion, unless you
also believe that Condorcet wanted us to write an X>Y opinion when
there isn't one.

There are 2 less absurd conclusions. Maybe a proposition can
also say X=Y. Or maybe, if a proposition must say X>Y, then we can
have fewer than n(n-1)/2, for the atypical case where there are 1 or
more pair-ties.

Your claim leads to the asinine conclusion in the paragraph before last,
and also requires the equally asinine conclusion that "eliminate"
must mean "reverse", and doesn't really mean "eliminate".

What English dictionary are you using. Would you mind quoting to us
its definition of "eliminate"? Or, better yet would be if you
have a dictionary for the French in Condorcet's period, and could
tell us how that dictionary translates the French word that has
been translated as "eliminate".

Mike Ossipoff




A "possible opinion" is a set of n*(n-1)/2 propositions
(one for each pair of candidates) that is compatible to
a ranking. An "impossible opinion" is a set of n*(n-1)/2
propositions (one for each pair of candidates) that is
incompatible to every ranking.

Due to Condorcet, when one "eliminates" a proposition of
an opinion then one still has an opinion. Therefore, it
is clear that "eliminating" can only mean "inverting".

Markus Schulze




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