[EM] Is "Inverse Nanson" better than standard Nanson?

[Markus Schulze]

Dear participants,

Mike Ossipoff wrote (10 July 2001):
> Markus wrote (8 July 2001):
> > Mike Ossipoff wrote (7 July 2001):
> > > 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.
> >
> > Even when there are only two candidates X and Y and there is a
> > pairwise tie between these two candidates, exactly one of these
> > two candidates must be elected. This is a matter of fact and not
> > a "silly claim". When the opinion "X > Y" and the opinion "Y > X"
> > each have the same probability, then this doesn't mean that
> > "there's no opinion at all".
>
> I didn't say that it's a silly claim that someone must be elected.
> I said that it's a silly claim that there's no opinion at all. You'd
> quoted Condorcet as saying that there's either a possible opinion or
> an impossible opinion. Also, as I said in that paragraph, if there's
> an initial pairwise tie, then there never can be an opinion, according
> to your interpretation, unless Condorcet would write a proposition
> where none exists. I thought that a proposition was a public
> expression that X>Y. If the voters return a pair-tie between X & Y,
> they're not giving us a proposition. But if you, creatively, call
> that 2 propositions, instead of no proposition, and so there are 2
> corresponding opinions, then there can be a possible opinion and an
> impossible opinion and an impossible one, and so you can throw out
> the impossible one and keep the impossible opinion, which means that
> you're writing in a proposition that the people never expressed.
> That's pretty questionable.

Condorcet wrote ("Essai sur l'application de l'analyse a la
probabilite des decisions rendues a la pluralite des voix,"
Imprimerie Royale, 1785, p. 105):
> When the opinions contain three distinct and independent propositions,
> then there can be eight different opinions, sixteen for four, and in
> general 2^n opinions for n propositions.

Due to Condorcet, a proposition can have only two states: "X > Y" or
"Y > X". There is no need to introduce a third state "X = Y" because
in Condorcet's stochastic model a pairwise tie simply means that
the state "X > Y" and the state "Y > X" each have the same probability
of 1/2.

******

Mike Ossipoff wrote (10 July 2001):
> Markus wrote (8 July 2001):
> > Mike Ossipoff wrote (7 July 2001):
> > > 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?
> >
> > Condorcet explicitely wrote that there are exactly 2^(n*(n-1)/2)
> > opinions. Therefore, it is clear (1) that an opinion consists of
> > exactly n*(n-1)/2 propositions and (2) that a pairwise tie is not
> > a proposition.
>
> Ok, I'll take your word it that he wrote that. If that's true,
> it means that there are a few contradictions or ambiguities in
> Condorcet's writing. But we already knew that. This started with
> your unusual definition of "eliminate". Your definition still
> bears no resemblence to what that word means to anyone else.

When an opinion always consists of n*(n-1)/2 propositions and when
an "elimination" of a proposition always changes one opinion into
another opinion, then "eliminating" necessarily means "inverting".

******

Mike Ossipoff wrote (4 July 2001):
> Eliminating a pairwise defeat is the same as dropping it.

And what does "dropping" mean? Already Blake Cretney criticized that
the meaning of "dropping" is unclear "to someone who doesn't know
how you [= Mike] have used the term in the past" (16 April 2001).

Mike Ossipoff wrote (4 July 2001):
> When you eliminate something, it's no longer there.

It doesn't make much sense to say that "when you eliminate something
then it's no longer there" as long as one doesn't say what it means
when although the candidate X and the candidate Y are still there the
pairwise comparison X:Y "is not longer there".

Markus Schulze