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

[Markus Schulze]

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. Condorcet suggested that
circular ties should be solved by successively _inverting_ defeats
in a way that gives priority to _inverting_ weaker defeats.

Markus Schulze