Tideman vs. Schulze

[Markus Schulze]

Dear participants,

Condorcet wrote ("Essai sur la probabilite des decisions;
rendues a la pluralite des voix," page 126, 1785):

> On formera un avis des n*(n-1)/2 propositions qui reunissent
> le plus de voix. Si cet avis est du nombre des n*(n-1)*...*2
> avis possibles, on regardera comme elu le Sujet a qui cet
> avis accorde la preference. Si cet avis est du nombre de
> (2^(n*(n-1)/2))-n*(n-1)*...*2 avis impossibles, alors on ecartera
> de cet avis impossible successivement les propositions qui
> ont une moindre pluralite, & l'on adoptera l'avis resultant de
> celles qui restent.

My own translation:

> 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, with 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.

You see, that the difference between French and English is
neglectable.

That some participants of the Election Methods Mailing List
believe that Tideman's Method is identical to Condorcet's Method
or that Schulze's Method is identical to Condorcet's Method seems
to me to be caused by the fact that the translator of their copies
of Condorcet's Essai has already interpreted Condorcet's
method in this direction. Condorcet explicitely wrote,
that the weakest pairwise comparisons should be eliminated
successively. He didn't write, that the largest pairwise
comparisons should be locked successively.

Markus Schulze