Condorect sub-cycle rule

[Markus Schulze]

Condorcet wrote ("Essai sur l'application de l'analyse a la probabilite
des decisions; Rendues a la pluralite des voix," Paris, 1785, page 126):
> 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 possible, 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 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.

Markus Schulze