# [EM] Condorcet cyclic drop rule

MIKE OSSIPOFF nkklrp at hotmail.com
Sat Apr 7 12:51:31 PDT 2001

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>In Condorcet's "Essai sur l'application de l'analyse a la probabilite
>des decisions rendues a la pluralite des voix" (Imprimerie Royale,
>Paris, 1785), the description of his bottom-up proposal is more
>concrete. He wrote:
>
> > 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.
>
>In short: Condorcet wants to find the best guess for best ranking
>and then extracts the winner from this ranking.

So then Condorcet meant, for his bottom-up method, drop the weakest
defeat till there are no cycles. That isn't something that we want to
do. If creating a transitive output ranking, and then electing the
candidate at the top of it, was his goal, then his top-down proposal
is a better idea. Was his top-down proposal written later than
the bottom-up proposal?

But I think most would agree that his words were often un-specific
enough so that we can still call PC & SSD "Condorcet's method", as
well as Ranked-Pairs, whether defeat-support or margins. (And BeatpathWinner
also, due to its equivalence with a version of SSD).

Mike Ossipoff

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