# [EM] Condorcet cyclic drop rule

Markus Schulze schulze at sol.physik.tu-berlin.de
Fri Apr 6 02:24:12 PDT 2001

```Dear Blake, dear Mike,

Blake wrote (5 Apr 2001):

> Mike wrote (4 Apr 2001):
> > You seem to think that Condorcet wanted to eliminate all cycles.
> > But he said to elect the voted CW. If he wanted to get rid of all
> > cycles, then he wouldn't have just said to elect the voted CW.
>
> Well, I advocate a method that gets rid of all cycles, and I also say
> to elect the CW.  The crucial point is that getting rid of the cycles
> can't change the CW.  You act as if advocating the CW and getting rid
> of all cycles are mutually exclusive goals.

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.

******

Mike wrote (4 Apr 2001):

> For instance, it seems to me that Condorcet's method is
> defined that way in Fishburn's well-known survey article
> -- probably in the '70s.

The exact reference is:

Peter C. Fishburn, "Condorcet Social Choice Functions",
SIAM Journal of Applied Mathematics, vol. 33, p. 469-489, 1977.

Markus Schulze

```