[EM] How would Condorcet himself have solved his paradox?

Markus Schulze markus.schulze at alumni.tu-berlin.de
Mon Apr 30 11:46:27 PDT 2012

Dear Remi,

in his "Essai sur l'application de l'analyse a la probabilite des
decisions rendues a la pluralite des voix" (Imprimerie Royale,
Paris, 1785), Condorcet gives two different formulations for his
election method.

On page LXVIII of the Preface of the Essai, he writes:

 > From the considerations, we have just made, we get the general
 > rule that in all those situations, in which we have to choose,
 > we have to take successively all those propositions that have
 > a plurality, beginning with those that have the largest,
 > & to pronounce the result that is created by those first
 > propositions, as soon as they create one, without considering
 > the following less probable propositions.

On page 126 of the Essai, he writes:

 > 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.

Markus Schulze 

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