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

Ted Stern araucaria.araucana at gmail.com
Mon Apr 30 12:03:56 PDT 2012

```On 30 Apr 2012 11:46:27 -0700, Markus Schulze wrote:
>
> 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
>

Markus,

To me, the first quote recommends something along the lines of min-max
pairwise opposition (MMPO).