Condorcet's theory of voting
Mathématiques et Sciences humaines, Tome 111 (1990) , pp. 45-59.

Condorcet pensait que le but d'un vote est de faire un choix qui soit le meilleur pour la société. Selon ce point de vue, il y a un choix qui est objectivement le meilleur, un autre vient en second et ainsi de suite. Malheureusement, les électeurs se trompent quelquefois, ils perçoivent mal quel est le meilleur choix. Par conséquence, pour l'établissement d'une règle de vote, l'objectif devrait être de choisir l'alternative qui est la plus probablement la meilleure. Condorcet résolut ce problème en utilisant une forme d'estimation par le maximum de vraisemblance. La procédure qu'il en a tirée peut aussi être justifiée à partir d'une perspective axiomatique moderne. C'est la seule fonction du choix social qui satisfasse une variante de l'axiome d'indépendance en même temps que plusieurs autres propriétés classiques.

Condorcet believed that the purpose of voting is to make a choice that is “best” for society. According to his view, there is one choice that is objectively best, another that is second-best, and so forth. Unfortunately, voters sometimes make mistakes ; they misperceive what is best. In designing a voting rule, therefore, the objective should be to choose the alternative that is most likely to be best. Condorcet solved this problem using a form of maximum likelihood estimation. The procedure that he derives can also be justified from a modern axiomatic perspective. It is the unique social welfare function that satisfies a variant of independant of irrelevant alternatives together with several other standard properties.

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     author = {Young, H. P.},
     title = {Condorcet's theory of voting},
     journal = {Math\'ematiques et Sciences humaines},
     pages = {45--59},
     publisher = {Ecole des hautes-\'etudes en sciences sociales},
     volume = {111},
     year = {1990},
     zbl = {0718.01011},
     mrnumber = {1082273},
     language = {en},
     url = {www.numdam.org/item/MSH_1990__111__45_0/}
}
Young, H. P. Condorcet's theory of voting. Mathématiques et Sciences humaines, Tome 111 (1990) , pp. 45-59. http://www.numdam.org/item/MSH_1990__111__45_0/

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