Condorcet's theory of voting
Mathématiques informatique 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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Young, H. P. Condorcet's theory of voting. Mathématiques informatique et sciences humaines, Tome 111 (1990), pp. 45-59. http://archive.numdam.org/item/MSH_1990__111__45_0/

Arrow, K.J., 1963, Social Choice and Individual Values, 2d ed., New York, John Wiley. Baker, K.M., 1975, Condorcet, Chicago, University of Chicago Press. | MR

Barthélemy, J.P., and Mcmorris, F.R., 1986, "The Median Procedure for n-Trees", Journal of Classification, 3, 329-334. | MR | Zbl

Barthélemy, J.P., and Monjardet, B., 1981, "The Median Procedure in Cluster Analysis and Social Choice Theory", Mathematical Social Sciences, 1, 235-267. | MR | Zbl

Batchelder, W., and Bershad, N.J., 1979, "The Statistical Analysis of a Thurstonian Model for Rating Chess Players", Journal of Mathematical Psychology, 19, 39-60. | MR | Zbl

Black, D., 1958, The Theory of Committees and Elections, Cambridge, Cambridge University Press. | Zbl

Borda, Jean-Charles (de), 1784, "Mémoire sur les Élections au Scrutin", in Histoire de l'Académie Royale des Sciences.

Condorcet, Marquis De, 1785, Essai sur l'application de l'analyse à la probabilité des décisions rendues à la probabilité des voix, Paris, de l'imprimerie royale.

Fishburn, P.C., 1973, The Theory of Social Choice, Princeton, Princeton University Press. | MR | Zbl

Gelfand, A., and Solomon, H., 1973, "A Study of Poisson's Models for Jury Verdicts in Criminal and Civil Trials", Journal of the American Statistical Association, 68, 271-278.

Good, I.J., 1955, "On the Marking of Chess Payers", The Mathematical Gazette, 39, 292-296. | MR | Zbl

Grofman, B., 1981, "When is the Condorcet Winner the Condorcet Winner ?", University of California, Irvine, typescript.

Grofman, B., and Feld S., 1988, "Rousseau's General Will : A Condorcetian Perspective ", American Political Science Review, 82, 567-576.

GROFMAN, B., and OWEN G., eds., 1986, Information Pooling and Group Decision Making, Greenwich, CT, JAI Press.

HENRY, C., eds., 1833, Correspondance Inédite de Condorcet et de Turgot 1770-1779, Paris, Charavay Frères.

Jacquet-Lagreze, E., 1969, "L'agrégation des opinions individuelles", in Informatique et Sciences humaines, vol.4.

Jech, T., 1983, "The ranking of Incomplete Tournaments : a Mathematician's Guide to Popular Sports", American Mathematical Monthly, 90, 246-266. | MR | Zbl

Kemeny, J., 1959, "Mathematics without Numbers", Daedalus, 88, 571-591.

Kemeny, J., and Snell L., 1960, Mathematical Models in the Social Sciences, Boston, Ginn. | Zbl

Kramer, G., 1977, "A Dynamical Model of Political Equilibrium", Journal of Economic Theory, 16, 310-334. | MR | Zbl

Mascart, J., 1919, La vie et les travaux du Chevalier Jean-Charles de Borda, Paris, Rey. | JFM

Michaud, P., 1985, "Hommage à Condorcet (version intégrale pour le bicentenaire de l'Essai de Condorcet)", Etude F-084, Centre scientifique-IBM France, Paris.

Michaud, P., and Marcotorchino, J.F., 1978, "Optimization in Ordinal Data Analysis", étude F-001, Centre scientifique-IBM France, Paris.

Nash, J., 1950, "The Bargaining Problem", Econometrica, 18, 155-162. | MR

Nitzan, S., and Paroush, J., 1982, "Optimal Decision Rules in Uncertain Dichotomous Situations ", International Economic Review, 23, 289-297. | MR | Zbl

Poisson, Siméon-Denis, 1837, Recherches sur la probabilité des jugements en matière criminale et en matière civile, précédées des règles générales du calcul des probabilités, Paris, Bachelier.

Rousseau, J.J., 1762, The Social Contract, Harmondsworth, England, Penguin (1968).

Shapley, L.S., and Grofman, B., 1984, "Optimizing Group Judgmental Accuracy in the Presence of Interdependencies", Public Choice, 43, 329-343.

Todhunter, I., 1949, A History of the Mathematical Theory of Probability, New York, Chelsea.

Urken, A.B., and Traflet, S., 1984, "Optimal Jury Design", Jurimetrics, 24, 218-235.

Young, H.P., 1974, "An Axiomatization of Borda's Rule", Journal of Economic Theory, 9, 43-52. | MR

Young, H.P., 1986, "Optimal Ranking and Choice from Pariwise Comparisons ", in Information Pooling and Group Decision Making, ed., B. Grofman and G. Owen, Greenwich, CT, JAI Press.

Young, H.P., and Levenglick, A., 1978, "A Consistent Extension of Condorcet's Election Principle ", SIAM Journal on Applied Mathematics, 35, 285-300. | MR | Zbl