Note sur le calcul de la probabilité des paradoxes du vote
Mathématiques informatique et sciences humaines, Tome 120 (1992), pp. 33-48.

De nombreux travaux se sont efforcés au cours des années récentes de calculer la probabilité des paradoxes ou des difficultés que la théorie des choix collectifs a mis en évidence. On passe en revue dans cette note les principaux modèles de calcul utilisés dans ces travaux. On applique en outre l'un des modèles présentés au calcul de la probabilité de quelques paradoxes bien connus de la théorie du vote.

A number of papers have recently attempted to calculate the probability of the paradoxes or difficulties that social choice theory has discovered. We review in this note most of the probabilistic models which have been used in these papers. Furthermore, we apply one of these models to the computation of the probability of some well known voting paradoxes.

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Berg, Sven; Lepelley, Dominique. Note sur le calcul de la probabilité des paradoxes du vote. Mathématiques informatique et sciences humaines, Tome 120 (1992), pp. 33-48. http://archive.numdam.org/item/MSH_1992__120__33_0/

Arrow K.J., Social choice and individual value, New York, Wiley, 1963. | Zbl

Berg S., "Paradox of voting under an urn model : the effect of homogeneity", Public Choice, 47, (1985a), 377-387.

Berg S., "A note on plurality distorsion in large committees", European Journal of Political Economy, 1, (1985b), 271-284.

Berg S., "The probability of casting a decisive vote : the effects of a caucus", Public Choice, 64, (1990), 73-92.

Berg S. et B. Bjurulf, "A note on the paradox of voting : anonymous preference profiles and May's formula", Public Choice, 40, (1983), 307-316.

Berg S. et D. Lepelley, "Voting cycles, plurality rule and strategic manipulation", Annals of Operations Research, 23, (1990), 247-256. | MR | Zbl

Borda J.C. (de), "Mémoire sur les élections au scrutin", Histoire de l'académie royale des sciences, Paris, 1781.

Condorcet M.J.A. (Marquis de), Essai sur l'application de l'analyse à la probabilité des décisions rendues à la pluralité des voix, Paris, 1785.

Feller W., An introduction to probability theory and its applications, New York, Wiley, 1957. | MR | Zbl

Fishburn P.C., "Monotonicity paradox in the theory of elections", Discrete Applied Mathematics, 4, (1982), 119-134. | MR | Zbl

Fishburn P.C. et W.V. Gehrlein, "Majorities efficiencies for simple voting procedures", Theory and Decision, 14, (1982), 141-153. | MR | Zbl

Gehrlein W.V., "Single-stage election procedures for large electorates", Journal of Mathematical Economics, 8, (1981), 263-275. | MR | Zbl

Gehrlein W.V., "Condorcet efficiency and constant scoring rules", Mathematical Social Sciences, 2, (1982), 123-130. | Zbl

Gehrlein W.V., "Condorcet's paradox", Theory and Decision, 15, (1983), 161-197. | MR | Zbl

Gehrlein W.V., A variant interpretation of the impartial anonymous culture condition, document dactylographié, University of Delaware, 1984.

Gehrlein W.V., "The expected likelihood of transitivity for a probabilistic chooser", Annals of Operations Research, 23, (1990), 235-246. | MR | Zbl

Gehrlein W.V., "Coincidence probabilities for simple majority and proportional lottery rules", Economics Letters, 35, (1991), 349-353. | Zbl

Gehrlein W.V., "Condorcet efficiency and social homogeneity", papier presenté au premier meeting de la "Society for Social Choice and Welfare", Caen, 1992. | Zbl

Gehrlein W.V. et S. Berg, "The effect of social homogeneity on coincidence probabilities for pairwise proportional lottery and simple majority rule", à paraître dans Social Choice and Welfare, 1992. | MR | Zbl

Gehrlein W.V. et P.C. Fishburn, "The probability of the paradox of voting : a computable solution", Journal of Economic Theory, 13, (1976a), 14-25. | MR | Zbl

Gehrlein W.V. et P.C. Fishburn, "Condorcet's paradox and anonymous preference profiles", Public Choice, 26, (1976b), 1-18.

Gehrlein W.V. et P.C. Fishburn, "Coincidence probabilities for simple majority and positionalist voting rules", Social Science Research 7, (1978), 272-283.

Gehrlein W.V. et P.C. Fishburn, "Effects of abstentions on voting procedures in three-alternative elections", Behavioral Science 24, (1979), 346-354.

Gehrlein W.V. et P.C. Fishburn, "Scoring rule sensitivity to weight selection", Public Choice,40, (1983), 249-261.

Gibbard A., "Manipulation of voting schemes : a general result", Econometrica, 41, (1973),587-601. | MR | Zbl

Gillett R., "Collective Indecision", Behavioral Science, 22, (1977), 383-390.

Gillett R., "The comparative likelihood of an equivocal outcome under plurality, Condorcet and Borda voting procedures", Public choice, 35, (1980), 483-491.

Guilbaud G.Th., "Les théories de l'intérêt général et le problème logique de l'agrégation ", Économie Appliquée, 5, (1952), 501-584.

Johnson N.L. et S. Kotz, Urns models and their application, New York, Wiley, 1977. | MR | Zbl

Kreweras G., "Les décisions collectives", Mathématiques et Sciences Humaines, 2, (1962), 25-35. | Numdam

Lepelley D., Remarques sur les calculs de probabilité dans la théorie des choix collectifs, document dactylographié, Université de Caen, 1984.

Lepelley D., Contribution à l'analyse des procédures de décision collective, Thèse de doctorat, Université de Caen, 1989.

Lepelley D., "On the probability of electing the Condorcet Loser", à paraître dans Mathematical Social Sciences, 1992. | MR | Zbl

Lepelley D. et B. Mbih, "The proportion of coalitionally unstable situations under the plurality rule", Economics Letters, 24, (1987), 311-315. | MR

Lepelley D. et B. Mbih, The vulnerability of four social choice functions to coalitional manipulation of preferences, document dactylographié, Université de Caen, 1992.

May R.M., "Some mathematical remarks on the paradox of voting", Behavioral Science, 16, (1971), 143-151.

Merrill S., Making multicandidate elections more democratic, Princeton [University Press, 1988.

Moulin H., "Condorcet's principle implies the no show paradox", Journal of Economic Theory, 45, (1988), 53-64. | MR | Zbl

Niemi R.G. et W.H. Riker, "The choice of voting systems", Scientific American, 234 (1976), 21-27

Nitzan S., "The vulnerability of point-voting schemes to preference variation and strategic manipulation", Public choice, 47 (1985) 249-270.

Nurmi H., "Probability models in constitutional choice", European Journal of Political Economy, 6, (1990), 107-117.

Nurmi H. et Y. Uusi-Heikkila, "Computer simulations of approval and plurality voting : the frequency of weak Pareto violations and Condorcet losers choice in impartial culture", European Journal of Political Economy, 2/1, (1985), 47-59.

Paris D.C., "Plurality distorsion and majority rule", Behavioral Science, 20, (1975), 125-133.

Peleg B., "A note on manipulability of large voting schemes", Theory and Decision, 11, (1979), 401-412. | MR | Zbl

Satterthwaite M.A., "Strategy-proofness and Arrow's conditions : existence and correspondence theorems for voting procedures and social welfare functions", Journal of Economic Theory, 10, (1975), 187-217. | MR | Zbl

Smith J.H., "Aggregation of preferences with variable electorates", Econometrica, 41, (1973), 1027-1041. | MR | Zbl

Young H.P., "Social choice scoring functions", SIAM Journal of Applied Mathematics, 28, (1975), 824-838. | MR | Zbl