Solutions de tournois : un spicilège
Mathématiques et Sciences humaines, Tome 133 (1996) , pp. 7-22.

L'article passe en revue quelques Solutions de Tournois (correspondances de choix définies sur les tournois). On compare ces solutions entre elles, et on mentionne certaines de leurs propriétés.

The article is a survey of some existing Tournament Solutions (Choice correspondences defined on tournaments). We compare these solutions and mention some of their properties.

@article{MSH_1996__133__7_0,
     author = {Laslier, Jean-Fran\c cois},
     title = {Solutions de tournois : un spicil\`ege},
     journal = {Math\'ematiques et Sciences humaines},
     pages = {7--22},
     publisher = {Ecole des hautes-\'etudes en sciences sociales},
     volume = {133},
     year = {1996},
     zbl = {0870.90014},
     mrnumber = {1411797},
     language = {fr},
     url = {http://www.numdam.org/item/MSH_1996__133__7_0/}
}
Laslier, Jean-François. Solutions de tournois : un spicilège. Mathématiques et Sciences humaines, Tome 133 (1996) , pp. 7-22. http://www.numdam.org/item/MSH_1996__133__7_0/

Banks, J. (1985) "Sophisticated voting outcomes and agenda control ", Social Choice and Welfare, 2, 295-306. | Zbl 0597.90011

Banks, J., G. Bordes et M. Le Breton (1991) "Covering relations, closest orderings and hamiltonian bypaths in tournaments", Social Choice and Welfare, 8, 355-363. | MR 1129431 | Zbl 0734.90027

Barthélémy, J.-P. et B. Monjardet (1981) "The median procedure in cluster analysis and social choice theory", Mathematical Social Sciences, 1,235-267. | MR 616379 | Zbl 0486.62057

Berge, C. (1970) Graphes, Gauthier-Villars.

Bermond, J.-C. (1972) "Ordres à distance minimum d'un tournoi et graphes partiels sans circuits maximaux", Math. Sci. hum, 37, 5-25. | Numdam | MR 300927 | Zbl 0239.05122

Charon, I., O. Hudry et F. Woirgard (1996) "Ordres médians et ordres de Slater des tournois ", Math. Inf. et Sci. hum., 133. | Numdam | MR 1411798 | Zbl 0870.90095

Copeland, A.H. (1951) "A 'reasonable' social welfare function", Seminar on applications of mathematics to social sciences, University of Michigan.

Duggan, J. et M. Le Breton (1995) "Dutta's minimal covering set and Shapley's saddle ", Document de travail du GREQAM 95A02, Aix-Marseille.

Dutta, B. (1988) "Covering sets and a new Condorcet choice correspondence ", Journal of Economic Theory, 44, 63-80. | MR 935663 | Zbl 0652.90013

Dutta, B. (1990) "On the Toumament Equilibrium set", Social Choice and Welfare, 7, 381- 383. | Zbl 0713.90007

Dutta, B. et A. Sen (1993) "Implementing generalized Condorcet social choice functions via backward induction", Social Choice and Welfare, 10, 149-160. | MR 1219927 | Zbl 0779.90004

Farquharson, R. (1969) Theory of voting. Yale University press, New Haven. | MR 255246

Fishburn, P. (1977) "Condorcet social choice functions", SIAM Journal of Applied Mathematics, 33, 469-489. | MR 449470 | Zbl 0369.90002

Fisher, D. et J. Ryan (1992) "Optimal strategies for a generalized "Scissors, Paper and Stone" game", American Mathematical Monthly, 99, 935-942. | MR 1190559 | Zbl 0776.05047

Fisher, D. et J. Ryan (1995a) "Toumament games and Positive Tournaments", Journal of Graph Theory, 19, 217-236. | MR 1315439 | Zbl 0823.90142

Fisher, D. et J. Ryan (1995b) "Probabilities within optimal strategies for tournament games", Discrete Applied Mathematics, 56, 87-91. | MR 1311308 | Zbl 0819.90132

Henriet, D. (1985) "The Copeland choice function : An axiomatic characterization ", Social Choice and Welfare, 2, 49-63. | MR 854836 | Zbl 0602.90010

Jensen, R. (1986) "Comparison of consensus methods for priority ranking problems", Decision Sciences, 17, 195-211.

Johnson, C., W. Beine et T. Wang (1979) "Left-right asymmetry in an eigenvector ranking procedure", Journal of Mathematical Psychology, 19, 61-64. | MR 529036

Keener, J. (1993) "The Perron-Frobenius theorem and the ranking of football teams", SIAM Review, 35 (1), 80-93. | MR 1207798 | Zbl 0788.62064

Kendall, M.G. (1955) "Further contributions to the theory of paired comparisons", Biometrics, 11, 43-62. | MR 75506

Laffond, G. et J. Lainé (1994) "Weak covering relations", Theory and Decision, 37, 245-265. | MR 1302001 | Zbl 0815.90005

Laffond, G., J. Lainé et J.-F. Laslier (1996) "Composition-consistency of social choice functions and tournament solutions", Social Choice and Welfare, 13, 75-93. | MR 1366403 | Zbl 0843.90007

Laffond, G. et J.-F. Laslier (1991) "Slater's winners of a toumament may not be in the Banks set", Social Choice and Welfare, 8, 355-363. | MR 1129432 | Zbl 0733.90008

Laffond, G., J.-F. Laslier et M. Le Breton (1993a) "The Bipartisan set of a toumament game", Games and Economic Behavior, 5, 182-201. | MR 1201480 | Zbl 0770.90080

Laffond, G., J.-F. Laslier et M. Le Breton (1993b) "More on the Tournament Equilibrium Set", Mathématiques, Informatique et Sciences Humaines, 123, 37-44. | Numdam | MR 1252567 | Zbl 0806.90002

Laffond, G., J.-F. Laslier et M. Le Breton (1994) "Social choice mediators", American Economic Review (proc.), 84 (2), 448-453.

Laffond, G., J.-F. Laslier et M. Le Breton (1995a) "A complete analysis of Condorcet choice correspondences ", Mathematical Social Sciences, 30 (1), 23-35. | MR 1341800 | Zbl 0886.90016

Laffond, G., J.-F. Laslier et M. Le Breton (1995b) "A theorem on symmetric, twoplayer zero-sum games ", Document de travail du GREQAM 95A01, Aix-Marseille.

Laslier, J.-F. (1993) Solutions de Tournois, Habilitation à diriger les recherches en Science Économique, Université de Cergy-Pontoise.

Laslier, J.-F. (1995) "Multivariate description of comparison matrices ", à paraître dans Multicriteria Decision analysis, 5 (2). | Zbl 0847.90005

Levchenkov, V.S. (1992) "Social choice theory : a new sight", Preprint of the Institute for System Analysis, Moscou.

Levchenkov, V.S. (1995a) "Self-consistent choice rule", Document de travail du Laboratoire d'Économétrie, CNAM, Paris.

Levchenkov, V.S. (1995b) "Cyclic tournaments : A matching solution", Document de travail du Laboratoire d'Econométrie, CNAM, Paris.

Mckelvey R. and R. Niemi (1978) "A multistage game representation of sophisticated voting for binary procedures", Journal of Economic Theory, 18,1-22. | MR 509571 | Zbl 0403.90004

Michel, P. (1984) Cours de mathématique pour économistes, Economica.

Miller, N. (1980) "A new solution set for tournaments and majority voting : Further graph-theoretical approaches to the theory of voting", American Journal of Political Science, 24 (1), 68-96.

Moon, J.W. (1968) Topics on tournaments, Holt, Rinehart and Winston. | MR 256919 | Zbl 0191.22701

Moulin, H. (1983) The Strategy of Social Choice, North Holland, Amsterdam. | MR 708280 | Zbl 0543.90002

Moulin, H. (1986) "Choosing from a tournament", Social Choice and Welfare, 3, 272-291. | MR 872651 | Zbl 0618.90004

Ordeshook, P.C. (1986) Game theory and political theory, an introduction, Cambridge University Press.

Rubinstein, A. (1980) "Ranking the participants in a toumament", SIAM Journal of Applied Mathematics, 98, 108-11. | MR 559085 | Zbl 0442.05028

Saaty, T. (1977) "A scaling method for priorities in hierarchical structures", Journal of Mathematical Psychology, 15, 234-281. | MR 682619 | Zbl 0372.62084

Saaty, T. (1986) "Axiomatic foundation of the analytical hierarchy process", Management Science, 32 (7), 84-855. | MR 846562 | Zbl 0596.90003

Schwartz, T. (1990) "Cyclic tournaments and cooperative majority voting : A solution", Social Choice and Welfare, 7, 19-29. | MR 1050748 | Zbl 0698.90008

Shapley, L. (1964) "Some topics in two-persons games", in Advances in Game Theory, Annals of Mathematic Studies 52, M. Dresher, L. Shapley et A. Tucker (eds), Princeton University Press, 1-28. | MR 198990 | Zbl 0126.16204

Shepsle, K. et B. Weingast (1982) "Uncovered sets and sophistigated voting outcomes with implications for agenda institutions", American Journal of Political Science, 21, 769-803.

Slater, P. (1961) "Inconsistencies in a schedule of paired comparisons ", Biometrika, 48, 303-312.

Wei, T. (1952) The Algebraic Foundations of ranking Theory, Ph. D. thesis, Cambridge University.

Zermelo, E. (1929) "Die Berechnung der Tumier-Ergebnisse als ein maximal Problem der Warscheinlichkeistsrechnung", Math. Zeitung, 29, 436-460. | JFM 54.0543.01 | MR 1545015