Abstract
In a coalitional voting game, an alternative is said to be in the core when no majority is willing to replace it with another alternative. A social choice correspondence is a mapping which associates any profile of voters’ preferences with a non-empty subset of the set of alternatives, which is understood as the set of selected outcomes. We characterize the social choice correspondences which always select the core of a simple game for any profile of preferences.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
References
Andjiga N.G. and Moulen J. (1988). Binary games in constitutional form and collective choice. Math Soc Sci 16: 189–201
Andjiga N.G. and Moulen J. (2003). Preference aggregation, collective choice and generalized binary constitutions. Math Sci Hum 163: 69–85
Chwe S.Y. (1994). Farsighted coalitional stability. J Econ Theory 63: 299–324
Condorcet: Essai sur l’Application de l’Analyse à la Probabilité des Décisions Rendues à la pluralité des voix. Paris (1785)
Danilov V. (1992). Implementation via Nash equilibrium. Econometrica 60: 43–56
Diffo Lambo, L.: Comportements rationnels dans un jeu de vote. University of Yaounde 1 PhD (Doctorat D’Etat) dissertation-Faculty of Science (1999)
Harsanyi J.C. (1974). An equilibrium-point interpretation of stable sets and a proposed alternative definition. Manage Sci 20: 1472–1495
Maskin E. (1985). The theory of implementation in Nash equilibrium: a survey. In: Hurwicz, L., Schmeidler, D. and Sonnenschein, H. (eds) Social Goals and Organisation: Essays in Memory of Elisha Panzer, pp 173–204. Cambridge University Press, Cambridge
Jackson M.O. (2001). A crash course in implementation theory. Soc Choice Welf 18: 255–708
Li S. (1992). Stability of voting game. Soc Choice Welf 10: 51–56
Moulen, J., Diffo Lambo, L.: Théorie du vote, Pouvoir, Procédure et Prévisions. Paris: Hermès Sc. Publications (2001)
Moulin H. and Peleg B. (1982). Cores of effectivity functions and implementation theory. J Math Econ 10: 115–145
Nakamura K. (1979). The core of simple game with ordinal preferences. Int J Game Theory 4: 95–104
Peleg B. (1984). Game theoretic analysis of voting in committees. Cambridge University Press, Cambridge
Pongou, R.: Rationalité collective dans l’ensemble de stabilit é de Rubinstein. University of Yaounde 1 Maitrise thesis-Faculty of Science (2000)
Pongou, R., Diffo Lambo, L., Tchantcho, B.: Cooperation, stability and social welfare under majority rule. Forthcoming in Econ Theory (2007)
Pongou, R., Tchantcho, B.: A theory of farsightedness in sequential committee games. Mimeo. Department of Economics, Brown University (2007)
Rubinstein A. (1980). Stability of decision systems under majority rule. J Econ Theory 23: 150–159
Tchantcho, B.: Systèmes de décision sociale: Comportements prudents et pouvoir électoral individuel. Thèse de Doctorat Ph/D, Université de Yaoundé I, Cameroun (2004)
Serrano R. (1995). A market to implement the core. J Econ Theory 67: 285–294
Vincenzo D. (1993). Fixed agenda social choice theory: correspondence and impossibility theorems for social choice correspondences and social decision functions. J Econ Theory 59: 324–332
Von Neumann J. and Morgenstern O. (1944). Theory of games and economic behavior. Princeton University Press, Princeton
Author information
Authors and Affiliations
Corresponding author
Additional information
This work was completed when B. Tchantcho was Visiting assistant Professor at UTA (University of Texas at Arlington). We acknowledge the support of the Department of Mathematics of UTA. We are most grateful to R. Pongou of Brown University, USA for his help and advice. We sincerely thank N.G Andjiga for his helpful comments and we are indebted to two anonymous referees for their helpful comments.
Rights and permissions
About this article
Cite this article
Tchantcho, B., Diffo Lambo, L. A characterization of social choice correspondences that implement the core of simple games. Econ Theory 37, 533–542 (2008). https://doi.org/10.1007/s00199-007-0317-5
Received:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s00199-007-0317-5