Social Choice and Welfare

, Volume 4, Issue 4, pp 295–305 | Cite as

On the core of voting games

  • M. Le Breton
Article

Abstract

The purpose of this paper is to analyse a special class of cooperative games called voting games in the cases where the set of alternatives is finite or a convex and compact subset of an Euclidean space. In a first part we provide a complete classification of these games according to the non-emptiness of the core. Then in a second part we prove that the set of continuous preference profiles having a core is small from a topological point of view. The contribution of the paper is mainly a simplification of the existing proofs and the introduction of a suitable topology to formulate the second question.

Keywords

Economic Theory Euclidean Space Compact Subset Special Class Cooperative Game 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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References

  1. 1.
    Berge C (1966) Espaces topologiques. Fonctions multivoques. Dunod, ParisGoogle Scholar
  2. 2.
    Blair DH, Pollak RA (1982) Acyclic collective choice rules. Econometrica 50:931–943Google Scholar
  3. 3.
    Brown DJ (1975) Aggregation of preferences. Q J Econ 89:456–469Google Scholar
  4. 4.
    Cox GW (1984) Non-collegial simple games and the nowhere denseness of the set of preference profiles having a core. Soc Choice Welfare 1:159–164Google Scholar
  5. 5.
    Ferejohn JA, Grether DM (1974) On a class of rational social decision procedures. J Econ Theory 8:471–482Google Scholar
  6. 6.
    Greenberg J (1979) Consistent majority rules over compact sets of alternatives. Econometrica 41:285–297Google Scholar
  7. 7.
    Hildenbrand W (1974) Core and equilibria of a large economy. Princeton University Press, PrincetonGoogle Scholar
  8. 8.
    Lang S (1969) Real analysis. Addison-Wesley, ReadingGoogle Scholar
  9. 9.
    Le Breton M (1985) Kannai topology with locally saturated preferences. d.p. 8507, Leme, Universite de Rennes 1Google Scholar
  10. 10.
    Mas-Colell A (1977) On the continuous representation of preorders. Int Econ Rev 18:509–513Google Scholar
  11. 11.
    Moulin H (1983) The strategy of social choice. North-Holland, AmsterdamGoogle Scholar
  12. 12.
    Nakamura K (1979) The vetoers in a simple game with ordinal preferences. Int J Game Theory 8:55–61Google Scholar
  13. 13.
    Peleg B (1984) Game theoretic analysis of voting in committees. Cambridge University Press, CambridgeGoogle Scholar
  14. 14.
    Rubinstein A (1979) A note on the nowhere denseness of societies having an equilibrium under majority rule. Econometrica 47:511–514Google Scholar
  15. 15.
    Schofield N (1980) Generic properties of simple Bergson Samuelson welfare functions. J Math Econ 7:175–192Google Scholar
  16. 16.
    Schofield N (1983) Generic instability of majority rule. Rev Econ Stud 50: 695–705Google Scholar
  17. 17.
    Schofield N (1984) Social equilibrium and cycles on compact sets. J Econ Theory 33:59–71Google Scholar
  18. 18.
    Schofield N (1984) Classification theorem for smooth social choice on a manifold. Soc Choice Welfare 1:187–210Google Scholar
  19. 19.
    Schofield N (1985) Social choice and democracy. Springer, Berlin Heidelberg New YorkGoogle Scholar
  20. 20.
    Schofield N (1986) Permutation cycles and manipulation of choice functions. Soc Choice Welfare 3:107–117Google Scholar
  21. 21.
    Sen A (1986) Social choice theory. In: Handbook in Mathematical Economics. Arrow KJ, Intriligation MD (eds) North-Holland, AmsterdamGoogle Scholar
  22. 22.
    Wagneur E (1979) Saturation locale et concepts primitifs de la theorie du consommateur. Econometrica 47:1549–1553Google Scholar

Copyright information

© Springer-Verlag 1987

Authors and Affiliations

  • M. Le Breton
    • 1
    • 2
  1. 1.C.R.E.M.E.R.CFaculté des Sciences EconomiquesRennesFrance
  2. 2.L.E.M.E.Faculté des Sciences EconomiquesRennesFrance

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