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International Journal of Game Theory

, Volume 7, Issue 2, pp 81–94 | Cite as

Representations of simple games by social choice functions

  • B. Peleg
Papers

Abstract

We investigate possible constructions of choice procedures (social choice functions) for committees (simple games). The notion of a capacity of a committee is derived from our construction. We determine the capacity of strong, symmetric and weak simple games. We also provide an upper bound on the capacity of a simple game without veto players.

Keywords

Economic Theory Game Theory Social Choice Choice Function Simple 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. Black, R.D.: The Theory of Committees and Elections, Cambridge 1958.Google Scholar
  2. Blin, J.-M., andM.A. Satterthwaite: Individual Decisions and Group Decisions: The Fundamental Differences. Forthcoming, 1975.Google Scholar
  3. Bott, R.: Symmetric Solutions to Majority Games. Annals of Mathematics Study28, 1953, 319–323.Google Scholar
  4. Dutta, B., andP.K. Pattanaik: On Nicely Consistent Voting Systems. Econometrica46, 1978, 163–170.Google Scholar
  5. Gibbard, A.: Manipulation of Voting Schemes: A General Result. Econometrica41, 1973, 587–601.Google Scholar
  6. Nakamura, K.: The Core of a Simple Game with Ordinal Preferences. International Journal of Game Theory4, 1975, 95–104.Google Scholar
  7. -: The Vetoers in a Simple Game with Ordinal Preferences. To appear in International Journal of Game Theory, 1976.Google Scholar
  8. Peleg, B.: Consistent Voting Systems. Econometrica46, 1978, 153–161.Google Scholar
  9. Plott, C.R.: Path Independence, Rationality and Social Choice. Econometrica41, 1973, 1075–1091.Google Scholar
  10. Sen, A.: Social Choice Theory: A Re-examination. Econometrica45, 1977, 53–89.Google Scholar
  11. Shapley, L.S.: Simple Games: An Outline of the Descriptive Theory. Behavioral Science7, 1962, 59–66.Google Scholar
  12. -: Compound Simple Games, III: On Committees. The Rand Corporation, RM-5438-PR, 1967.Google Scholar
  13. Wilson, R.B.: The Game-Theoretic Structure of Arrow's General Possibility Theorem. Journal of Economic Theory5, 1972, 14–20.Google Scholar

Copyright information

© Physica-Verlag 1978

Authors and Affiliations

  • B. Peleg
    • 1
  1. 1.Institute of Mathematicsthe Hebrew UniversityJerusalemIsrael

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