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Binary Effectivity Rules

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  • Hans Keiding

    ()

  • Bezalel Peleg

    ()

Abstract

A social choice rule is a collection of social choice correspondences, one for each agenda. An effectivity rule is a collection of effectivity functions, one for each agenda. We prove that every monotonic and superadditive effectivity rule is the effectivity rule of some social choice rule. A social choice rule is binary if it is rationalized by an acyclic binary relation. The foregoing result motivates our definition of a binary effectivity rule as the effectivity rule of some binary social choice rule. A binary social choice rule is regular if it satisfies unanimity, monotonicity, and independence of infeasible alternatives. A binary effectivity rule is regular if it is the effectivity rule of some regular binary social choice rule. We characterize completely the family of regular binary effectivity rules. Quite surprisingly, intrinsically defined von Neumann-Morgenstern solutions play an important role in this characterization.

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Bibliographic Info

Paper provided by The Center for the Study of Rationality, Hebrew University, Jerusalem in its series Discussion Paper Series with number dp378.

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Length: 16 pages
Date of creation: Oct 2004
Date of revision:
Publication status: Published in Review of Economic Design, 2006, vol. 10, pp. 167-181.
Handle: RePEc:huj:dispap:dp378

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Keywords: social choice correspondences; effectivity functions; Nakamura’s number; von Neumann-Morgenstern solutions;

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References

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  1. Moulin, Hervé & Peleg, B., 1982. "Cores of effectivity functions and implementation theory," Economics Papers from University Paris Dauphine 123456789/13220, Paris Dauphine University.
  2. Moulin, Herve, 1985. "From social welfare ordering to acyclic aggregation of preferences," Mathematical Social Sciences, Elsevier, vol. 9(1), pages 1-17, February.
  3. Peleg, Bezalel & Peters, Hans & Storcken, Ton, 2002. "Nash consistent representation of constitutions: a reaction to the Gibbard paradox," Mathematical Social Sciences, Elsevier, vol. 43(2), pages 267-287, March.
  4. Hans Keiding & Bezalel Peleg, 1999. "Representation of Effectivity Functions in Coalition Proof Nash Equilibrium: A Complete Characterization," Discussion Papers 99-21, University of Copenhagen. Department of Economics.
  5. Bezalel Peleg, 1997. "Effectivity functions, game forms, games, and rights," Social Choice and Welfare, Springer, vol. 15(1), pages 67-80.
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Cited by:
  1. Bezalel Peleg & Hans Peters, 2005. "Nash Consistent Representation of Effectivity Functions through Lottery Models," Discussion Paper Series dp404, The Center for the Study of Rationality, Hebrew University, Jerusalem.
  2. Bezalel Peleg & Shmuel Zamir, 2013. "Representation of constitutions under incomplete information," Discussion Paper Series dp634, The Center for the Study of Rationality, Hebrew University, Jerusalem.

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