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Binary Effectivity Rules

Author

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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.

Suggested Citation

  • Hans Keiding & Bezalel Peleg, 2004. "Binary Effectivity Rules," Discussion Paper Series dp378, The Federmann Center for the Study of Rationality, the Hebrew University, Jerusalem.
  • Handle: RePEc:huj:dispap:dp378
    as

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    References listed on IDEAS

    as
    1. Moulin, H. & Peleg, B., 1982. "Cores of effectivity functions and implementation theory," Journal of Mathematical Economics, Elsevier, vol. 10(1), pages 115-145, June.
    2. Bezalel Peleg, 1997. "Effectivity functions, game forms, games, and rights," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 15(1), pages 67-80.
    3. Hans Keiding & Bezalel Peleg, 2002. "Representation of effectivity functions in coalition proof Nash equilibrium: A complete characterization," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 19(2), pages 241-263.
    4. 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.
    5. repec:dau:papers:123456789/13220 is not listed on IDEAS
    6. Moulin, Herve, 1985. "From social welfare ordering to acyclic aggregation of preferences," Mathematical Social Sciences, Elsevier, vol. 9(1), pages 1-17, February.
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    Cited by:

    1. Peleg, Bezalel & Peters, Hans, 2009. "Nash consistent representation of effectivity functions through lottery models," Games and Economic Behavior, Elsevier, vol. 65(2), pages 503-515, March.
    2. Bezalel Peleg & Ron Holzman, 2017. "Representations of Political Power Structures by Strategically Stable Game Forms: A Survey," Games, MDPI, Open Access Journal, vol. 8(4), pages 1-17, October.
    3. Bezalel Peleg & Shmuel Zamir, 2014. "Representation of constitutions under incomplete information," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 57(2), pages 279-302, October.

    More about this item

    Keywords

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

    JEL classification:

    • D71 - Microeconomics - - Analysis of Collective Decision-Making - - - Social Choice; Clubs; Committees; Associations

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