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Binary Effectivity Rules

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Author Info
Hans Keiding ()
Bezalel Peleg ()

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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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Publisher Info
Paper provided by Center for Rationality and Interactive Decision Theory, Hebrew University, Jerusalem in its series Discussion Paper Series with number dp378.

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

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

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Find related papers by JEL classification:
D71 - Microeconomics - - Analysis of Collective Decision-Making - - - Social Choice; Clubs; Committees; Associations

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References listed on IDEAS
Please report citation or reference errors to , or , if you are the registered author of the cited work, log in to your RePEc Author Service profile, click on "citations" and make appropriate adjustments.:
  1. Hans Keiding & Bezalel Peleg, 2002. "Representation of effectivity functions in coalition proof Nash equilibrium: A complete characterization," Social Choice and Welfare, Springer, vol. 19(2), pages 241-263. [Downloadable!] (restricted)
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  2. Moulin, H. & Peleg, B., 1982. "Cores of effectivity functions and implementation theory," Journal of Mathematical Economics, Elsevier, vol. 10(1), pages 115-145, June. [Downloadable!] (restricted)
  3. Moulin, Herve, 1985. "From social welfare ordering to acyclic aggregation of preferences," Mathematical Social Sciences, Elsevier, vol. 9(1), pages 1-17, February. [Downloadable!] (restricted)
  4. Bezalel Peleg, 1997. "Effectivity functions, game forms, games, and rights," Social Choice and Welfare, Springer, vol. 15(1), pages 67-80. [Downloadable!] (restricted)
  5. 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. [Downloadable!] (restricted)
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  1. Bezalel Peleg & Hans Peters, 2005. "Nash Consistent Representation of Effectivity Functions through Lottery Models," Discussion Paper Series dp404, Center for Rationality and Interactive Decision Theory, Hebrew University, Jerusalem. [Downloadable!]
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