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Preference aggregation theory without acyclicity: The core without majority dissatisfaction

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  • Kumabe, Masahiro
  • Mihara, H. Reiju

Abstract

Acyclicity of individual preferences is a minimal assumption in social choice theory. We replace that assumption by the direct assumption that preferences have maximal elements on a fixed agenda. We show that the core of a simple game is nonempty for all profiles of such preferences if and only if the number of alternatives in the agenda is less than the Nakamura number of the game. The same is true if we replace the core by the core without majority dissatisfaction, obtained by deleting from the agenda all the alternatives that are non-maximal for all players in a winning coalition. Unlike the core, the core without majority dissatisfaction depends only onthe players' sets of maximal elements and is included in the union of such sets. A result for an extended framework gives another sense in which the core without majority dissatisfaction behaves better than the core.

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Bibliographic Info

Paper provided by University Library of Munich, Germany in its series MPRA Paper with number 11728.

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Date of creation: 24 Nov 2008
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Handle: RePEc:pra:mprapa:11728

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Keywords: Core; Nakamura number; kappa number; simple games; voting games; maximal elements; acyclic preferences; limit ordinals;

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  1. H. Reiju Mihara, 1996. "Coalitionally strategyproof functions depend only on the most-preferred alternatives," Public Economics 9604003, EconWPA, revised 24 Apr 1996.
  2. Mathieu Martin & Vincent Merlin, 2006. "On The Chacteristic Numbers Of Voting Games," International Game Theory Review (IGTR), World Scientific Publishing Co. Pte. Ltd., vol. 8(04), pages 643-654.
  3. Masahiro Kumabe & H. Reiju Mihara, 2008. "The Nakamura numbers for computable simple games," Social Choice and Welfare, Springer, vol. 31(4), pages 621-640, December.
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  8. Mihara, H.R., 1994. "Arrow's Theorem and Turing Computability," Papers 276, Minnesota - Center for Economic Research.
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Cited by:
  1. Kumabe, Masahiro & Mihara, H. Reiju, 2006. "Computability of simple games: A complete investigation of the sixty-four possibilities," MPRA Paper 440, University Library of Munich, Germany.
  2. Momo Kenfack, Joseph Armel & Pongou, Roland & Tchantcho, Bertrand, 2014. "The stability of decision making in committees: The one-core," Economics Letters, Elsevier, vol. 122(3), pages 390-395.

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