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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. Mathieu Martin & Vincent Merlin, 2006. "On the Chacteristic Numbers of Voting Games," Economics Working Paper Archive (University of Rennes 1 & University of Caen) 200609, Center for Research in Economics and Management (CREM), University of Rennes 1, University of Caen and CNRS.
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  7. Kumabe, Masahiro & Mihara, H. Reiju, 2006. "Computability of simple games: A characterization and application to the core," MPRA Paper 437, University Library of Munich, Germany.
  8. Attila Ambrus & Kareen Rozen, 2008. "Rationalizing Choice with Multi-Self Models," Cowles Foundation Discussion Papers 1670, Cowles Foundation for Research in Economics, Yale University, revised May 2012.
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Cited by:
  1. 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.
  2. 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.

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