Kumabe, Masahiro and Mihara, H. Reiju (2008): Preference aggregation theory without acyclicity: The core without majority dissatisfaction.
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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 nonmaximal 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.
Item Type:  MPRA Paper 

Original Title:  Preference aggregation theory without acyclicity: The core without majority dissatisfaction 
Language:  English 
Keywords:  Core; Nakamura number; kappa number; simple games; voting games; maximal elements; acyclic preferences; limit ordinals 
Subjects:  D  Microeconomics > D7  Analysis of Collective DecisionMaking > D71  Social Choice ; Clubs ; Committees ; Associations C  Mathematical and Quantitative Methods > C7  Game Theory and Bargaining Theory > C71  Cooperative Games C  Mathematical and Quantitative Methods > C0  General > C02  Mathematical Methods 
Item ID:  11728 
Depositing User:  H. Reiju Mihara 
Date Deposited:  24 Nov 2008 00:27 
Last Modified:  27 Sep 2019 03:45 
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URI:  https://mpra.ub.unimuenchen.de/id/eprint/11728 
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