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Preference aggregation theory without acyclicity: The core without majority dissatisfaction

Masahiro Kumabe and H. Mihara

MPRA Paper from University Library of Munich, Germany

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.

Keywords: Core; Nakamura number; kappa number; simple games; voting games; maximal elements; acyclic preferences; limit ordinals (search for similar items in EconPapers)
JEL-codes: D71 C71 C02 (search for similar items in EconPapers)
New Economics Papers: this item is included in nep-cdm, nep-dcm, nep-gth, nep-pol and nep-upt
Date: 2008-11-24
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https://mpra.ub.uni-muenchen.de/11728/1/MPRA_paper_11728.pdf original version (application/pdf)
https://mpra.ub.uni-muenchen.de/23918/2/MPRA_paper_23918.pdf revised version (application/pdf)

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Journal Article: Preference aggregation theory without acyclicity: The core without majority dissatisfaction (2011) Downloads
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