Kumabe, Masahiro and Mihara, H. Reiju (2007): The Nakamura numbers for computable simple games.
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Abstract
The Nakamura number of a simple game plays a critical role in preference aggregation (or multicriterion ranking): the number of alternatives that the players can always deal with rationally is less than this number. We comprehensively study the restrictions that various properties for a simple game impose on its Nakamura number. We find that a computable game has a finite Nakamura number greater than three only if it is proper, nonstrong, and nonweak, regardless of whether it is monotonic or whether it has a finite carrier. The lack of strongness often results in alternatives that cannot be strictly ranked.
Item Type:  MPRA Paper 

Original Title:  The Nakamura numbers for computable simple games 
Language:  English 
Keywords:  Nakamura number; voting games; core; Turing computability; axiomatic method; multicriterion decisionmaking 
Subjects:  C  Mathematical and Quantitative Methods > C6  Mathematical Methods ; Programming Models ; Mathematical and Simulation Modeling > C69  Other 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 
Item ID:  5849 
Depositing User:  H. Reiju Mihara 
Date Deposited:  21. Nov 2007 05:01 
Last Modified:  17. Feb 2013 15:17 
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URI:  https://mpra.ub.unimuenchen.de/id/eprint/5849 
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The Nakamura numbers for computable simple games. (deposited 23. Jun 2007)
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