Kumabe, Masahiro and Mihara, H. Reiju (2007): The Nakamura numbers for computable simple games.
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The Nakamura number of a simple game plays a critical role in preference aggregation (or multi-criterion 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|
|Keywords:||Nakamura number; voting games; the core; Turing computability; axiomatic method; multi-criterion decision-making|
|Subjects:||C - Mathematical and Quantitative Methods > C6 - Mathematical Methods ; Programming Models ; Mathematical and Simulation Modeling > C69 - Other
D - Microeconomics > D7 - Analysis of Collective Decision-Making > D71 - Social Choice ; Clubs ; Committees ; Associations
C - Mathematical and Quantitative Methods > C7 - Game Theory and Bargaining Theory > C71 - Cooperative Games
|Depositing User:||H. Reiju Mihara|
|Date Deposited:||23. Jun 2007|
|Last Modified:||15. Feb 2013 13:59|
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