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The Nakamura numbers for computable simple games

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Published Article
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DOI: 10.1007/s00355-008-0300-5
arXiv ID: 1107.0439
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arXiv
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Abstract

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.

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