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The Nakamura numbers for computable simple games

Masahiro Kumabe and H. Reiju Mihara

MPRA Paper from University Library of Munich, Germany

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.

Keywords: Nakamura number; voting games; the core; Turing computability; axiomatic method; multi-criterion decision-making (search for similar items in EconPapers)
JEL-codes: C69 D71 C71 (search for similar items in EconPapers)
Date: 2007-06-23
New Economics Papers: this item is included in nep-cdm and nep-gth
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