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The Nakamura numbers for computable simple games

  • Masahiro Kumabe
  • H. Reiju Mihara

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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File URL: http://hdl.handle.net/10.1007/s00355-008-0300-5
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Article provided by Springer in its journal Social Choice and Welfare.

Volume (Year): 31 (2008)
Issue (Month): 4 (December)
Pages: 621-640

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Handle: RePEc:spr:sochwe:v:31:y:2008:i:4:p:621-640
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  1. Andjiga, Nicolas Gabriel & Mbih, Boniface, 2000. "A note on the core of voting games," Journal of Mathematical Economics, Elsevier, vol. 33(3), pages 367-372, April.
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