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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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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. Kelly, Jerry S., 1988. "Social choice and computational complexity," Journal of Mathematical Economics, Elsevier, vol. 17(1), pages 1-8, February.
  2. Peleg, Bezalel, 2002. "Game-theoretic analysis of voting in committees," Handbook of Social Choice and Welfare, in: K. J. Arrow & A. K. Sen & K. Suzumura (ed.), Handbook of Social Choice and Welfare, edition 1, volume 1, chapter 8, pages 395-423 Elsevier.
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