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The Nakamura numbers for computable simple games

  • Kumabe, Masahiro
  • Mihara, H. Reiju

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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Paper provided by University Library of Munich, Germany in its series MPRA Paper with number 3684.

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Date of creation: 23 Jun 2007
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Handle: RePEc:pra:mprapa:3684
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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. Kumabe, Masahiro & Mihara, H. Reiju, 2006. "Computability of simple games: A characterization and application to the core," MPRA Paper 437, University Library of Munich, Germany.
  3. H. Reiju Mihara, 1994. "Arrow's Theorem and Turing Computability," Public Economics 9408001, EconWPA, revised 23 Aug 1994.
  4. Richter, Marcel K. & Wong, Kam-Chau, 1999. "Computable preference and utility," Journal of Mathematical Economics, Elsevier, vol. 32(3), pages 339-354, November.
  5. Kumabe, Masahiro & Mihara, H. Reiju, 2011. "Computability of simple games: A complete investigation of the sixty-four possibilities," Journal of Mathematical Economics, Elsevier, vol. 47(2), pages 150-158, March.
  6. Lewis, Alain A., 1988. "An infinite version of arrow's theorem in the effective setting," Mathematical Social Sciences, Elsevier, vol. 16(1), pages 41-48, August.
  7. Truchon, Michel, 1995. "Voting games and acyclic collective choice rules," Mathematical Social Sciences, Elsevier, vol. 29(2), pages 165-179, April.
  8. 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.
  9. Weber, Robert J., 1994. "Games in coalitional form," Handbook of Game Theory with Economic Applications, in: R.J. Aumann & S. Hart (ed.), Handbook of Game Theory with Economic Applications, edition 1, volume 2, chapter 36, pages 1285-1303 Elsevier.
  10. Rajat Deb, 2004. "Rights as alternative game forms," Social Choice and Welfare, Springer, vol. 22(1), pages 83-111, 02.
  11. Kolpin, Van, 1990. "Equivalent game forms and coalitional power," Mathematical Social Sciences, Elsevier, vol. 20(3), pages 239-249, December.
  12. 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.
  13. Mihara, H. Reiju, 2004. "Nonanonymity and sensitivity of computable simple games," Mathematical Social Sciences, Elsevier, vol. 48(3), pages 329-341, November.
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  2. 協力ゲーム in Wikipedia Japanese ne '')
  3. 中村ナンバー in Wikipedia Japanese ne '')
  4. قالب:Cite doi/10.1007.2Fs00355-008-0300-5 in Wikipedia Arabic ne '')
  5. User:Theorist2/Archived in Wikipedia English ne '')
  6. الگو:Cite doi/10.1007.2Fs00355-008-0300-5 in Wikipedia Persian ne '')
  7. 利用者:Theorist2/Archived in Wikipedia Japanese ne '')
  8. Nakamura number in Wikipedia English ne '')
  9. Txantiloi:Cite doi/10.1007.2Fs00355-008-0300-5 in Wikipedia Basque ne '')
  10. ライスの定理 in Wikipedia Japanese ne '')
  11. Cooperative game in Wikipedia English ne '')
  12. Rice's theorem in Wikipedia English ne '')
  13. Template:Cite doi/10.1007.2Fs00355-008-0300-5 in Wikipedia Japanese ne '')
  14. Template:Cite doi/10.1007.2Fs00355-008-0300-5 in Wikipedia English ne '')

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