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Computational Complexity in the Design of Voting Rules

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  • Koji Takamiya
  • Akira Tanaka

Abstract

This paper discusses an aspect of computational complexity in social choice theory. We consider the problem of designing voting rules, which is formulated in terms of simple games. We prove that it is an NP-complete problem to decide whether a given simple game is stable, or not.

Suggested Citation

  • Koji Takamiya & Akira Tanaka, 2006. "Computational Complexity in the Design of Voting Rules," ISER Discussion Paper 0653, Institute of Social and Economic Research, Osaka University, revised Jul 2006.
    • Handle: RePEc:dpr:wpaper:0653
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    File URL: https://www.iser.osaka-u.ac.jp/library/dp/2006/DP0653.pdf
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    References listed on IDEAS

    as
    1. Moulin, H. & Peleg, B., 1982. "Cores of effectivity functions and implementation theory," Journal of Mathematical Economics, Elsevier, vol. 10(1), pages 115-145, June.
    2. Boros, Endre & Gurvich, Vladimir, 2000. "Stable effectivity functions and perfect graphs," Mathematical Social Sciences, Elsevier, vol. 39(2), pages 175-194, March.
    3. Alvin E. Roth & Tayfun Sönmez & M. Utku Ünver, 2004. "Kidney Exchange," The Quarterly Journal of Economics, President and Fellows of Harvard College, vol. 119(2), pages 457-488.
    4. Roth, Alvin E. & Sotomayor, Marilda, 1992. "Two-sided matching," Handbook of Game Theory with Economic Applications, in: R.J. Aumann & S. Hart (ed.), Handbook of Game Theory with Economic Applications, edition 1, volume 1, chapter 16, pages 485-541, Elsevier.
    5. repec:dau:papers:123456789/13220 is not listed on IDEAS
    6. Mizutani, Masayoshi & Hiraide, Yasuhiko & Nishino, Hisakazu, 1993. "Computational Complexity to Verify the Unstability of Effectivity Function," International Journal of Game Theory, Springer;Game Theory Society, vol. 22(3), pages 225-239.
    7. Shinotsuka, Tomoichi & Takamiya, Koji, 2003. "The weak core of simple games with ordinal preferences: implementation in Nash equilibrium," Games and Economic Behavior, Elsevier, vol. 44(2), pages 379-389, August.
    8. Atila Abdulkadiroglu & Tayfun Sönmez, 2003. "School Choice: A Mechanism Design Approach," American Economic Review, American Economic Association, vol. 93(3), pages 729-747, June.
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    Cited by:

    1. Joseph Abdou, 2012. "The structure of unstable power mechanisms," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 50(2), pages 389-415, June.

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