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Axiomatizations for the Shapley–Shubik power index for games with several levels of approval in the input and output

Author

Listed:
  • Sascha Kurz

    (University of Bayreuth)

  • Issofa Moyouwou

    (University of Yaounde I)

  • Hilaire Touyem

    (University of Yaounde I)

Abstract

The Shapley–Shubik index is a specialization of the Shapley value and is widely applied to evaluate the power distribution in committees drawing binary decisions. It was generalized to decisions with more than two levels of approval both in the input and the output. The corresponding games are called (j, k) simple games. Here we present a new axiomatization for the Shapley–Shubik index for (j, k) simple games as well as for a continuous variant, which may be considered as the limit case.

Suggested Citation

  • Sascha Kurz & Issofa Moyouwou & Hilaire Touyem, 2021. "Axiomatizations for the Shapley–Shubik power index for games with several levels of approval in the input and output," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 56(3), pages 569-594, April.
    • Handle: RePEc:spr:sochwe:v:56:y:2021:i:3:d:10.1007_s00355-020-01296-6
    DOI: 10.1007/s00355-020-01296-6
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    References listed on IDEAS

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    1. Kurz, Sascha & Napel, Stefan, 2018. "The roll call interpretation of the Shapley value," Economics Letters, Elsevier, vol. 173(C), pages 108-112.
    2. Sascha Kurz, 2018. "Importance In Systems With Interval Decisions," Advances in Complex Systems (ACS), World Scientific Publishing Co. Pte. Ltd., vol. 21(06n07), pages 1-23, September.
    3. Dan S. Felsenthal & Moshé Machover, 1998. "The Measurement of Voting Power," Books, Edward Elgar Publishing, number 1489.
    4. Xingwei Hu, 2006. "An Asymmetric Shapley–Shubik Power Index," International Journal of Game Theory, Springer;Game Theory Society, vol. 34(2), pages 229-240, August.
    5. Shapley, L. S. & Shubik, Martin, 1954. "A Method for Evaluating the Distribution of Power in a Committee System," American Political Science Review, Cambridge University Press, vol. 48(3), pages 787-792, September.
    6. R. Amer & F. Carreras & A. Magaña, 1998. "Extension of values to games withmultiple alternatives," Annals of Operations Research, Springer, vol. 84(0), pages 63-78, December.
    7. Sascha Kurz, 2014. "Measuring Voting Power in Convex Policy Spaces," Economies, MDPI, vol. 2(1), pages 1-33, March.
    8. Michel Grabisch & Jean-Luc Marichal & Radko Mesiar & Endre Pap, 2009. "Aggregation functions," Université Paris1 Panthéon-Sorbonne (Post-Print and Working Papers) halshs-00445120, HAL.
    9. Martin J. Osborne & Ariel Rubinstein, 1994. "A Course in Game Theory," MIT Press Books, The MIT Press, edition 1, volume 1, number 0262650401, April.
    10. Hsiao Chih-Ru & Raghavan T. E. S., 1993. "Shapley Value for Multichoice Cooperative Games, I," Games and Economic Behavior, Elsevier, vol. 5(2), pages 240-256, April.
    11. Josep Freixas & William S. Zwicker, 2003. "Weighted voting, abstention, and multiple levels of approval," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 21(3), pages 399-431, December.
    12. Friedman, Jane & Parker, Cameron, 2018. "The conditional Shapley–Shubik measure for ternary voting games," Games and Economic Behavior, Elsevier, vol. 108(C), pages 379-390.
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    Cited by:

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