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Banzhaf–Coleman–Dubey–Shapley sensitivity index for simple multichoice voting games

Author

Listed:
  • Bertrand Mbama Engoulou

    (The University of Douala)

  • Pierre Wambo

    (Ecole Normale Superieure)

  • Lawrence Diffo Lambo

    (Ecole Normale Superieure)

Abstract

In this paper, we extend the Banzhaf–Coleman–Dubey–Shapley sensitivity index to the class of dichotomous voting games with several levels of approval in input, also known as (j, 2)-simple games. For previous works, on classical simple games ((2, 2)-simple games), a sensitivity index reflects the volatility or degree of suspense in the voting body. Using a set of independent axioms, we provide an axiomatic characterization of that extension on the class of (j, 2)-simple games.

Suggested Citation

  • Bertrand Mbama Engoulou & Pierre Wambo & Lawrence Diffo Lambo, 2023. "Banzhaf–Coleman–Dubey–Shapley sensitivity index for simple multichoice voting games," Annals of Operations Research, Springer, vol. 328(2), pages 1349-1364, September.
    • Handle: RePEc:spr:annopr:v:328:y:2023:i:2:d:10.1007_s10479-023-05411-5
    DOI: 10.1007/s10479-023-05411-5
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    References listed on IDEAS

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    1. Josep Freixas & Montserrat Pons, 2021. "An Appropriate Way to Extend the Banzhaf Index for Multiple Levels of Approval," Group Decision and Negotiation, Springer, vol. 30(2), pages 447-462, April.
    2. Annick Laruelle & Federico Valenciano, 2001. "Shapley-Shubik and Banzhaf Indices Revisited," Mathematics of Operations Research, INFORMS, vol. 26(1), pages 89-104, February.
    3. Giulia Bernardi, 2018. "A New Axiomatization of the Banzhaf Index for Games with Abstention," Group Decision and Negotiation, Springer, vol. 27(1), pages 165-177, February.
    4. Dan S. Felsenthal & Moshé Machover, 1998. "The Measurement of Voting Power," Books, Edward Elgar Publishing, number 1489.
    5. Pradeep Dubey & Lloyd S. Shapley, 1979. "Mathematical Properties of the Banzhaf Power Index," Mathematics of Operations Research, INFORMS, vol. 4(2), pages 99-131, May.
    6. 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.
    7. Josep Freixas, 2020. "The Banzhaf Value for Cooperative and Simple Multichoice Games," Group Decision and Negotiation, Springer, vol. 29(1), pages 61-74, February.
    8. Barua, Rana & Chakravarty, Satya R. & Roy, Sonali & Sarkar, Palash, 2004. "A characterization and some properties of the Banzhaf-Coleman-Dubey-Shapley sensitivity index," Games and Economic Behavior, Elsevier, vol. 49(1), pages 31-48, October.
    9. Freixas, Josep, 2012. "Probabilistic power indices for voting rules with abstention," Mathematical Social Sciences, Elsevier, vol. 64(1), pages 89-99.
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