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Amplitude of weighted representation of voting games with several levels of approval

Author

Listed:
  • Bertrand Mbama Engoulou

    (The University of Douala)

  • Lawrence Diffo Lambo

    (Ecole Normale Superieure)

Abstract

In this paper, we evaluate in the context of weighted (j, k)-simple games, the maximal degree of perturbations which may be allowed, in voters weights and/or in the quotas, without changing the structure of the game. For this purpose, we extend on (j, k)-simple games the notion of amplitude well known for ordinary simple games. Recall that, (j, k)-simple games provide a model of decision making in which each voter has j levels of approval (inputs), while k levels of approval are permitted as collective decision (outputs). Here, the j inputs are qualitatively ordered, same are the k outputs. Ordinary simple games correspond to the particular case $$j=k=2$$ j = k = 2 . Our results generalize those obtained by Freixas and Puente (Qüestiió 23(1):43–60, 1999) on ordinary simple games. We illustrate by computing the amplitude of some real world examples like the United Nations Security Council which is a (3, 2)-simple game.

Suggested Citation

  • Bertrand Mbama Engoulou & Lawrence Diffo Lambo, 2019. "Amplitude of weighted representation of voting games with several levels of approval," International Journal of Game Theory, Springer;Game Theory Society, vol. 48(4), pages 1111-1137, December.
    • Handle: RePEc:spr:jogath:v:48:y:2019:i:4:d:10.1007_s00182-019-00696-y
    DOI: 10.1007/s00182-019-00696-y
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    References listed on IDEAS

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    1. Tchantcho, Bertrand & Lambo, Lawrence Diffo & Pongou, Roland & Engoulou, Bertrand Mbama, 2008. "Voters' power in voting games with abstention: Influence relation and ordinal equivalence of power theories," Games and Economic Behavior, Elsevier, vol. 64(1), pages 335-350, September.
    2. Houy, Nicolas & Zwicker, William S., 2014. "The geometry of voting power: Weighted voting and hyper-ellipsoids," Games and Economic Behavior, Elsevier, vol. 84(C), pages 7-16.
    3. 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.
    4. Dominique Lepelley & N. Andjiga & F. Chantreuil, 2003. "La mesure du pouvoir de vote," Post-Print halshs-00069255, HAL.
    5. Freixas, Josep & Zwicker, William S., 2009. "Anonymous yes-no voting with abstention and multiple levels of approval," Games and Economic Behavior, Elsevier, vol. 67(2), pages 428-444, November.
    6. Rubinstein, Ariel, 1980. "Stability of decision systems under majority rule," Journal of Economic Theory, Elsevier, vol. 23(2), pages 150-159, October.
    7. Lawrence Diffo Lambo & Joël Moulen, 2002. "Ordinal equivalence of power notions in voting games," Theory and Decision, Springer, vol. 53(4), pages 313-325, December.
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