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Influence relation in two-output multichoice voting games

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  • Siani, Joseph
  • Tedjeugang, Narcisse
  • Tchantcho, Bertrand

Abstract

The influence relation, defined within the set of simple games, is identified as a preorder. Additionally, it is proved to be a subpreorder of the preorders induced by the Shapley–Shubik and Banzhaf–Coleman indices. When this relation extends to voting games with abstention, detailed in Tchantcho et al. (2008), and further to multichoice voting games as in Pongou et al. (2014), it is shown that these extensions aren't always preorders. Even when they are, they don't necessarily align with the preorders induced by the extended Banzhaf–Coleman and Shapley–Shubik power indices in Freixas (2005a) and Freixas (2005b). In this paper, we introduce extensions for two-output multichoice voting games that are both preorders and subpreorders of the Banzhaf–Coleman power index defined in Freixas (2005b). Further, we characterize the two-output multichoice voting games for which one of these new power theories agrees with the generalized Banzhaf–Coleman and Shapley–Shubik power indices in Freixas (2005a) and Freixas (2005b) respectively.

Suggested Citation

  • Siani, Joseph & Tedjeugang, Narcisse & Tchantcho, Bertrand, 2023. "Influence relation in two-output multichoice voting games," Games and Economic Behavior, Elsevier, vol. 142(C), pages 879-895.
    • Handle: RePEc:eee:gamebe:v:142:y:2023:i:c:p:879-895
    DOI: 10.1016/j.geb.2023.10.003
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    References listed on IDEAS

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    1. Parker, Cameron, 2012. "The influence relation for ternary voting games," Games and Economic Behavior, Elsevier, vol. 75(2), pages 867-881.
    2. Josep Freixas, 2005. "Banzhaf Measures for Games with Several Levels of Approval in the Input and Output," Annals of Operations Research, Springer, vol. 137(1), pages 45-66, July.
    3. Pongou, Roland & Tchantcho, Bertrand & Tedjeugang, Narcisse, 2014. "Power theories for multi-choice organizations and political rules: Rank-order equivalence," Operations Research Perspectives, Elsevier, vol. 1(1), pages 42-49.
    4. Freixas, Josep & Tchantcho, Bertrand & Tedjeugang, Narcisse, 2014. "Achievable hierarchies in voting games with abstention," European Journal of Operational Research, Elsevier, vol. 236(1), pages 254-260.
    5. Dominique Lepelley & N. Andjiga & F. Chantreuil, 2003. "La mesure du pouvoir de vote," Post-Print halshs-00069255, HAL.
    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. 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.
    8. 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.
    9. 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.
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