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Are Weighted Games Sufficiently Good for Binary Voting?

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  • Sascha Kurz

    (University of Bayreuth)

Abstract

Binary “yes”–“no” decisions in a legislative committee or a shareholder meeting are commonly modeled as a weighted game. However, there are noteworthy exceptions. E.g., the voting rules of the European Council according to the Treaty of Lisbon use a more complicated construction. Here we want to study the question if we lose much from a practical point of view, if we restrict ourselves to weighted games. To this end, we invoke power indices that measure the influence of a member in binary decision committees. More precisely, we compare the achievable power distributions of weighted games with those from a reasonable superset of weighted games. It turns out that the deviation is relatively small.

Suggested Citation

  • Sascha Kurz, 2021. "Are Weighted Games Sufficiently Good for Binary Voting?," Homo Oeconomicus: Journal of Behavioral and Institutional Economics, Springer, vol. 38(1), pages 29-36, December.
    • Handle: RePEc:spr:homoec:v:38:y:2021:i:1:d:10.1007_s41412-021-00111-6
    DOI: 10.1007/s41412-021-00111-6
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    References listed on IDEAS

    as
    1. Sascha Kurz & Stefan Napel, 2014. "Heuristic and exact solutions to the inverse power index problem for small voting bodies," Annals of Operations Research, Springer, vol. 215(1), pages 137-163, April.
    2. Werner Kirsch & Jessica Langner, 2011. "Invariably Suboptimal: An Attempt to Improve the Voting Rules of the Treaties of Nice and Lisbon," Journal of Common Market Studies, Wiley Blackwell, vol. 49(6), pages 1317-1338, November.
    3. De, Anindya & Diakonikolas, Ilias & Servedio, Rocco A., 2017. "The Inverse Shapley value problem," Games and Economic Behavior, Elsevier, vol. 105(C), pages 122-147.
    4. Sascha Kurz, 2016. "The inverse problem for power distributions in committees," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 47(1), pages 65-88, June.
    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. Noga Alon & Paul Edelman, 2010. "The inverse Banzhaf problem," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 34(3), pages 371-377, March.
    7. Carreras, Francesc & Freixas, Josep, 1996. "Complete simple games," Mathematical Social Sciences, Elsevier, vol. 32(2), pages 139-155, October.
    Full references (including those not matched with items on IDEAS)

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    More about this item

    Keywords

    Power measurement; Weighted games;

    JEL classification:

    • C61 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - Optimization Techniques; Programming Models; Dynamic Analysis
    • C71 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Cooperative Games

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