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Weighted Scoring Committees

Author

Listed:
  • Alexander Mayer

    (Department of Economics, University of Bayreuth, 95440 Bayreuth, Germany)

  • Stefan Napel

    (Department of Economics, University of Bayreuth, 95440 Bayreuth, Germany)

Abstract

Weighted committees allow shareholders, party leaders, etc. to wield different numbers of votes or voting weights as they decide between multiple candidates by a given social choice method. We consider committees that apply scoring methods such as plurality, Borda, or antiplurality rule. Many different weights induce the same mapping from committee members’ preferences to winning candidates. The numbers of respective weight equivalence classes and hence of structurally distinct plurality committees, Borda commitees, etc. differ widely. There are 6, 51, and 5 plurality, Borda, and antiplurality committees, respectively, if three players choose between three candidates and up to 163 (229) committees for scoring rules in between plurality and Borda (Borda and antiplurality). A key implication is that plurality, Borda, and antiplurality rule are much less sensitive to weight changes than other scoring rules. We illustrate the geometry of weight equivalence classes, with a map of all Borda classes, and identify minimal integer representations.

Suggested Citation

  • Alexander Mayer & Stefan Napel, 2021. "Weighted Scoring Committees," Games, MDPI, vol. 12(4), pages 1-17, December.
    • Handle: RePEc:gam:jgames:v:12:y:2021:i:4:p:94-:d:702287
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    References listed on IDEAS

    as
    1. Yakov Ben-Haim, 2021. "Approval and plurality voting with uncertainty: Info-gap analysis of robustness," Public Choice, Springer, vol. 189(1), pages 239-256, October.
    2. Alexander Mayer & Stefan Napel, 2020. "Weighted voting on the IMF Managing Director," Economics of Governance, Springer, vol. 21(3), pages 237-244, September.
    3. Josep Freixas & Marc Freixas & Sascha Kurz, 2017. "On the characterization of weighted simple games," Theory and Decision, Springer, vol. 83(4), pages 469-498, December.
    4. Kurz, Sascha & Mayer, Alexander & Napel, Stefan, 2020. "Weighted committee games," European Journal of Operational Research, Elsevier, vol. 282(3), pages 972-979.
    5. Kurz, Sascha & Mayer, Alexander & Napel, Stefan, 2021. "Influence in weighted committees," European Economic Review, Elsevier, vol. 132(C).
    Full references (including those not matched with items on IDEAS)

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