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On Weights and Quotas for Weighted Majority Voting Games

Author

Listed:
  • Xavier Molinero

    (Mathematics Department, Universitat Politècnica de Catalunya · BarcelonaTech, E-08222 Terrassa, Spain)

  • Maria Serna

    (Computer Science Department, Institut de Matemàtiques de la UPC-BarcelonaTech (IMTech), Universitat Politècnica de Catalunya · BarcelonaTech, E-08034 Barcelona, Spain)

  • Marc Taberner-Ortiz

    (School of Mathematics and Statistics, Universitat Politècnica de Catalunya · BarcelonaTech, E-08034 Barcelona, Spain)

Abstract

In this paper, we analyze the frequency distributions of weights and quotas in weighted majority voting games (WMVG) up to eight players. We also show different procedures that allow us to obtain some minimum or minimum sum representations of WMVG, for any desired number of players, starting from a minimum or minimum sum representation. We also provide closed formulas for the number of WMVG with n players having a minimum representation with quota up to three, and some subclasses of this family of games. Finally, we complement these results with some upper bounds related to weights and quotas.

Suggested Citation

  • Xavier Molinero & Maria Serna & Marc Taberner-Ortiz, 2021. "On Weights and Quotas for Weighted Majority Voting Games," Games, MDPI, vol. 12(4), pages 1-25, December.
    • Handle: RePEc:gam:jgames:v:12:y:2021:i:4:p:91-:d:695836
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    References listed on IDEAS

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    1. Molinero, Xavier & Riquelme, Fabián & Roura, Salvador & Serna, Maria, 2023. "On the generalized dimension and codimension of simple games," European Journal of Operational Research, Elsevier, vol. 306(2), pages 927-940.

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