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Inconsistent weighting in weighted voting games

Author

Listed:
  • Sylvain Béal

    (CRESE - Centre de REcherches sur les Stratégies Economiques (UR 3190) - UFC - Université de Franche-Comté - UBFC - Université Bourgogne Franche-Comté [COMUE])

  • Marc Deschamps

    (CRESE - Centre de REcherches sur les Stratégies Economiques (UR 3190) - UFC - Université de Franche-Comté - UBFC - Université Bourgogne Franche-Comté [COMUE], UFC - Université de Franche-Comté - UBFC - Université Bourgogne Franche-Comté [COMUE])

  • Issofa Moyouwou

    (ENS, Yaoundé 1, Cameroun)

  • Mostapha Diss

    (CRESE - Centre de REcherches sur les Stratégies Economiques (UR 3190) - UFC - Université de Franche-Comté - UBFC - Université Bourgogne Franche-Comté [COMUE], UFC - Université de Franche-Comté - UBFC - Université Bourgogne Franche-Comté [COMUE])

Abstract

In a weighted voting game, each voter has a given weight and a coalition of voters is successful if the sum of its weights exceeds a given quota. Such voting systems translate the idea that voters are not all equal by assigning them different weights. In such a situation, two voters are symmetric in a game if interchanging the two voters leaves the outcome of the game unchanged. Two voters with the same weight are naturally symmetric in every weighted voting game, but the converse statement is not necessarily true. We call this latter type of scenario inconsistent weighting. We investigate the conditions that give rise to such a phenomenon within the class of weighted voting games. We also study how the choice of the quota and the total weight can affect the probability of observing inconsistent weighting. Finally, we investigate various applications where inconsistent weighting is observed.

Suggested Citation

  • Sylvain Béal & Marc Deschamps & Issofa Moyouwou & Mostapha Diss, 2022. "Inconsistent weighting in weighted voting games," Post-Print hal-04416052, HAL.
  • Handle: RePEc:hal:journl:hal-04416052
    DOI: 10.1007/s11127-021-00951-5
    Note: View the original document on HAL open archive server: https://univ-fcomte.hal.science/hal-04416052
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    References listed on IDEAS

    as
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    More about this item

    Keywords

    Weighted voting games; symmetric voters; inconsistent weighting; probability;
    All these keywords.

    JEL classification:

    • C7 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory
    • D7 - Microeconomics - - Analysis of Collective Decision-Making

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