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Winning coalitions in plurality voting democracies

Author

Listed:
  • René van den Brink

    (VU - Vrije Universiteit Amsterdam [Amsterdam])

  • Dinko Dimitrov

    (Universität des Saarlandes [Saarbrücken] = Saarland University [Saarbrücken])

  • Agnieszka Rusinowska

    (CNRS - Centre National de la Recherche Scientifique, CES - Centre d'économie de la Sorbonne - UP1 - Université Paris 1 Panthéon-Sorbonne - CNRS - Centre National de la Recherche Scientifique, PSE - Paris School of Economics - UP1 - Université Paris 1 Panthéon-Sorbonne - ENS-PSL - École normale supérieure - Paris - PSL - Université Paris Sciences et Lettres - EHESS - École des hautes études en sciences sociales - ENPC - École nationale des ponts et chaussées - CNRS - Centre National de la Recherche Scientifique - INRAE - Institut National de Recherche pour l’Agriculture, l’Alimentation et l’Environnement)

Abstract

We consider plurality voting games being simple games in partition function form such that in every partition there is at least one winning coalition. Such a game is said to be weighted if it is possible to assign weights to the players in such a way that a winning coalition in a partition is always one for which the sum of the weights of its members is maximal over all coalitions in the partition. A plurality game is called decisive if in every partition there is exactly one winning coalition. We show that in general, plurality games need not be weighted, even not when they are decisive. After that, we prove that (i) decisive plurality games with at most four players, (ii) majority games with an arbitrary number of players, and (iii) decisive plurality games that exhibit some kind of symmetry, are weighted. Complete characterizations of the winning coalitions in the corresponding partitions are provided as well.

Suggested Citation

  • René van den Brink & Dinko Dimitrov & Agnieszka Rusinowska, 2021. "Winning coalitions in plurality voting democracies," Université Paris1 Panthéon-Sorbonne (Post-Print and Working Papers) hal-03153465, HAL.
    • Handle: RePEc:hal:cesptp:hal-03153465
    DOI: 10.1007/s00355-020-01290-y
    Note: View the original document on HAL open archive server: https://hal.science/hal-03153465v1
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    2. Rene van den Brink & Dinko Dimitrov & Agnieszka Rusinowska, 2024. "Power in plurality games," Tinbergen Institute Discussion Papers 24-076/II, Tinbergen Institute.

    More about this item

    JEL classification:

    • C71 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Cooperative Games
    • D62 - Microeconomics - - Welfare Economics - - - Externalities
    • D72 - Microeconomics - - Analysis of Collective Decision-Making - - - Political Processes: Rent-seeking, Lobbying, Elections, Legislatures, and Voting Behavior

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