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Extensions of the Simpson voting rule to the committee selection setting

Author

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  • Daniela Bubboloni

    (Università degli Studi di Firenze = University of Florence [Firenze])

  • Mostapha Diss

    () (GATE Lyon Saint-Étienne - Groupe d'analyse et de théorie économique - CNRS - Centre National de la Recherche Scientifique - Université de Lyon - UJM - Université Jean Monnet [Saint-Étienne] - UCBL - Université Claude Bernard Lyon 1 - Université de Lyon - UL2 - Université Lumière - Lyon 2 - ENS Lyon - École normale supérieure - Lyon)

  • Michele Gori

    (Università degli Studi di Firenze = University of Florence [Firenze])

Abstract

Committee selection rules are procedures selecting sets of candidates of a given size on the basis of the preferences of the voters. There are in the literature two natural extensions of the well-known single-winner Simpson voting rule to the multiwinner setting. The first method gives a ranking of candidates according to their minimum number of wins against the other candidates. Then, if a fixed number k of candidates are to be elected, the k best ranked candidates are chosen as the overall winners. The second method gives a ranking of committees according to the minimum number of wins of committee members against committee nonmembers. Accordingly, the committee of size k with the highest score is chosen as the winner. We propose an in-depth analysis of those committee selection rules, assessing and comparing them with respect to several desirable properties among which unanimity, fixed majority, non-imposition, stability, local stability, Condorcet consistency, some kinds of monotonicity, resolvability and consensus committee. We also investigate the probability that the two methods are resolute and suffer the reversal bias, the Condorcet loser paradox and the leaving member paradox. We compare the results obtained with the ones related to further well-known committee selection rules. The probability assumption on which our results are based is the widely used Impartial Anonymous Culture.

Suggested Citation

  • Daniela Bubboloni & Mostapha Diss & Michele Gori, 2018. "Extensions of the Simpson voting rule to the committee selection setting," Working Papers halshs-01827668, HAL.
  • Handle: RePEc:hal:wpaper:halshs-01827668
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    Cited by:

    1. Mostapha Diss & Eric Kamwa & Abdelmonaim Tlidi, 2020. "On Some k -scoring Rules for Committee Elections: Agreement and Condorcet Principle," Revue d'économie politique, Dalloz, vol. 130(5), pages 699-725.
    2. Mostapha Diss & Michele Gori, 2020. "Majority properties of positional social preference correspondences," Working Papers 2020-06, CRESE.
    3. Abdelhalim El Ouafdi & Dominique Lepelley & Hatem Smaoui, 2020. "Probabilities of electoral outcomes: from three-candidate to four-candidate elections," Theory and Decision, Springer, vol. 88(2), pages 205-229, March.
    4. Mostapha Diss & Eric Kamwa & Abdelmonaim Tlidi, 2019. "On some k-scoring rules for committee elections: agreement and Condorcet Principle," Working Papers hal-02147735, HAL.
    5. Sylvain Béal & Marc Deschamps & Mostapha Diss & Issofa Moyouwou, 2021. "Inconsistent weighting in weighted voting games," Working Papers 2021-01, CRESE.

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    More about this item

    Keywords

    Multiwinner Elections; Committee Selection Rule; Simpson Voting Rule; Paradoxes; Probability;
    All these keywords.

    JEL classification:

    • D71 - Microeconomics - - Analysis of Collective Decision-Making - - - Social Choice; Clubs; Committees; Associations
    • D72 - Microeconomics - - Analysis of Collective Decision-Making - - - Political Processes: Rent-seeking, Lobbying, Elections, Legislatures, and Voting Behavior

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