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Multi-winner scoring election methods: Condorcet consistency and paradoxes

Author

Listed:
  • Mostapha Diss

    (Univ Lyon, UJM Saint-Etienne, CNRS, GATE L-SE UMR 5824)

  • Ahmed Doghmi

    (University of Rabat, Mohammadia School of Engineering, the QSM Laboratory)

Abstract

The goal of this paper is to propose a comparison of four multi-winner voting rules, k-Plurality, k-Negative Plurality, k-Borda, and Bloc. These four election methods are extensions of usual scoring rules designed for electing a single winner and are compared on the basis of two criteria. The first comparison is based on the Condorcet committee efficiency which is defined as the conditional probability for a peculiar voting rule to select the Condorcet committee, provided that such a committee exists. The second comparison is based on the likelihood of two paradoxes of committee elections: the Prior Successor Paradox and the Leaving Member Paradox, which occur when a member of an elected committee exits. Aside from these two extensions, this paper is one of the very rare contributions giving exact results under the Impartial Anonymous Culture (IAC) condition for the case of four candidates.

Suggested Citation

  • Mostapha Diss & Ahmed Doghmi, 2016. "Multi-winner scoring election methods: Condorcet consistency and paradoxes," Public Choice, Springer, vol. 169(1), pages 97-116, October.
    • Handle: RePEc:kap:pubcho:v:169:y:2016:i:1:d:10.1007_s11127-016-0376-x
    DOI: 10.1007/s11127-016-0376-x
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    Cited by:

    1. Fatma Aslan & Hayrullah Dindar & Jean Lainé, 2022. "When are committees of Condorcet winners Condorcet winning committees?," Review of Economic Design, Springer;Society for Economic Design, vol. 26(3), pages 417-446, September.
    2. Mostapha Diss & Eric Kamwa & Issofa Moyouwou & Hatem Smaoui, 2021. "Condorcet Efficiency of General Weighted Scoring Rules Under IAC: Indifference and Abstention," Studies in Choice and Welfare, in: Mostapha Diss & Vincent Merlin (ed.), Evaluating Voting Systems with Probability Models, pages 55-73, Springer.
    3. Mostapha Diss & Eric Kamwa & Abdelmonaim Tlidi, 2018. "The Chamberlin-Courant Rule and the k-Scoring Rules: Agreement and Condorcet Committee Consistency," Working Papers 1812, Groupe d'Analyse et de Théorie Economique Lyon St-Étienne (GATE Lyon St-Étienne), Université de Lyon.
    4. Daniela Bubboloni & Mostapha Diss & Michele Gori, 2020. "Extensions of the Simpson voting rule to the committee selection setting," Public Choice, Springer, vol. 183(1), pages 151-185, April.
    5. Mostapha Diss & Eric Kamwa, 2020. "Simulations in Models of Preference Aggregation," Post-Print hal-02424936, HAL.
    6. Diss, Mostapha & Mahajne, Muhammad, 2020. "Social acceptability of Condorcet committees," Mathematical Social Sciences, Elsevier, vol. 105(C), pages 14-27.
    7. Edith Elkind & Piotr Faliszewski & Piotr Skowron & Arkadii Slinko, 2017. "Properties of multiwinner voting rules," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 48(3), pages 599-632, March.
    8. Sylvain Béal & Marc Deschamps & Mostapha Diss & Issofa Moyouwou, 2022. "Inconsistent weighting in weighted voting games," Public Choice, Springer, vol. 191(1), pages 75-103, April.
    9. Mostapha Diss & Clinton Gubong Gassi & Issofa Moyouwou, 2023. "Social acceptability and the majoritarian compromise rule," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 61(3), pages 489-510, October.
    10. 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.
    11. Mostapha Diss & Eric Kamwa & Issofa Moyouwou & Hatem Smaoui, 2019. "Condorcet efficiency of general weighted scoring rules under IAC: indifference and abstention," Working Papers hal-02196387, HAL.
    12. Moyouwou, Issofa & Tchantcho, Hugue, 2017. "Asymptotic vulnerability of positional voting rules to coalitional manipulation," Mathematical Social Sciences, Elsevier, vol. 89(C), pages 70-82.
    13. 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.
    14. Eric Kamwa, 2022. "The Condorcet Loser Criterion in Committee Selection," Working Papers hal-03880064, HAL.
    15. Mostapha Diss & Clinton Gubong Gassi & Issofa Moyouwou, 2023. "Combining diversity and excellence in multi winner elections," Working Papers 2023-05, CRESE.
    16. Harrison-Trainor, Matthew, 2022. "An analysis of random elections with large numbers of voters," Mathematical Social Sciences, Elsevier, vol. 116(C), pages 68-84.
    17. Mostapha Diss & Eric Kamwa & Abdelmonaim Tlidi, 2019. "On some k-scoring rules for committee elections: agreement and Condorcet Principle," Working Papers hal-02147735, HAL.
    18. Mostapha Diss & Eric Kamwa, 2019. "Simulations in Models of Preference Aggregation," Working Papers hal-02424936, HAL.
    19. Keith L. Dougherty & Robi Ragan, 2024. "Borda count in a forward agenda," Public Choice, Springer, vol. 199(1), pages 27-44, April.
    20. Dan S. Felsenthal & Hannu Nurmi, 2018. "Monotonicity Violations by Borda’s Elimination and Nanson’s Rules: A Comparison," Group Decision and Negotiation, Springer, vol. 27(4), pages 637-664, August.
    21. Dougherty, Keith L. & Heckelman, Jac C., 2020. "The probability of violating Arrow’s conditions," European Journal of Political Economy, Elsevier, vol. 65(C).

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    More about this item

    Keywords

    Multi-winner voting rules; Committee; Condorcet committee efficiency; 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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