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On the price of diversity for multiwinner elections under (weakly) separable scoring rules

Author

Listed:
  • Mostapha Diss

    (Université de Franche-Comté, CRESE, UR3190, F-25000 Besançon, France)

  • Clinton Gabon Gassi

    (Université de Franche-Comté, CRESE, UR3190, F-25000 Besançon, France)

  • Eric Kamwa

    (Université des Antilles, LC2S, UMR CNRS 8053, Martinique, France)

Abstract

We consider a model of multi-winner elections, where each voter expresses a linear preference over a finite set of alternatives. Based on voters’ preferences, the primary goal is to select a subset of admissible alternatives, forming what is referred to as a committee. We explore (weakly) separable committee scoring rules, the voting mechanisms that assess each alternative individually using a scoring vector and select the top k alternatives, where k represents the committee’s size. Furthermore, we operate under the assumption that alternatives are categorized based on specific attributes. Within each attribute category, there exists a targeted minimum number of alternatives that the selected committee should encompass, emphasizing the necessity for diversity. In this context, we assess the cost associated with imposing such a diversity constraint on the voting process. This assessment is conducted through two methodologies, referred to as the “price of diversity” and the “individual price of diversity”. We set the upper bounds for both prices across all (weakly) separable committee scoring rules. Additionally, we show how the maximum price of diver- sity can be used to discriminate between different voting rules in this context. Ultimately, we illustrate that concentrating on the candidates’ performance yields a more accurate estimation of the price of diversity compared to a focus on the enforced diversity constraint.

Suggested Citation

  • Mostapha Diss & Clinton Gabon Gassi & Eric Kamwa, 2024. "On the price of diversity for multiwinner elections under (weakly) separable scoring rules," Working Papers 2024-02, CRESE.
  • Handle: RePEc:crb:wpaper:2024-02
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    References listed on IDEAS

    as
    1. Piotr Faliszewski & Piotr Skowron & Arkadii Slinko & Nimrod Talmon, 2018. "Multiwinner analogues of the plurality rule: axiomatic and algorithmic perspectives," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 51(3), pages 513-550, October.
    2. Steven J. Brams, 1990. "Constrained Approval Voting: A Voting System to Elect a Governing Board," Interfaces, INFORMS, vol. 20(5), pages 67-80, October.
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    4. Mostapha Diss & Vincent Merlin (ed.), 2021. "Evaluating Voting Systems with Probability Models," Studies in Choice and Welfare, Springer, number 978-3-030-48598-6, June.
    5. Haris Aziz, 2019. "A Rule for Committee Selection with Soft Diversity Constraints," Group Decision and Negotiation, Springer, vol. 28(6), pages 1193-1200, December.
    6. D. Marc Kilgour, 2010. "Approval Balloting for Multi-winner Elections," Studies in Choice and Welfare, in: Jean-François Laslier & M. Remzi Sanver (ed.), Handbook on Approval Voting, chapter 0, pages 105-124, Springer.
    7. Yuichiro Kamada & Fuhito Kojima, 2015. "Efficient Matching under Distributional Constraints: Theory and Applications," American Economic Review, American Economic Association, vol. 105(1), pages 67-99, January.
    8. Chamberlin, John R. & Courant, Paul N., 1983. "Representative Deliberations and Representative Decisions: Proportional Representation and the Borda Rule," American Political Science Review, Cambridge University Press, vol. 77(3), pages 718-733, September.
    9. William V. Gehrlein & Dominique Lepelley, 2017. "Elections, Voting Rules and Paradoxical Outcomes," Studies in Choice and Welfare, Springer, number 978-3-319-64659-6, June.
    10. Skowron, Piotr & Faliszewski, Piotr & Slinko, Arkadii, 2019. "Axiomatic characterization of committee scoring rules," Journal of Economic Theory, Elsevier, vol. 180(C), pages 244-273.
    11. William V. Gehrlein & Dominique Lepelley, 2011. "Voting Paradoxes and Group Coherence," Studies in Choice and Welfare, Springer, number 978-3-642-03107-6, June.
    12. 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.
    13. Masahiro Goto & Fuhito Kojima & Ryoji Kurata & Akihisa Tamura & Makoto Yokoo, 2017. "Designing Matching Mechanisms under General Distributional Constraints," American Economic Journal: Microeconomics, American Economic Association, vol. 9(2), pages 226-262, May.
    Full references (including those not matched with items on IDEAS)

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    More about this item

    Keywords

    Group decisions and negotiations; voting; multiwinner elections; scoring rules; price of diversity;
    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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