Pareto-efficiency of ordinal multiwinner voting rules

Jean Lainé (), Jérôme Lang, İpek Özkal-Sanver and M. Remzi Sanver ()
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Jean Lainé: Cnam - Conservatoire National des Arts et Métiers [Cnam], LIRSA - Laboratoire interdisciplinaire de recherche en sciences de l'action - Cnam - Conservatoire National des Arts et Métiers [Cnam], Murat Sertel Center - Murat Sertel Center for Advanced Economic Studies - Istanbul Bilgi University
Jérôme Lang: LAMSADE - Laboratoire d'analyse et modélisation de systèmes pour l'aide à la décision - Université Paris Dauphine-PSL - PSL - Université Paris Sciences et Lettres - CNRS - Centre National de la Recherche Scientifique
İpek Özkal-Sanver: Istanbul Bilgi University
M. Remzi Sanver: LAMSADE - Laboratoire d'analyse et modélisation de systèmes pour l'aide à la décision - Université Paris Dauphine-PSL - PSL - Université Paris Sciences et Lettres - CNRS - Centre National de la Recherche Scientifique

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Abstract: We investigate the Pareto-efficiency of ordinal multiwinner voting rules, that is, voting rules based on ordinal preference profiles over candidates. Defining Pareto-optimality of a committee requires relating the voters' rankings over individual candidates to their preferences over committees.We consider two well-known extension principles that extend rankings over candidates to preferences over committees: the responsive extension and the lexicographic extension. As the responsive extension outputs partial orders, we consider two Pareto-optimality notions: a committee is possibly (respectively, necessary) Pareto-optimal if it is Pareto-optimal for some (respectively, every) completion of these partial orders. As the lexicographic extension principle outputs a total order, it leads to only one Pareto-optimality notion.We then define several notions of Pareto-efficiency of multiwinner rules, depending on whether some (respectively, all) committees in the output are Pareto-optimal for one of the latter notions. We review what we believe to be a complete list of ordinal multiwinner rules that have been studied in the literature, and identify which Pareto-efficiency notions they satisfy. Our finding is that, somewhat surprisingly, these rules show a huge diversity: some satisfy the strongest notion, some do not even satisfy the weakest one, with many other rules at various intermediate levels.

Date: 2025-05-20
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Published in Review of Economic Design, 2025, ⟨10.1007/s10058-025-00382-4⟩

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Persistent link: https://EconPapers.repec.org/RePEc:hal:journl:hal-05076777

DOI: 10.1007/s10058-025-00382-4

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