Coincidence of Condorcet committees

Kamwa, Éric; Merlin, Vincent

doi:10.1007/s00355-017-1079-z

Cited by 7 publications

(6 citation statements)

References 23 publications

(58 reference statements)

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“…In particular, this approach defines a Condorcet committee as a committee that is preferred to every other committee by a majority of voters. Notice that, Hill (1988), Kaymak and Sanver (2003), and Kamwa and Merlin (2013) examined under which condition a Condorcet committee in the sense of Fishburn coincide with the one in the sense of Gehrlein. Obviously, the answer depends on the extension function used for lifting individual preferences from alternatives to subsets.…”

Section: Discussionmentioning

confidence: 99%

Multi-Winner Scoring Election Methods: Condorcet Consistency and Paradoxes

Diss

Doghmi

2016

SSRN Journal

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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, which can be considered as generalisations of well-known single-winner scoring rules. The first comparison is based on the Condorcet committee efficiency which is defined as the conditional probability that a given voting rule picks out the Condorcet committee, given 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 leaves. In doing so, using the well-known Impartial Anonymous Culture condition, we extend the results of Kamwa and Merlin (2015) in two directions. First, our paper is concerned with the probability of the paradoxes no matter the ranking of the leaving candidate. Second, we do not only focus on the occurrence of these paradoxes when one wishes to select a committee of size k = 2 out of m = 4 candidates but we consider more values of k and m. Keywords:Multi-winner voting rules, committee, Condorcet committee efficiency, paradoxes, probability. JEL codes:D71, D72 AbstractThe goal of this paper is to propose a comparison of four multi-winner voting rules, k−Plurality, k−Negative Plurality, k−Borda, and Bloc, which can be considered as generalisations of well-known single-winner scoring rules. The first comparison is based on the Condorcet committee efficiency which is defined as the conditional probability that a given voting rule picks out the Condorcet committee, given 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 leaves. In doing so, using the well-known Impartial Anonymous Culture condition, we extend the results of Kamwa and Merlin (2015) in two directions. First, our paper is concerned with the probability of the paradoxes no matter the ranking of the leaving candidate. Second, we do not only focus on the occurrence of these paradoxes when one wishes to select a committee of size k = 2 out of m = 4 candidates but we consider more values of k and m.

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Section: Discussionmentioning

confidence: 99%

Multi-Winner Scoring Election Methods: Condorcet Consistency and Paradoxes

Diss

Doghmi

2016

SSRN Journal

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Section: Discussionmentioning

confidence: 97%

Multi-winner scoring election methods: Condorcet consistency and paradoxes

Diss

Doghmi

2016

Public Choice

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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, which can be considered as generalisations of well-known single-winner scoring rules. The first comparison is based on the Condorcet committee efficiency which is defined as the conditional probability that a given voting rule picks out the Condorcet committee, given 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 leaves. In doing so, using the well-known Impartial Anonymous Culture condition, we extend the results of Kamwa and Merlin (2015) in two directions. First, our paper is concerned with the probability of the paradoxes no matter the ranking of the leaving candidate. Second, we do not only focus on the occurrence of these paradoxes when one wishes to select a committee of size k = 2 out of m = 4 candidates but we consider more values of k and m.

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“…Obviously, there are many other contributions where various multiwinner systems are used with different types of individual preferences and votes. The reader may refer for instance to the works of Aziz et al (2017), Barberà and Coelho (2008), Brams (2008), Brams et al (2005Brams et al ( , 2006, ), Fishburn (1981, Kamwa (2017), Kamwa and Merlin (2018), Kaymak and Sanver (2003), Kilgour (2010), Kilgour and Marshall (2012), Ratliff (2003), among others. Scholars have conducted many comparative studies of single-winner voting rules according to various principles.…”

Section: Introductionmentioning

confidence: 99%

On Some k -scoring Rules for Committee Elections: Agreement and Condorcet Principle

Diss¹,

Kamwa²,

Tlidi³

2020

Revue d'Économie Politique

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Given a collection of individual preferences on a set of candidates and a desired number of winners, a multi-winner voting rule outputs groups of winners, which we call committees. In this paper, we consider five multi-winner voting rules widely studied in the literature of social choice theory: the k-Plurality rule, the k-Borda rule, the k-Negative Plurality rule, the Bloc rule, and the Chamberlin-Courant rule. The objective of this paper is to provide a comparison of these multi-winner voting rules according to many principles by taking into account a probabilistic approach using the well-known Impartial Anonymous Culture (IAC) assumption. We first evaluate the probability that each pair of the considered voting rules selects the same unique committee in order to identify which multi-winner rules are the most likely to agree for a given number of candidates and a fixed target size of the committee. In this matter, our results show that the Chamberlin-Courant rule and the k-Plurality rule on one side, and the k-Borda rule and the Bloc rule on the other side, are the pairs of rules that most agree in comparison to other pairs. Furthermore, we evaluate the probability of every multi-winner voting rule selecting the Condorcet committee à la Gehrlein when it exists. The Condorcet committee à la Gehrlein is a fixed-size committee such that every member defeats every non-member in

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Coincidence of Condorcet committees

Abstract: International audienc

Cited by 7 publications

References 23 publications

Multi-Winner Scoring Election Methods: Condorcet Consistency and Paradoxes

Multi-Winner Scoring Election Methods: Condorcet Consistency and Paradoxes

Multi-winner scoring election methods: Condorcet consistency and paradoxes

On Some k -scoring Rules for Committee Elections: Agreement and Condorcet Principle

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