Multiwinner Approval Voting: An Apportionment Approach

Brams, Steven J.; Kilgour, D. Marc; Potthoff, Richard F.

doi:10.2139/ssrn.2940994

Cited by 3 publications

(4 citation statements)

References 15 publications

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“… 10. The fact that the Thiele rule based on the weight sequence (1, 1∕3, 1∕5,…) induces the Sainte-Laguë method in the party-list setting is also stated (without proof) by Pereira (2016) and Brams et al (2017). …”

mentioning

confidence: 86%

“…The observation that PAV reduces to the D’Hondt method in the party-list setting occasionally occurs (without proof) in the literature (e.g. see Brams et al, 2017; Pereira, 2016; Sánchez-Fernández et al, 2016). 7 Theorem 1 shows that this is just one special case of the general relationship between Thiele rules and divisor methods (see also Janson, 2016: Remark 11.4).…”

Section: Apportionment Via Multiwinner Election Rulesmentioning

confidence: 99%

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Multiwinner approval rules as apportionment methods

Brill

Laslier

Skowron

2018

Journal of Theoretical Politics

101

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We establish a link between multiwinner elections and apportionment problems by showing how approval-based multiwinner election rules can be interpreted as methods of apportionment. We consider several multiwinner rules and observe that they induce apportionment methods that are well-established in the literature on proportional representation. For instance, we show that Proportional Approval Voting induces the D'Hondt method and that Monroe's rule induces the largest remainder method. We also consider properties of apportionment methods and exhibit multiwinner rules that induce apportionment methods satisfying these properties.

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mentioning

confidence: 86%

Section: Apportionment Via Multiwinner Election Rulesmentioning

confidence: 99%

Multiwinner approval rules as apportionment methods

Brill

Laslier

Skowron

2018

Journal of Theoretical Politics

101

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“…For instance, Brams, Kilgour, and Potthoff (2019) study multiwinner approval rules that are inspired by classical apportionment methods. Besides the setting of candidate approval, they explicitly consider the case where voters cast party-approval votes.…”

Section: Related Workmentioning

confidence: 99%

Approval-Based Apportionment

Brill¹,

Gölz²,

Peters³

et al. 2020

AAAI

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In the apportionment problem, a fixed number of seats must be distributed among parties in proportion to the number of voters supporting each party. We study a generalization of this setting, in which voters cast approval ballots over parties, such that each voter can support multiple parties. This approval-based apportionment setting generalizes traditional apportionment and is a natural restriction of approval-based multiwinner elections, where approval ballots range over individual candidates. Using techniques from both apportionment and multiwinner elections, we are able to provide representation guarantees that are currently out of reach in the general setting of multiwinner elections: First, we show that core-stable committees are guaranteed to exist and can be found in polynomial time. Second, we demonstrate that extended justified representation is compatible with committee monotonicity.

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“…This research subject is still of interest in the recent literature. For instance, Brams and Brill (2018), Brams et al (2019), Brill et al (2018), Elkind et al (2017), Faliszewski et al (2018), Kilgour (2018), Skowron et al (2016) have recently examined the properties of some voting rules in multi-winner contexts and studied a set of natural properties against which these voting rules can be examined.…”

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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Multiwinner Approval Voting: An Apportionment Approach

Cited by 3 publications

References 15 publications

Multiwinner approval rules as apportionment methods

Multiwinner approval rules as apportionment methods

Approval-Based Apportionment

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

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