Multiwinner approval rules as apportionment methods

Brill, Markus; Laslier, Jean‐François; Skowron, Piotr

doi:10.1177/0951629818775518

Cited by 77 publications

(104 citation statements)

References 33 publications

(46 reference statements)

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“…Proof. Since sequential PAV satisfies lower quota [11], the upper bound of 2 √ k − 1 k follows from Proposition 1. In the remaining part of the proof we will prove the lower-bound.…”

Section: Proofmentioning

confidence: 97%

A Quantitative Analysis of Multi-Winner Rules

Lackner

Skowron

2019

Proceedings of the Twenty-Eighth International Joint Conference on Artificial Intelligence

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To choose a suitable multi-winner rule, i.e., a voting rule for selecting a subset of k alternatives based on a collection of preferences, is a hard and ambiguous task. Depending on the context, it varies widely what constitutes the choice of an "optimal" subset. In this paper, we offer a new perspective to measure the quality of such subsets and-consequentlymulti-winner rules. We provide a quantitative analysis using methods from the theory of approximation algorithms and estimate how well multi-winner rules approximate two extreme objectives: diversity as captured by the (Approval) Chamberlin-Courant rule and individual excellence as captured by Multi-winner Approval Voting. With both theoretical and experimental methods we classify multi-winner rules in terms of their quantitative alignment with these two opposing objectives.

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“…Proof. Since sequential PAV satisfies lower quota [11], the upper bound of 2 √ k − 1 k follows from Proposition 1. In the remaining part of the proof we will prove the lower-bound.…”

Section: Proofmentioning

confidence: 97%

A Quantitative Analysis of Multi-Winner Rules

Lackner

Skowron

2019

Proceedings of the Twenty-Eighth International Joint Conference on Artificial Intelligence

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“…In response, "proportional representation" rules [35,9], that ensure that the political affiliations of the electorate are reflected proportionately in the elected body, are being deployed. Formally, let P 1 , .…”

Section: Introductionmentioning

confidence: 99%

“…For any i ∈ [p], let f i be the fraction of voters who belong to (or, more generally, prefer) group i. Then, a voting rule achieving full proportionality would ensure that the selected committee S satisfies k · f i ≤ |S ∩ P i | ≤ k · f i ; see also [9,Definition 5]. Other proportional representative schemes include the proportional approval voting (PAV) rule [9] and the Chamberlain Courant-rule [17].…”

Section: Introductionmentioning

confidence: 99%

“…Then, a voting rule achieving full proportionality would ensure that the selected committee S satisfies k · f i ≤ |S ∩ P i | ≤ k · f i ; see also [9,Definition 5]. Other proportional representative schemes include the proportional approval voting (PAV) rule [9] and the Chamberlain Courant-rule [17]. Other approaches, such as Brill et al [9], consider different notions of "fair" representation; e.g., Koriyama et al [30] argue that minorities should have disproportionately many representatives.…”

Section: Introductionmentioning

confidence: 99%

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Multiwinner Voting with Fairness Constraints

Celis

Huang

Vishnoi

2018

Proceedings of the Twenty-Seventh International Joint Conference on Artificial Intelligence

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Multiwinner voting rules are used to select a small representative subset of candidates or items from a larger set given the preferences of voters. However, if candidates have sensitive attributes such as gender or ethnicity (when selecting a committee), or specified types such as political leaning (when selecting a subset of news items), an algorithm that chooses a subset by optimizing a multiwinner voting rule may be unbalanced in its selection -it may under or over represent a particular gender or political orientation in the examples above. We introduce an algorithmic framework for multiwinner voting problems when there is an additional requirement that the selected subset should be "fair" with respect to a given set of attributes. Our framework provides the flexibility to (1) specify fairness with respect to multiple, non-disjoint attributes (e.g., ethnicity and gender) and (2) specify a score function. We study the computational complexity of this constrained multiwinner voting problem for monotone and submodular score functions and present several approximation algorithms and matching hardness of approximation results for various attribute group structure and types of score functions. We also present simulations that suggest that adding fairness constraints may not affect the scores significantly when compared to the unconstrained case.

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“…For details, see Balinski andYoung (1982/2001). 2 A downside to the nonsequential versions of the apportionment methods is that they are computationally complex, not implementable in polynomial time (Brill, Laslier, and Skowron, 2016 In elections in which voters can vote for only one candidate or party, the Jefferson and Webster apportionment methods satisfy several desirable properties (Balinski andYoung, 1982, 2001), but they are not flawless. Like all divisor apportionment methods, they are vulnerable to manipulation; furthermore, they may not always give political parties the number of representatives to which they are entitled after rounding (either up or down).…”

Section: Introductionmentioning

confidence: 99%

Multiwinner Approval Voting: An Apportionment Approach

2017

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We extend approval voting so as to elect multiple candidates, who may be either individuals or members of a political party, in rough proportion to their approval in the electorate. We analyze two divisor methods of apportionment, first proposed by Jefferson and Webster, that iteratively depreciate the approval votes of voters who have one or more of their approved candidates already elected. We compare the usual sequential version of these methods with a nonsequential version, which is computationally complex but feasible for many elections. Whereas Webster apportionments tend to be more representative of the electorate than those of Jefferson, the latter, whose equally spaced vote thresholds for winning seats duplicate those of cumulative voting in 2-party elections, is even-handed or balanced.

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Multiwinner approval rules as apportionment methods

Cited by 77 publications

References 33 publications

A Quantitative Analysis of Multi-Winner Rules

A Quantitative Analysis of Multi-Winner Rules

Multiwinner Voting with Fairness Constraints

Multiwinner Approval Voting: An Apportionment Approach

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