Properties of multiwinner voting rules

Elkind, Edith; Faliszewski, Piotr; Skowron, Piotr; Slinko, Arkadii

doi:10.1007/s00355-017-1026-z

Cited by 181 publications

(283 citation statements)

References 53 publications

(84 reference statements)

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“…A rule is said to satisfy justified representation if it always outputs a committee that provides justified representation. This concept is related to the Droop proportionality criterion (Droop 1881) and Dummett's solid coalition property (Dummett 1984;Tideman and Richardson 2000;Elkind et al 2014), but is specific to approval-based elections.…”

Section: Introductionmentioning

confidence: 99%

Justified representation in approval-based committee voting

et al. 2017

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We consider approval-based committee voting, i.e. the setting where each voter approves a subset of candidates, and these votes are then used to select a fixedsize set of winners (committee). We propose a natural axiom for this setting, which we call justified representation (JR). This axiom requires that if a large enough group of voters exhibits agreement by supporting the same candidate, then at least one voter in this group has an approved candidate in the winning committee. We show that for every list of ballots it is possible to select a committee that provides JR. However, it turns out that several prominent approval-based voting rules may fail to output such a committee. In particular, while Proportional Approval Voting (PAV) always outputs a committee that provides JR, Reweighted Approval Voting (RAV), a tractable approximation to PAV, does not have this property. We then introduce a stronger version of the JR axiom, which we call extended justified representation (EJR), and show that PAV satisfies EJR, while other rules we consider do not; indeed, EJR can be used to characterize PAV within the class of weighted PAV rules. We also consider several other questions related to JR and EJR, including the relationship between JR/EJR and core stability, and the complexity of the associated algorithmic problems.

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Section: Introductionmentioning

confidence: 99%

Justified representation in approval-based committee voting

et al. 2017

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“…Note that when using approval balloting, several committees supported by all the voters may exist. The 1-unanimity is related to the strong unanimity property in Elkind et al (2014), which conveys that if a committee supported by all the voters exists, the committee selected must therefore be supported by all the voters as well.…”

Section: An Approval Ballot Profile Is a Vectormentioning

confidence: 99%

“…When the goal is to choose a committee that represents the greatest number of voters this lack of representativeness is an important handicap. Monroe (1995) and Elkind et al (2014) propose examples where representation is a focal objective. Although they use a non dichotomous approach, their examples (the selection of a set of newspapers for a graduate common room (Monroe, 1995), or the selection of movies for a long-distance flight (Elkind et al, 2014)) are clear situations in which having a representative for the greatest number of voters would be the main goal and the information about the preferences might be dichotomous in a natural way.…”

Section: Introductionmentioning

confidence: 99%

“…Monroe (1995) and Elkind et al (2014) propose examples where representation is a focal objective. Although they use a non dichotomous approach, their examples (the selection of a set of newspapers for a graduate common room (Monroe, 1995), or the selection of movies for a long-distance flight (Elkind et al, 2014)) are clear situations in which having a representative for the greatest number of voters would be the main goal and the information about the preferences might be dichotomous in a natural way. Committees that are constituted, not to make final decisions (where the committee should be a reflection of the electorate) but rather to elaborate pre-proposals where each voter's opinion should be considered, are rather common.…”

Section: Introductionmentioning

confidence: 99%

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A Representative Committee by Approval Balloting

Subiza

Peris

2017

Group Decis Negot

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A new voting rule for electing committees is described. Specifically, we use approval balloting and propose a new voting procedure that guarantees that if there is a committee that represents (with a given proportion of representatives) all of the existing voters, then the selected committee has to represent all of voters in at least the same proportion. This property is a way of selecting a committee that represents completely all of voters when such a committee exists. The usual voting rules in this context do not satisfy this condition.

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“…Brams (1990Brams ( , 2008 analyzed "constrained approval voting," in which winners are determined by both their vote shares and the categories of voters who approve of them, with constraints put on the numbers that can be elected from different categories. Kilgour, Brams, and Sanver (2006), Kilgour (2010), Kilgour and Marshall (2012), and Elkind, Faliszewski, Skowron, and Slinko (2017) review a variety of methods for electing committees using approval ballots. A number of analysts (Sánches-Fernández, Fernández Garcia, and Fisteus, 2016;Subiza and Peris, 2014;Brill, Laslier, and Skowron, 2016) have suggested using divisor methods of apportionment (more on these methods later) as a basis for selecting multiple winners.…”

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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Properties of multiwinner voting rules

Cited by 181 publications

References 53 publications

Justified representation in approval-based committee voting

Justified representation in approval-based committee voting

A Representative Committee by Approval Balloting

Multiwinner Approval Voting: An Apportionment Approach

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