Approval-Based Apportionment

Brill, Markus; Gölz, Paul; Peters, Dominik; Schmidt-Kraepelin, Ulrike; Wilker, Kai

doi:10.1609/aaai.v34i02.5553

Cited by 20 publications

(22 citation statements)

References 28 publications

(29 reference statements)

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“…Assumptions (A1) and (A2) together ensure that the DM can be forced to implement a candidate approved by a voter, by populating the top h positions exclusively with such candidates. Arguably the most natural way to ensure (A2) is to assume that we are in the party-approval setting (Brill et al, 2020), where candidates are interpreted as parties and can be selected arbitrarily often. In the motivating example of live Q&A platforms, party-approval preferences could result from assigning attributes to questions and eliciting participants' approval preferences over attributes.…”

Section: Proportionality Of Implemented Candidatesmentioning

confidence: 99%

Dynamic Proportional Rankings

Israel¹,

Brill²

2021

Preprint

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Proportional ranking rules aggregate approval-style preferences of agents into a collective ranking such that groups of agents with similar preferences are adequately represented. Motivated by the application of live Q&A platforms, where submitted questions need to be ranked based on the interests of the audience, we study a dynamic extension of the proportional rankings setting. In our setting, the goal is to maintain the proportionality of a ranking when alternatives (i.e., questions)-not necessarily from the top of the ranking-get selected sequentially. We propose generalizations of well-known aggregation rules to this setting and study their monotonicity and proportionality properties. We also evaluate the performance of these rules experimentally, using realistic probabilistic assumptions on the selection procedure.

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Section: Proportionality Of Implemented Candidatesmentioning

confidence: 99%

Dynamic Proportional Rankings

Israel¹,

Brill²

2021

Preprint

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“…The main difference is that in probabilistic social choice, the whole value that we want to divide among the candidates can be assigned to fewer than k candidates; in particular it is feasible to set p(c) = k for one candidate and p(c ′ ) = 0 for all c ′ , c ′ = c. Thus, intuitively, in probabilistic social choice each candidate is divisible and appears in an unlimited quantity. Viewing from this perspective, probabilistic social choice extends the discrete model of approval-based apportionment [Brill et al, 2020]. Several works have considered axioms of proportionality for probabilistic social choice [Aziz et al, 2019, Fain et al, 2016], yet unfortunately their results do not apply to fractional committees.…”

Section: Elections Preferences and Committteesmentioning

confidence: 99%

Core-Stable Committees under Restricted Domains

Grzegorz¹,

Skowron²

2021

Preprint

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We study the setting of committee elections, where a group of individuals needs to collectively select a given size subset of available objects. This model is relevant for a number of real-life scenarios including political elections, participatory budgeting, and facility-location. We focus on the core-the classic notion of proportionality, stability and fairness. We show that for a number of restricted domains including voter-interval, candidate-interval, single-peaked, and single-crossing preferences the core is non-empty and can be found in polynomial time. We show that the core might be empty for strict top-monotonic preferences, yet we introduce a relaxation of this class, which guarantees non-emptiness of the core. Our algorithms work both in the randomized and discrete models. We also show that the classic known proportional rules do not return committees from the core even for the most restrictive domains among those we consider (in particular for 1D-Euclidean preferences). We additionally prove a number of structural results that give better insights into the nature of some of the restricted domains, and which in particular give a better intuitive understanding of the class of top-monotonic preferences.

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“…A party-approval election [14] is a tuple (N, C, A, k), where N is a set of agents, C a set of candidates, A = (A a ) a∈N a preference profile with A a ⊆ C denoting the approval set of agent a, and k ∈ N the committee size. 2 A committee W : C → N 0 is a multiset of candidates, with the interpretation that W (c) is the number of copies of candidate c contained in W .…”

Section: Party-approval Electionsmentioning

confidence: 99%

“…Symmetric Matching Elections w-Thiele NP-hard [14] NP-hard (Theorem 3) P (Theorem 4, Corollary 1) seq-w-Thiele P [2] P (Observation 4) P seq-Phragmén P [12] P (Theorem 1) P Rule X P [35] P (Theorem 2) P Table 1: Summary of results on the complexity of computing a winning committee for several multiwinner voting rules. We remark that the previously known results within the setting of party-approval elections do not have any implications for the matching election setting.…”

Section: Party-approval Elections Matching Electionsmentioning

confidence: 99%

“…As a rationale for our decision, observe that such a constraint would be rather artificial in our setting: Two matchings which only differ in a few pairs would already be considered as two distinct candidates in a matching election. Allowing matchings to be selected multiple times positions matching elections within the class of party-approval elections [14], a recently introduced subclass of approval-based multiwinner elections for which stronger axiomatic guarantees are obtainable.…”

Section: Introductionmentioning

confidence: 99%

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Selecting Matchings via Multiwinner Voting: How Structure Defeats a Large Candidate Space

Boehmer,

Brill,

Schmidt-Kraepelin

2021

Preprint

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Given a set of agents with approval preferences over each other, we study the task of finding k matchings fairly representing everyone's preferences. We model the problem as an approval-based multiwinner election where the set of candidates consists of matchings of the agents, and agents' preferences over each other are lifted to preferences over matchings. Due to the exponential number of candidates in such elections, standard algorithms for classical sequential voting rules (such as those proposed by Thiele and Phragmén) are rendered inefficient. We show that the computational tractability of these rules can be regained by exploiting the structure of the approval preferences. Moreover, we establish algorithmic results and axiomatic guarantees that go beyond those obtainable in the general multiwinner setting. Assuming that approvals are symmetric, we show that Proportional Approval Voting (PAV), a well-established but computationally intractable voting rule, becomes polynomial-time computable, and its sequential variant (seq-PAV ), which does not provide any proportionality guarantees in general, fulfills a rather strong guarantee known as extended justified representation. Some of our algorithmic results extend to other types of compactly representable elections with an exponential candidate space.

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Approval-Based Apportionment

Cited by 20 publications

References 28 publications

Dynamic Proportional Rankings

Dynamic Proportional Rankings

Core-Stable Committees under Restricted Domains

Selecting Matchings via Multiwinner Voting: How Structure Defeats a Large Candidate Space

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