On the Complexity of Winner Verification and Candidate Winner for Multiwinner Voting Rules

Sonar, Chinmay; Dey, Palash; Misra, Neeldhara

doi:10.24963/ijcai.2020/13

Cited by 5 publications

(7 citation statements)

References 1 publication

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“…Our reduction can be modified to give coW[1]-hardness for the following winner verification problem: given a profile and a committee, is the committee winning under the CC rule? This result strengthens a recent one by Sonar et al (2020).…”

Section: Our Contribution and Techniquessupporting

confidence: 91%

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The Complexity of Learning Approval-Based Multiwinner Voting Rules

Caragiannis¹,

Karl²

2021

Preprint

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We study the PAC learnability of multiwinner voting, focusing on the class of approvalbased committee scoring (ABCS) rules. These are voting rules applied on profiles with approval ballots, where each voter approves some of the candidates. ABCS rules adapt positional scoring rules in single-winner voting by assuming that each committee of k candidates collects from each voter a score, that depends on the size of the voter's ballot and on the size of its intersection with the committee. Then, committees of maximum score are the winning ones. Our goal is to learn a target rule (i.e., to learn the corresponding scoring function) using information about the winning committees of a small number of sampled profiles. Despite the existence of exponentially many outcomes compared to single-winner elections, we show that the sample complexity is still low: a polynomial number of samples carries enough information for learning the target committee with high confidence and accuracy. Unfortunately, even simple tasks that need to be solved for learning from these samples are intractable. We prove that deciding whether there exists some ABCS rule that makes a given committee winning in a given profile is a computationally hard problem. Our results extend to the class of sequential Thiele rules, which have received attention due to their simplicity.

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Section: Our Contribution and Techniquessupporting

confidence: 91%

“…The problem was later proved to be W[2]-hard by Betzler et al (2013). Sonar et al (2020) considered the question of whether a given candidate belongs to a winning committee for a given profile. They also prove that winner verification for the CC rule is coNP-hard, using a reduction from a variant of 3-HittingSet.…”

Section: Related Workmentioning

confidence: 99%

The Complexity of Learning Approval-Based Multiwinner Voting Rules

Caragiannis¹,

Karl²

2021

Preprint

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Section: Introductionsupporting

confidence: 91%

“…The problem was later proved to be W[2]-hard by Betzler, Slinko, and Uhlmann (2013). Sonar, Dey, and Misra (2020) considered the question of whether a given candidate belongs to a winning committee for a given profile. They also prove that winner verification for the CC rule is coNP-hard, using a reduction from a variant of 3-HITTINGSET.…”

Section: Introductionmentioning

confidence: 99%

The Complexity of Learning Approval-Based Multiwinner Voting Rules

Caragiannis

Karl

2022

AAAI

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We study the PAC learnability of multiwinner voting, focusing on the class of approval-based committee scoring (ABCS) rules. These are voting rules applied on profiles with approval ballots, where each voter approves some of the candidates. According to ABCS rules, each committee of k candidates collects from each voter a score, that depends on the size of the voter's ballot and on the size of its intersection with the committee. Then, committees of maximum score are the winning ones. Our goal is to learn a target rule (i.e., to learn the corresponding scoring function) using information about the winning committees of a small number of sampled profiles. Despite the existence of exponentially many outcomes compared to single-winner elections, we show that the sample complexity is still low: a polynomial number of samples carries enough information for learning the target rule with high confidence and accuracy. Unfortunately, even simple tasks that need to be solved for learning from these samples are intractable. We prove that deciding whether there exists some ABCS rule that makes a given committee winning in a given profile is a computationally hard problem. Our results extend to the class of sequential Thiele rules, which have received attention due to their simplicity.

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“…On the other hand, Misra et al (2017) show NP-hardness for a generalization of single-peaked preferences where up to three peaks are allowed. Sonar et al (2020) study the problem of deciding whether a given alternative appears in some optimal Chamberlin-Courant committee. They show that this problem is Θ p 2 -complete in general, but becomes polynomial-time solvable for single-peaked preferences.…”

Section: Single-peaked Preferencesmentioning

confidence: 99%

Preference Restrictions in Computational Social Choice: A Survey

Elkind¹,

Lackner²,

Peters³

2022

Preprint

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Social choice becomes easier on restricted preference domains such as single-peaked, single-crossing, and Euclidean preferences. Many impossibility theorems disappear, the structure makes it easier to reason about preferences, and computational problems can be solved more efficiently. In this survey, we give a thorough overview of many classic and modern restricted preference domains and explore their properties and applications. We do this from the viewpoint of computational social choice, letting computational problems drive our interest, but we include a comprehensive discussion of the economics and social choice literatures as well. Particular focus areas of our survey include algorithms for recognizing whether preferences belong to a particular preference domain, and algorithms for winner determination of voting rules that are hard to compute if preferences are unrestricted.

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On the Complexity of Winner Verification and Candidate Winner for Multiwinner Voting Rules

Cited by 5 publications

References 1 publication

The Complexity of Learning Approval-Based Multiwinner Voting Rules

The Complexity of Learning Approval-Based Multiwinner Voting Rules

The Complexity of Learning Approval-Based Multiwinner Voting Rules

Preference Restrictions in Computational Social Choice: A Survey

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