Preference Restrictions in Computational Social Choice: A Survey

Elkind, Edith; Lackner, Martin; Peters, Dominik

doi:10.48550/arxiv.2205.09092

Cited by 9 publications

(9 citation statements)

References 158 publications

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“…We mention that Inada's original definition is different from the one that we provided, but they are equivalent [Karpov, 2019] and the tree-based one is algorithmically much more convenient. We point readers interested in structured domains to the recent survey of Elkind et al [2022].…”

Section: Structured Domainsmentioning

confidence: 99%

Properties of Position Matrices and Their Elections

Boehmer¹,

Cai²,

Faliszewski³

et al. 2023

Preprint

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We study the properties of elections that have a given position matrix (in such elections each candidate is ranked on each position by a number of voters specified in the matrix). We show that counting elections that generate a given position matrix is #P-complete. Consequently, sampling such elections uniformly at random seems challenging and we propose a simpler algorithm, without hard guarantees. Next, we consider the problem of testing if a given matrix can be implemented by an election with a certain structure (such as single-peakedness or groupseparability). Finally, we consider the problem of checking if a given position matrix can be implemented by an election with a Condorcet winner. We complement our theoretical findings with experiments.

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Section: Structured Domainsmentioning

confidence: 99%

Properties of Position Matrices and Their Elections

Boehmer¹,

Cai²,

Faliszewski³

et al. 2023

Preprint

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show abstract

“…We mention that a number of other preference domains are considered in the literature-see, e.g., the works of Yang [2019] and Godziszewski et al [2021]-but the CI and VI ones are by far the most popular. For a very detailed discussion of structured domains, albeit in the world of ordinal preferences, we point to the survey of Elkind et al [2022].…”

Section: Structured Preferencesmentioning

confidence: 99%

The Complexity of Proportionality Degree in Committee Elections

Janeczko¹,

Faliszewski²

2022

Preprint

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Over the last few years, researchers have put significant effort into understanding of the notion of proportional representation in committee election. In particular, recently they have proposed the notion of proportionality degree. We study the complexity of computing committees with a given proportionality degree and of testing if a given committee provides a particular one. This way, we complement recent studies that mostly focused on the notion of (extended) justified representation. We also study the problems of testing if a cohesive group of a given size exists and of counting such groups.

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“…Since IRV can behave very erratically across ballot lengths for general profiles, we might hope that imposing restrictions on the space of profiles makes IRV more well-behaved. We consider three classic profile restrictions from voting theory, single-peaked [8,5], single-crossing [19], and 1-Euclidean preferences (see [15] for a survey of preference restrictions). Definition 1.…”

Section: Restrictions On Profilesmentioning

confidence: 99%

Ballot Length in Instant Runoff Voting

Tomlinson¹,

Ugander²,

Kleinberg³

2022

Preprint

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Instant runoff voting (IRV) is an increasingly-popular alternative to traditional plurality voting in which voters submit rankings over the candidates rather than individual votes. In practice, municipalities often restrict the ballot length, the number of candidates a voter is allowed to rank on their ballot. We theoretically and empirically analyze how ballot length can influence the outcome of an election, given fixed voter preferences. We show that there exist preference profiles over k candidates such that up to k − 1 different candidates win at different ballot lengths. We derive exact lower bounds on the number of voters required for such profiles and provide constructions matching these bounds. Additionally, we fully characterize which sequences of winners are possible over ballot lengths and provide explicit profile constructions achieving any feasible winner sequence. Finally, we analyze a collection of 168 real-world elections, where we truncate rankings to simulate shorter ballots. We find that shorter ballots could have changed the outcome in one quarter of these elections and that longer ballots can favor particular candidates. Our results highlight ballot length as a consequential degree of freedom in the design of IRV elections.

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Preference Restrictions in Computational Social Choice: A Survey

Cited by 9 publications

References 158 publications

Properties of Position Matrices and Their Elections

Properties of Position Matrices and Their Elections

The Complexity of Proportionality Degree in Committee Elections

Ballot Length in Instant Runoff Voting

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