On the Number of Group-Separable Preference Profiles

Karpov, Alexander

doi:10.1007/s10726-019-09621-w

Cited by 12 publications

(7 citation statements)

References 36 publications

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“…The definition of group-separable preferences can be rephrased in terms of clone sets: it says that for each A ⊆ A there is a proper subset B ⊂ A such that both B and A \ B are clone sets with respect to P | A . Building on this idea, Karpov (2019) provides a characterization of group-separable profiles in terms of the properties of their clone decompositions trees: specifically, he establishes that a profile is group-separable if and only if all internal nodes of its clone decomposition tree are Q-nodes.…”

Section: Group-separable Preferencesmentioning

confidence: 99%

“…We note that Karpov (2019) provides an exact formula for the number of group-separable profiles with n voters and m alternatives, as well as an expression for the number of such profiles that are narcissistic. Each of the many domain restrictions introduced in Section 3 is associated with a natural algorithmic question: given a profile P , does P belong to this restricted domain?…”

Section: Group-separable Preferencesmentioning

confidence: 99%

“…Recall the characterization of group-separable profiles in terms of their canonical clone tree decompositions: a profile is group-separable if and only if its canonical clone tree decomposition does not contain P-nodes (Karpov, 2019). Since a canonical clone tree decomposition of a given profile can be computed in linear time (Elkind et al, 2012), we obtain a linear-time algorithm for recognizing group-separable preferences.…”

Section: Algorithms For Group-separable Preferencesmentioning

confidence: 99%

See 2 more Smart Citations

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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Section: Group-separable Preferencesmentioning

confidence: 99%

Section: Group-separable Preferencesmentioning

confidence: 99%

Section: Algorithms For Group-separable Preferencesmentioning

confidence: 99%

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Preference Restrictions in Computational Social Choice: A Survey

Elkind¹,

Lackner²,

Peters³

2022

Preprint

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“…Group-Separable Group-separable elections were introduced by Inada [17,18]. We use a definition based on trees (see, e.g., the works of Karpov [19] and Faliszewski et al [13] for a discussion and motivation). Consider an ordered, rooted tree where each leaf is a unique candidate.…”

Section: Sp Sc and Spocmentioning

confidence: 99%

Understanding Distance Measures Among Elections

Boehmer¹,

Faliszewski²,

Niedermeier³

et al. 2022

Preprint

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Motivated by putting empirical work based on (synthetic) election data on a more solid mathematical basis, we analyze six distances among elections, including, e.g., the challenging-to-compute but very precise swap distance and the distance used to form the so-called map of elections. Among the six, the latter seems to strike the best balance between its computational complexity and expressiveness.* An extended abstract of this article has been accepted for publication in the proceedings of IJCAI 2022. 1 Generally, we use the word distance when we refer to a value of a metric, but occasionally, reflecting the literature, we break this rule (e.g., to speak of the earth mover's distance or the swap distance).

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“…Note that the election from Example 2.1 is single-peaked with respect to the axis a b c d e. We also consider group-separable elections, introduced by Inada [1964]. For our purposes, it will be convenient to use the tree-based definition of Karpov [2019]. Let C = {c 1 , .…”

Section: Structured Domainsmentioning

confidence: 99%

Expected Frequency Matrices of Elections: Computation, Geometry, and Preference Learning

Boehmer¹,

Bredereck²,

Elkind³

et al. 2022

Preprint

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We use the "map of elections" approach of Szufa et al. (AAMAS-2020) to analyze several well-known vote distributions. For each of them, we give an explicit formula or an efficient algorithm for computing its frequency matrix, which captures the probability that a given candidate appears in a given position in a sampled vote. We use these matrices to draw the "skeleton map" of distributions, evaluate its robustness, and analyze its properties. We further use them to identify the nature of several real-world elections.

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On the Number of Group-Separable Preference Profiles

Cited by 12 publications

References 36 publications

Preference Restrictions in Computational Social Choice: A Survey

Preference Restrictions in Computational Social Choice: A Survey

Understanding Distance Measures Among Elections

Expected Frequency Matrices of Elections: Computation, Geometry, and Preference Learning

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