Stable roommates with narcissistic, single-peaked, and single-crossing preferences

Bredereck, Robert; Finnendahl, Ugo Paavo; Niedermeier, Rolf

doi:10.1007/s10458-020-09470-x

Cited by 11 publications

(6 citation statements)

References 48 publications

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“…For narcissistic single-crossing preferences, Bredereck et al (2020) show that the same result holds: there exists a unique stable matching, and it can be found in O(n 2 ) time. They also extend the results for single-peaked and single-crossing preferences to the case with ties allowed, for which the same results hold except that uniqueness is not guaranteed.…”

Section: Matching and Assignmentmentioning

confidence: 64%

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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: Matching and Assignmentmentioning

confidence: 64%

“…They also give a simple algorithm for finding this matching. Bredereck et al (2020) show that this algorithm runs in time O(n 2 ). (Bartholdi III and Trick (1986) had claimed an O(n) runtime.…”

Section: Matching and Assignmentmentioning

confidence: 96%

Preference Restrictions in Computational Social Choice: A Survey

Elkind¹,

Lackner²,

Peters³

2022

Preprint

View full text Add to dashboard Cite

show abstract

“…By definition, every BP-stable matching is r BP -EF, implying that an r BP -EF matching always exists under globally-ranked [4] or narcissistically single-peaked preferences [13]. Yet, in general, an r BP -EF matching may not exist, as shown in the next example.…”

Section: Observation 2 An R Bp -Ef Matching Matches Every Agent Ranke...mentioning

confidence: 90%

Rank-Envy-Freeness in Roommate Matchings

Coutance,

Maddila,

Wilczynski

2023

Frontiers in Artificial Intelligence and Applications

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In the roommate problem, pairs of agents must be formed, based on ordinal preferences of the agents over each other. In this article, we examine fair roommate matchings by relaxing envy-freeness to account for justified envy based on the rank in the agents’ preferences. A rank-envy-free matching prevents that an agent prefers the partner of another agent whereas she has ranked it better. Although this requirement is pretty weak in house allocation [9], we show that it is more demanding in the roommate setting. We study parameterizations of rank-envy-freeness, as well as further natural relaxations of this concept. We also investigate the connections between the family of rank-based fairness criteria and known optimality or stability concepts.

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“…We will improve the consensus reaching process for the decision-making aggregation problem of network groups under trust networks [104][105][106][107][108][109][110], apply rough sets [111] and concurrency [75], and identify group preference biases, opinion preference changes, and chaos. Additionally, we will consider any consistency and consensus in any linguistic, fuzzy, or social network large-group decision making process during the CRP.…”

Section: Discussionmentioning

confidence: 99%

The Greatest Common Decision Maker: A Novel Conflict and Consensus Analysis Compared with Other Voting Procedures

García-del-Valle-y-Durán

Hernández‐Martínez

Fernández‐Anaya

2022

Mathematics

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Consensus or conflict agreements, and how these change over time, have significant consequences for understanding the network behavior of human beings, especially when it is necessary to have agreements to move companies and countries forward peacefully. This paper proposes a new Greatest Common Decision Maker (GCDM) aggregation voting procedure applied to square preference matrices of n alternatives and n decision makers. An analysis of the mathematical combinatory ranking of consensus and conflicts generated by the GCDM is realized, and compared to the well-known Borda, Pluralism and Condorcet aggregation procedures to cover the entire class of dynamic accountable group decision-making phenomena. A classification for the family of magic squares is reviewed and it is determined that a conflict decision matrix corresponds to a Latin square. As an original contribution, a 2D color heatmap is generated as a visual tool to compare the consensus and conflict cases generated by the compared methods. Finally, a new consensus reaching model is proposed to compare these aggregation methods defining cost and effort change matrices to convert the cases of conflicts into consensus according to the change in individual preferences. The incorporation of social concepts into our research makes the results obtained stronger.

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Stable roommates with narcissistic, single-peaked, and single-crossing preferences

Cited by 11 publications

References 48 publications

Preference Restrictions in Computational Social Choice: A Survey

Preference Restrictions in Computational Social Choice: A Survey

Rank-Envy-Freeness in Roommate Matchings

The Greatest Common Decision Maker: A Novel Conflict and Consensus Analysis Compared with Other Voting Procedures

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