Multiwinner analogues of the plurality rule: axiomatic and algorithmic perspectives

We characterize the class of committee scoring rules that satisfy the fixed-majority criterion. We argue that rules in this class are multiwinner analogues of the single-winner Plurality rule, which is uniquely characterized as the only single-winner scoring rule that satisfies the simple majority c...

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Bibliographic Details
Published in:Social choice and welfare Vol. 51; no. 3; pp. 513 - 550
Main Authors: Faliszewski, Piotr, Skowron, Piotr, Slinko, Arkadii, Talmon, Nimrod
Format: Journal Article
Language:English
Published: Berlin/Heidelberg Springer 01.10.2018
Springer Berlin Heidelberg
Springer Nature B.V
Subjects:
Algorithms
Committees
Counting
Economic Theory/Quantitative Economics/Mathematical Methods
Economics
Economics and Finance
Game Theory
International Political Economy
Majority rule
Original Paper
Public Finance
Rules
Scores
Social and Behav. Sciences
Social Policy
ISSN:0176-1714, 1432-217X
Online Access:Get full text
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Summary:We characterize the class of committee scoring rules that satisfy the fixed-majority criterion. We argue that rules in this class are multiwinner analogues of the single-winner Plurality rule, which is uniquely characterized as the only single-winner scoring rule that satisfies the simple majority criterion. We define top-k-counting committee scoring rules and show that the fixed-majority consistent rules are a subclass of the top-k-counting rules. We give necessary and sufficient conditions for a top-k-counting rule to satisfy the fixed-majority criterion. We show that, for many top-k-counting rules, the complexity of winner determination is high (formally, we show that the problem of deciding if there exists a committee with at least a given score is NP-hard), but we also show examples of rules with polynomial-time winner determination procedures. For some of the computationally hard rules, we provide either exact FPT algorithms or approximate polynomial-time algorithms.
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ISSN:0176-1714
1432-217X
DOI:10.1007/s00355-018-1126-4