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Fault Tolerance in Euclidean Committee Selection

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Listed:
  • Chinmay Sonar
  • Subhash Suri
  • Jie Xue

Abstract

In the committee selection problem, the goal is to choose a subset of size $k$ from a set of candidates $C$ that collectively gives the best representation to a set of voters. We consider this problem in Euclidean $d$-space where each voter/candidate is a point and voters' preferences are implicitly represented by Euclidean distances to candidates. We explore fault-tolerance in committee selection and study the following three variants: (1) given a committee and a set of $f$ failing candidates, find their optimal replacement; (2) compute the worst-case replacement score for a given committee under failure of $f$ candidates; and (3) design a committee with the best replacement score under worst-case failures. The score of a committee is determined using the well-known (min-max) Chamberlin-Courant rule: minimize the maximum distance between any voter and its closest candidate in the committee. Our main results include the following: (1) in one dimension, all three problems can be solved in polynomial time; (2) in dimension $d \geq 2$, all three problems are NP-hard; and (3) all three problems admit a constant-factor approximation in any fixed dimension, and the optimal committee problem has an FPT bicriterion approximation.

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  • Chinmay Sonar & Subhash Suri & Jie Xue, 2023. "Fault Tolerance in Euclidean Committee Selection," Papers 2308.07268, arXiv.org.
  • Handle: RePEc:arx:papers:2308.07268
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    References listed on IDEAS

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    1. Skowron, Piotr & Faliszewski, Piotr & Slinko, Arkadii, 2019. "Axiomatic characterization of committee scoring rules," Journal of Economic Theory, Elsevier, vol. 180(C), pages 244-273.
    2. Edith Elkind & Piotr Faliszewski & Piotr Skowron & Arkadii Slinko, 2017. "Properties of multiwinner voting rules," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 48(3), pages 599-632, March.
    3. Kamesh Munagala & Zeyu Shen & Kangning Wang, 2021. "Optimal Algorithms for Multiwinner Elections and the Chamberlin-Courant Rule," Papers 2106.00091, arXiv.org.
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