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Efficient Algorithms for Monroe and CC Rules in Multi-Winner Elections with (Nearly) Structured Preferences
Jiehua Chen, Christian Hatschka, Sofia Simola
397 - 404
10.3233/FAIA230296
Research Article
Frontiers in Artificial Intelligence and Applications
Volume 372: ECAI 2023
Abstract

We investigate winner determination for two popular proportional representation systems: the Monroe and Chamberlin-Courant (abbrv. CC) systems. Our study focuses on (nearly) single-peaked resp. single-crossing preferences. We show that for single-crossing approval preferences, winner determination of the Monroe rule is polynomial, and for both rules, winner determination mostly admits FPT algorithms with respect to the number of voters to delete to obtain single-peaked or single-crossing preferences. Our results answer some complexity questions from the literature [19, 29, 22].

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