2025/01/25 by Zack Fitzsimmons, Fitzsimmons, Zack, Zohair Raza Hassan +3
Business, Management and Accounting · Social Sciences · #Computer Science and Game Theory (cs.GT) #Digitalization, Law, and Regulation #Dispute Resolution and Class Actions #FOS: Computer and information sciences #International Arbitration and Investment Law
paper · pdf · doi:10.48550/arxiv.2501.15006
openalex publication_date 2025/01/25 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
Approval-Based Committee (ABC) rules are an important tool for choosing a fair set of candidates when given the preferences of a collection of voters. Though finding a winning committee for many ABC rules is NP-hard, natural variations for these rules with polynomial-time algorithms exist. The recently introduced Method of Equal Shares, an important ABC rule with desirable properties, is also computable in polynomial time. However, when working with very large elections, polynomial time is not enough and parallelization may be necessary. We show that computing a winning committee using these polynomial-time ABC rules (including the Method of Equal Shares) is P-hard, thus showing they cannot be parallelized. In contrast, we show that finding a winning committee can be parallelized when the votes are single-peaked or single-crossing for the important ABC rule Chamberlin-Courant.