Technology Category
Game Theory and Economic Paradigms: Social Choice / VotingKnowledge Representation and Reasoning: Computational Complexity of ReasoningData Mining & Knowledge Management: Scalability, Parallel & Distributed Systems
On the Parallelizability of Approval-Based Committee Rules
🤖 AI Summary
This paper investigates the parallel computability of Approval-Based Committee (ABC) rules in large-scale elections. We establish that computing winning committees under prominent ABC rules—such as the Method of Equal Shares—is P-hard, thereby proving their inherent sequentiality and fundamental intractability in parallel settings. Subsequently, we identify structural preference classes—namely single-peaked and single-crossing preferences—under which the Chamberlin–Courant rule admits efficient parallelization. Our analysis integrates computational complexity theory, parallel computation models (e.g., PRAM), and social choice theory, employing rigorous polynomial-time reductions to delineate precise theoretical boundaries: while ABC rules are generally not amenable to parallel speedup, specific domain restrictions enable parallel feasibility for certain rules. These results provide foundational theoretical guarantees for designing scalable, fair election algorithms in massive participatory systems.
Technology Category
Application Category
📝 Abstract
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 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 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.
Problem
Research questions and friction points this paper is trying to address.
Parallel Computing
Efficient Decision-Making
Voting Preferences
Innovation
Methods, ideas, or system contributions that make the work stand out.
Chamberlin-Courant rule
Parallelization
Large-scale elections
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