[Paper Review] Approval-Based Committee Voting: Axioms, Algorithms, and Applications.

Martin Lackner, Piotr Skowron|arXiv (Cornell University)|Jul 3, 2020

Game Theory and Voting SystemsEconomics, Econometrics and Finance191 references18 citations

TL;DR

This survey provides a comprehensive analysis of approval-based committee (ABC) voting rules, which select fixed-size committees from candidates based on voters' dichotomous approvals. It unifies axiomatic foundations, algorithmic design, and real-world applications, establishing a principled framework for practical use in multiwinner elections.

ABSTRACT

Approval-based committee (ABC) rules are voting rules that output a fixed-size subset of candidates, a so-called committee. ABC rules select committees based on dichotomous preferences, i.e., a voter either approves or disapproves a candidate. This simple type of preferences makes ABC rules widely suitable for practical use. In this survey, we summarize the current understanding of ABC rules from the viewpoint of computational social choice. The main focus is on axiomatic analysis, algorithmic results, and relevant applications.

Motivation & Objective

• To systematize the understanding of approval-based committee (ABC) rules within computational social choice.
• To identify and formalize key axioms that ensure fairness and representativeness in committee selection.
• To survey algorithmic methods for computing ABC rules efficiently, especially under computational constraints.
• To connect theoretical properties of ABC rules with practical applications in real-world decision-making.
• To provide a unified reference for researchers and practitioners on the design and analysis of ABC rules.

Proposed method

• Formalizing ABC rules as mechanisms that select a fixed-size subset of candidates based on dichotomous voter preferences (approve/disapprove).
• Applying axiomatic analysis to evaluate ABC rules according to fairness, representation, and consistency criteria.
• Surveying exact and approximation algorithms for computing ABC rules, including polynomial-time methods and heuristics.
• Integrating theoretical results with practical case studies to demonstrate applicability in real-world settings.
• Classifying ABC rules by their properties, such as proportionality, monotonicity, and stability.
• Using computational complexity analysis to assess feasibility and scalability of different ABC rule implementations.

Experimental results

Research questions

• RQ1 Which axioms best characterize fair and representative ABC rules in multiwinner elections?
• RQ2 How can ABC rules be computed efficiently while preserving desirable theoretical properties?
• RQ3 What are the trade-offs between fairness, computational efficiency, and representativeness in ABC rule design?
• RQ4 In what practical scenarios do ABC rules outperform other multiwinner voting methods?
• RQ5 How do different ABC rules behave under varying voter preference distributions and committee sizes?

Key findings

• ABC rules based on proportional representation principles ensure fair distribution of committee seats across voter groups.
• Several ABC rules, such as Phragmen’s rules and Method of Equal Shares, achieve strong fairness guarantees while remaining computationally tractable.
• Theoretical analysis confirms that some ABC rules satisfy key axioms like justified representation and proportionality of support.
• Algorithmic advances enable scalable computation of ABC rules even for large electorates and candidate sets.
• Empirical evaluations demonstrate that ABC rules outperform traditional methods in balancing diversity and representation.
• The integration of axiomatic and algorithmic analysis provides a robust framework for designing real-world ABC systems.