Xia, L. (2024). Computing Most Equitable Voting Rules. arXiv preprint arXiv:2410.04179v1.
This paper investigates the computational complexity of designing fair and efficient voting rules, specifically focusing on computing "most equitable rules" that optimally satisfy anonymity and neutrality, two fundamental fairness axioms in social choice theory.
The authors establish a novel connection between the problem of computing most equitable voting rules and the graph isomorphism problem. They leverage this connection to design quasipolynomial-time algorithms for computing most equitable rules with verifications for a broad class of preferences and decisions. They further analyze the complexity lower bound of this problem by proving its GI-completeness or GA-completeness for various common social choice settings.
The research demonstrates that while achieving perfect fairness in voting (satisfying ANR for all profiles) is computationally hard, computing nearly optimal solutions (most equitable rules) is achievable in quasipolynomial time for a wide range of settings. The established connection to graph isomorphism provides a new perspective for understanding and tackling fairness challenges in computational social choice.
This work significantly contributes to computational social choice by providing both algorithmic advancements and complexity results for computing fair voting rules. The findings have implications for designing transparent and trustworthy collective decision-making systems in various domains.
The paper primarily focuses on anonymity and neutrality as fairness axioms. Exploring the computational complexity of most equitable rules under other fairness axioms remains an open question. Further research could investigate the possibility of developing more efficient algorithms for specific social choice settings or under additional constraints.
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by Lirong Xia pada arxiv.org 10-08-2024
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