What Voting Rules Actually Do: A Data-Driven Analysis of Multi-Winner Voting

TL;DR

This paper introduces a data-driven framework to evaluate multi-winner voting rules' performance in real-world preference distributions, revealing neural networks can outperform traditional rules in reducing axiom violations.

Contribution

It presents a novel data-driven approach to assess voting rules' axiomatic compliance and demonstrates neural networks' potential to improve voting system design.

Findings

Neural networks can outperform traditional voting rules in minimizing axiom violations.

The framework reveals how often voting rules violate axioms across different preference distributions.

Data-driven analysis informs the design of more effective voting systems.

Abstract

Committee-selection problems arise in many contexts and applications, and there has been increasing interest within the social choice research community on identifying which properties are satisfied by different multi-winner voting rules. In this work, we propose a data-driven framework to evaluate how frequently voting rules violate axioms across diverse preference distributions in practice, shifting away from the binary perspective of axiom satisfaction given by worst-case analysis. Using this framework, we analyze the relationship between multi-winner voting rules and their axiomatic performance under several preference distributions. We then show that neural networks, acting as voting rules, can outperform traditional rules in minimizing axiom violations. Our results suggest that data-driven approaches to social choice can inform the design of new voting systems and support the continuation of data-driven research in social choice.