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

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, and propose a methodology for systematically minimizing axioms 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.