An Experimental Comparison of Multiwinner Voting Rules on Approval Elections
Piotr Faliszewski, Martin Lackner, Krzysztof Sornat, Stanisław Szufa
TL;DR
This work addresses the problem of comparing approval-based multiwinner voting rules beyond traditional axiomatic classifications by introducing a distance-based framework that measures how similar the output committees are under different rules. It computes candidate distances from approvals, extends them to committees via the minimum-weight matching, and visualizes rule relationships as maps across multiple synthetic cultures. Key findings include the clustering of proportional rules, distinct positions for AV and CC, and that rules like seq-Phragmén and seq-PAV can share proximity with proportional rules in practice, while Equal Shares and PAV satisfy priceability and EJR in many instances. The approach provides a practical, data-driven complement to axiomatic analysis with potential to guide rule selection in applications and to illuminate the landscape of multiwinner voting rules.
Abstract
In this paper, we experimentally compare major approval-based multiwinner voting rules. To this end, we define a measure of similarity between two equal-sized committees subject to a given election. Using synthetic elections coming from several distributions, we analyze how similar are the committees provided by prominent voting rules. Our results can be visualized as ``maps of voting rules'', which provide a counterpoint to a purely axiomatic classification of voting rules. The strength of our proposed method is its independence from preimposed classifications (such as the satisfaction of concrete axioms), and that it indeed offers a much finer distinction than the current state of axiomatic analysis.