An Experimental Comparison of Multiwinner Voting Rules on Approval Elections

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.

Approval-Based Committee Voting in Practice: A Case Study of (over-)Representation in the Polkadot Blockchain

“…In Table 1, we show the similarity between voting rules in terms of the average overlap of their computed committees. We observe a high consensus of all rules, thereby confirming previous findings on synthetic data (Reichert and Elkind 2023;Faliszewski et al 2023b); in fact, across all elections, two rules never disagree on more than 51 out of the k = 300 candidates. However, there are some differences: The four considered proportional rules have a particularly high agreement.…”

“…Formally capturing proportional representation in the form of axioms, and designing rules that are guaranteed to satisfy these axioms, is a very active area of research; see the book by Lackner and Skowron (2022). While this effort has resulted in a good theoretical understanding of the axiomatic aspects of different voting rules, there are only very few studies that examine the actual behavior of such rules on specific real-world or synthetically generated voting instances (Elkind et al 2017;Szufa et al 2022;Faliszewski et al 2023b;Mehra, Sreenivas, and Larson 2023). Nevertheless, these few empirical works have already proved useful, as they found that different voting rules often produce similar outcomes and that most voting rules tend to significantly outperform their worst-case proportionality guarantees.…”

“…There is a large literature developing (axiomatic) measures to assess the proportionality of a committee (Aziz et al 2017;Sánchez-Fernández et al 2017;Lackner and Skowron 2022;Skowron 2021). Questions typically examined in empirical works on ABC voting concern the similarity of outcomes returned by different voting rules (Reichert and Elkind 2023;Faliszewski et al 2023b;Elkind et al 2017), how often voting rules satisfy proportionality axioms (Faliszewski et al 2023b;Mehra, Sreenivas, and Larson 2023), and how often such axioms are satisfied by randomly selected committees (Bredereck et al 2019;. Complementary to our work, Szufa et al (2022) provided tools for more empirical studies of ABC rules by proposing several synthetic models for generating data and a framework for visualizing the data and experimental results.…”