# What Do Multiwinner Voting Rules Do? An Experiment Over the Two-Dimensional Euclidean Domain

## TL;DR

This paper visualizes and compares the outputs of various multiwinner voting rules in a two-dimensional Euclidean setting, providing insights into their suitability for different real-world applications.

## Contribution

It offers a comprehensive visualization and analysis of popular multiwinner voting rules in a geometric model, highlighting their strengths and weaknesses for practical use.

## Key findings

- STV performs well across applications
- Bloc rule performs poorly in the studied settings
- Different rules are suited for different applications

## Abstract

We visualize aggregate outputs of popular multiwinner voting rules--SNTV, STV, Bloc, k-Borda, Monroe, Chamberlin--Courant, and HarmonicBorda--for elections generated according to the two-dimensional Euclidean model. We consider three applications of multiwinner voting, namely, parliamentary elections, portfolio/movie selection, and shortlisting, and use our results to understand which of our rules seem to be best suited for each application. In particular, we show that STV (one of the few nontrivial rules used in real high-stake elections) exhibits excellent performance, whereas the Bloc rule (also often used in practice) performs poorly.