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

arXiv: https://arxiv.org/abs/1901.09217 · HTML: https://mlsanity.com/paper/1901.09217/

## Key facts

- Cited by 10 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 26 Jan 2019.

## Built on by (most cited first, 10 of 10)

- [Proportional Aggregation of Preferences for Sequential Decision Making](https://mlsanity.com/paper/2306.14858/) (2023)
- [Expected Frequency Matrices of Elections: Computation, Geometry, and Preference Learning](https://mlsanity.com/paper/2205.07831/) (2022)
- [Drawing a Map of Elections](https://mlsanity.com/paper/2504.03809/) (2025)
- [AI-Generated Compromises for Coalition Formation](https://mlsanity.com/paper/2506.06837/) (2025)
- [Subset Selection Based On Multiple Rankings in the Presence of Bias: Effectiveness of Fairness Constraints for Multiwinner Voting Score Functions](https://mlsanity.com/paper/2306.09835/) (2023)
- [Selecting the Most Conflicting Pair of Candidates](https://mlsanity.com/paper/2405.05870/) (2024)
- [Proportional Selection in Networks](https://mlsanity.com/paper/2502.03545/) (2025)
- [Large Language Models for Designing Participatory Budgeting Rules](https://mlsanity.com/paper/2602.09349/) (2026)
- [Private Multi-Winner Voting for Machine Learning](https://mlsanity.com/paper/2211.15410/) (2022)
- [AI-Generated Compromises for Coalition Formation: Modeling, Simulation, and a Textual Case Study](https://mlsanity.com/paper/2512.05983/) (2025)

## Abstract (arXiv)

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.