# Proportional Fairness in Clustering: A Social Choice Perspective

arXiv: https://arxiv.org/abs/2310.18162 · HTML: https://mlsanity.com/paper/2310.18162/

## Key facts

- Cited by 13 papers in the map (data through 14 Oct 2026).
- Builds on 21 of its 42 references that are in the map.
- First posted on arXiv 27 Oct 2023.

## Builds on (most cited first, 21 of 21)

- [Fair Clustering Through Fairlets](https://mlsanity.com/paper/1802.05733/) (2018)
- [Proportionally Fair Clustering](https://mlsanity.com/paper/1905.03674/) (2019)
- [Individual Fairness for k-Clustering](https://mlsanity.com/paper/2002.06742/) (2020)
- [Justified Representation in Approval-Based Committee Voting](https://mlsanity.com/paper/1407.8269/) (2014)
- [Multi-Winner Voting with Approval Preferences](https://mlsanity.com/paper/2007.01795/) (2020)
- [Proportional Participatory Budgeting with Additive Utilities](https://mlsanity.com/paper/2008.13276/) (2020)
- [Improved Approximation Algorithms for Individually Fair Clustering](https://mlsanity.com/paper/2106.14043/) (2021)
- [Better Algorithms for Individually Fair k-Clustering](https://mlsanity.com/paper/2106.12150/) (2021)
- [Robust and Verifiable Proportionality Axioms for Multiwinner Voting](https://mlsanity.com/paper/2302.01989/) (2023)
- [Proportionality and the Limits of Welfarism](https://mlsanity.com/paper/1911.11747/) (2019)
- [A New Notion of Individually Fair Clustering: α-Equitable k-Center](https://mlsanity.com/paper/2106.05423/) (2021)
- [Group Fairness in Committee Selection](https://mlsanity.com/paper/1905.04438/) (2019)
- [Proportionally Representative Participatory Budgeting with Ordinal Preferences](https://mlsanity.com/paper/1911.00864/) (2019)
- [Doubly Constrained Fair Clustering](https://mlsanity.com/paper/2305.19475/) (2023)
- [Individual Preference Stability for Clustering](https://mlsanity.com/paper/2207.03600/) (2022)
- [Proportionally Representative Clustering](https://mlsanity.com/paper/2304.13917/) (2023)
- [Approximately Stable Committee Selection](https://mlsanity.com/paper/1910.14008/) (2019)
- [The Metric Distortion of Multiwinner Voting](https://mlsanity.com/paper/2201.13332/) (2022)
- [Approximate Group Fairness for Clustering](https://mlsanity.com/paper/2203.17146/) (2022)
- [Feature-based Individual Fairness in k-Clustering](https://mlsanity.com/paper/2109.04554/) (2021)
- [Individual Representation in Approval-Based Committee Voting](https://mlsanity.com/paper/2112.05193/) (2021)

## Built on by (most cited first, 13 of 13)

- [Generative Social Choice: The Next Generation](https://mlsanity.com/paper/2505.22939/) (2025)
- [Proportional Fairness in Non-Centroid Clustering](https://mlsanity.com/paper/2410.23273/) (2024)
- [Proportional Representation in Metric Spaces and Low-Distortion Committee Selection](https://mlsanity.com/paper/2312.10369/) (2023)
- [Fair Clustering: Critique, Caveats, and Future Directions](https://mlsanity.com/paper/2406.15960/) (2024)
- [A Computational Approach to Improving Fairness in K-means Clustering](https://mlsanity.com/paper/2505.22984/) (2025)
- [The Core in Max-Loss Non-Centroid Clustering Can Be Empty](https://mlsanity.com/paper/2511.19107/) (2025)
- [Fair Transit Stop Placement: A Clustering Perspective and Beyond](https://mlsanity.com/paper/2602.06776/) (2026)
- [Embeddings for Preferences, Not Semantics](https://mlsanity.com/paper/2605.08360/) (2026)
- [Fairness in the Multi-Secretary Problem](https://mlsanity.com/paper/2511.23097/) (2025)
- [Temporal Panel Selection in Ongoing Citizens' Assemblies](https://mlsanity.com/paper/2602.16194/) (2026)
- [Optimally Selecting Representative Agents from a Metric Space](https://mlsanity.com/paper/2608.29097/) (2026)
- [Social Choice Foundations for Simulation-Augmented Generation](https://mlsanity.com/paper/2609.38287/) (2026)
- [Aggregating User Preferences while Ensuring Equity, Diversity, and Inclusion using Graph Summarization](https://mlsanity.com/paper/2610.07128/) (2026)

## Abstract (arXiv)

We study the proportional clustering problem of Chen et al. [ICML'19] and relate it to the area of multiwinner voting in computational social choice. We show that any clustering satisfying a weak proportionality notion of Brill and Peters [EC'23] simultaneously obtains the best known approximations to the proportional fairness notion of Chen et al. [ICML'19], but also to individual fairness [Jung et al., FORC'20] and the "core" [Li et al. ICML'21]. In fact, we show that any approximation to proportional fairness is also an approximation to individual fairness and vice versa. Finally, we also study stronger notions of proportional representation, in which deviations do not only happen to single, but multiple candidate centers, and show that stronger proportionality notions of Brill and Peters [EC'23] imply approximations to these stronger guarantees.