# Multiwinner Elections with Diversity Constraints

arXiv: https://arxiv.org/abs/1711.06527 · HTML: https://mlsanity.com/paper/1711.06527/

## Key facts

- Cited by 10 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 17 Nov 2017.

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

- [Temporal Fairness in Multiwinner Voting](https://mlsanity.com/paper/2312.04417/) (2023)
- [DiRe Committee : Diversity and Representation Constraints in Multiwinner Elections](https://mlsanity.com/paper/2107.07356/) (2021)
- [Online Selection of Diverse Committees](https://mlsanity.com/paper/2105.09295/) (2021)
- [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)
- [Participatory Budgeting with Donations and Diversity Constraints](https://mlsanity.com/paper/2104.15075/) (2021)
- [Fairly Allocating Utility in Constrained Multiwinner Elections](https://mlsanity.com/paper/2211.12820/) (2022)
- [On the Complexity of Finding a Diverse and Representative Committee using a Monotone, Separable Positional Multiwinner Voting Rule](https://mlsanity.com/paper/2211.13217/) (2022)
- [Ranking with Slot Constraints](https://mlsanity.com/paper/2310.17870/) (2023)
- [A General Theory of Proportionality with Additive Utilities](https://mlsanity.com/paper/2602.08504/) (2026)
- [AI of the People, by the People, for the People: A Social Choice Approach to Collective Control of Artificial Intelligence](https://mlsanity.com/paper/2605.16291/) (2026)

## Abstract (arXiv)

We develop a model of multiwinner elections that combines performance-based measures of the quality of the committee (such as, e.g., Borda scores of the committee members) with diversity constraints. Specifically, we assume that the candidates have certain attributes (such as being a male or a female, being junior or senior, etc.) and the goal is to elect a committee that, on the one hand, has as high a score regarding a given performance measure, but that, on the other hand, meets certain requirements (e.g., of the form "at least 30% of the committee members are junior candidates and at least 40% are females"). We analyze the computational complexity of computing winning committees in this model, obtaining polynomial-time algorithms (exact and approximate) and NP-hardness results. We focus on several natural classes of voting rules and diversity constraints.