# Balanced Ranking with Diversity Constraints

arXiv: https://arxiv.org/abs/1906.01747 · HTML: https://mlsanity.com/paper/1906.01747/

## Key facts

- Cited by 20 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 4 Jun 2019.

## Built on by (most cited first, 20 of 20)

- [Maxmin-Fair Ranking: Individual Fairness under Group-Fairness Constraints](https://mlsanity.com/paper/2106.08652/) (2021)
- [Fair Ranking with Noisy Protected Attributes](https://mlsanity.com/paper/2211.17067/) (2022)
- [Do Large Language Models Rank Fairly? An Empirical Study on the Fairness of LLMs as Rankers](https://mlsanity.com/paper/2404.03192/) (2024)
- [Fairness Through Regularization for Learning to Rank](https://mlsanity.com/paper/2102.05996/) (2021)
- [Individually Fair Ranking](https://mlsanity.com/paper/2103.11023/) (2021)
- [Disaggregated Interventions to Reduce Inequality](https://mlsanity.com/paper/2107.00593/) (2021)
- [Maximizing Submodular Functions for Recommendation in the Presence of Biases](https://mlsanity.com/paper/2305.02806/) (2023)
- [WLD-Reg: A Data-dependent Within-layer Diversity Regularizer](https://mlsanity.com/paper/2301.01352/) (2023)
- [Fairness in Ranking under Disparate Uncertainty](https://mlsanity.com/paper/2309.01610/) (2023)
- [DiRe Committee : Diversity and Representation Constraints in Multiwinner Elections](https://mlsanity.com/paper/2107.07356/) (2021)
- [MANI-Rank: Multiple Attribute and Intersectional Group Fairness for Consensus Ranking](https://mlsanity.com/paper/2207.10020/) (2022)
- [On the Within-Group Fairness of Screening Classifiers](https://mlsanity.com/paper/2302.00025/) (2023)
- [Sampling Individually-Fair Rankings that are Always Group Fair](https://mlsanity.com/paper/2306.11964/) (2023)
- [Robust Allocations with Diversity Constraints](https://mlsanity.com/paper/2109.15015/) (2021)
- [Reranking individuals: The effect of fair classification within-groups](https://mlsanity.com/paper/2401.13391/) (2024)
- [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)
- [Reducing Biases in Record Matching Through Scores Calibration](https://mlsanity.com/paper/2411.01685/) (2024)
- [A Tutorial On Intersectionality in Fair Rankings](https://mlsanity.com/paper/2502.05333/) (2025)
- [Generalizing Fair Top-k Selection: An Integrative Approach](https://mlsanity.com/paper/2603.04689/) (2026)

## Abstract (arXiv)

Many set selection and ranking algorithms have recently been enhanced with diversity constraints that aim to explicitly increase representation of historically disadvantaged populations, or to improve the overall representativeness of the selected set. An unintended consequence of these constraints, however, is reduced in-group fairness: the selected candidates from a given group may not be the best ones, and this unfairness may not be well-balanced across groups. In this paper we study this phenomenon using datasets that comprise multiple sensitive attributes. We then introduce additional constraints, aimed at balancing the ∈-group fairness across groups, and formalize the induced optimization problems as integer linear programs. Using these programs, we conduct an experimental evaluation with real datasets, and quantify the feasible trade-offs between balance and overall performance in the presence of diversity constraints.