# FA*IR: A Fair Top-k Ranking Algorithm

arXiv: https://arxiv.org/abs/1706.06368 · HTML: https://mlsanity.com/paper/1706.06368/

## Key facts

- Cited by 113 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 20 Jun 2017.

## Built on by (most cited first, 30 of 113)

- [Fair and Optimal Classification via Post-Processing](https://mlsanity.com/paper/2211.01528/) (2022)
- [User-centered Evaluation of Popularity Bias in Recommender Systems](https://mlsanity.com/paper/2103.06364/) (2021)
- [Societal Biases in Retrieved Contents: Measurement Framework and Adversarial Mitigation for BERT Rankers](https://mlsanity.com/paper/2104.13640/) (2021)
- [Human-Centric Multimodal Machine Learning: Recent Advances and Testbed on AI-based Recruitment](https://mlsanity.com/paper/2302.10908/) (2023)
- [A Comprehensive Survey on Trustworthy Recommender Systems](https://mlsanity.com/paper/2209.10117/) (2022)
- [Fairness in Ranking under Uncertainty](https://mlsanity.com/paper/2107.06720/) (2021)
- [Fairness in Recommendation: Foundations, Methods and Applications](https://mlsanity.com/paper/2205.13619/) (2022)
- [When Fair Ranking Meets Uncertain Inference](https://mlsanity.com/paper/2105.02091/) (2021)
- [Joint Multisided Exposure Fairness for Recommendation](https://mlsanity.com/paper/2205.00048/) (2022)
- [RecSim NG: Toward Principled Uncertainty Modeling for Recommender Ecosystems](https://mlsanity.com/paper/2103.08057/) (2021)
- [Strategic Ranking](https://mlsanity.com/paper/2109.08240/) (2021)
- [Fair ranking: a critical review, challenges, and future directions](https://mlsanity.com/paper/2201.12662/) (2022)
- [De-biasing "bias" measurement](https://mlsanity.com/paper/2205.05770/) (2022)
- [Maxmin-Fair Ranking: Individual Fairness under Group-Fairness Constraints](https://mlsanity.com/paper/2106.08652/) (2021)
- [End-to-end Learning for Fair Ranking Systems](https://mlsanity.com/paper/2111.10723/) (2021)
- [Improving Recommendation Fairness via Data Augmentation](https://mlsanity.com/paper/2302.06333/) (2023)
- [Do Large Language Models Rank Fairly? An Empirical Study on the Fairness of LLMs as Rankers](https://mlsanity.com/paper/2404.03192/) (2024)
- [Towards Fair RAG: On the Impact of Fair Ranking in Retrieval-Augmented Generation](https://mlsanity.com/paper/2409.11598/) (2024)
- [A Graph-based Approach for Mitigating Multi-sided Exposure Bias in Recommender Systems](https://mlsanity.com/paper/2107.03415/) (2021)
- [Estimation of Fair Ranking Metrics with Incomplete Judgments](https://mlsanity.com/paper/2108.05152/) (2021)
- [FairCanary: Rapid Continuous Explainable Fairness](https://mlsanity.com/paper/2106.07057/) (2021)
- [Introducing the Expohedron for Efficient Pareto-optimal Fairness-Utility Amortizations in Repeated Rankings](https://mlsanity.com/paper/2202.03237/) (2022)
- [Uncertainty Quantification for Fairness in Two-Stage Recommender Systems](https://mlsanity.com/paper/2205.15436/) (2022)
- [Towards Foundation-model-based Multiagent System to Accelerate AI for Social Impact](https://mlsanity.com/paper/2412.07880/) (2024)
- [CatRAG: Functor-Guided Structural Debiasing with Retrieval Augmentation for Fair LLMs](https://mlsanity.com/paper/2603.21524/) (2026)
- [Fairness Through Regularization for Learning to Rank](https://mlsanity.com/paper/2102.05996/) (2021)
- [Measuring Disparate Outcomes of Content Recommendation Algorithms with Distributional Inequality Metrics](https://mlsanity.com/paper/2202.01615/) (2022)
- [Popularity Bias in Collaborative Filtering-Based Multimedia Recommender Systems](https://mlsanity.com/paper/2203.00376/) (2022)
- [Intersectional Two-sided Fairness in Recommendation](https://mlsanity.com/paper/2402.02816/) (2024)
- [Individually Fair Ranking](https://mlsanity.com/paper/2103.11023/) (2021)

## Abstract (arXiv)

In this work, we define and solve the Fair Top-k Ranking problem, in which we want to determine a subset of k candidates from a large pool of n >> k candidates, maximizing utility (i.e., select the "best" candidates) subject to group fairness criteria. Our ranked group fairness definition extends group fairness using the standard notion of protected groups and is based on ensuring that the proportion of protected candidates in every prefix of the top-k ranking remains statistically above or indistinguishable from a given minimum. Utility is operationalized in two ways: (i) every candidate included in the top-k should be more qualified than every candidate not included; and (ii) for every pair of candidates in the top-k, the more qualified candidate should be ranked above. An efficient algorithm is presented for producing the Fair Top-k Ranking, and tested experimentally on existing datasets as well as new datasets released with this paper, showing that our approach yields small distortions with respect to rankings that maximize utility without considering fairness criteria. To the best of our knowledge, this is the first algorithm grounded in statistical tests that can mitigate biases in the representation of an under-represented group along a ranked list.