# Fairness in Ranking under Uncertainty

arXiv: https://arxiv.org/abs/2107.06720 · HTML: https://mlsanity.com/paper/2107.06720/

## Key facts

- Cited by 27 papers in the map (data through 14 Oct 2026).
- Builds on 32 of its 58 references that are in the map.
- First posted on arXiv 14 Jul 2021.

## Builds on (most cited first, 30 of 32)

- [Equality of Opportunity in Supervised Learning](https://mlsanity.com/paper/1610.02413/) (2016)
- [A Survey on Bias and Fairness in Machine Learning](https://mlsanity.com/paper/1908.09635/) (2019)
- [Counterfactual Fairness](https://mlsanity.com/paper/1703.06856/) (2017)
- [On Fairness and Calibration](https://mlsanity.com/paper/1709.02012/) (2017)
- [Fairness Beyond Disparate Treatment & Disparate Impact: Learning Classification without Disparate Mistreatment](https://mlsanity.com/paper/1610.08452/) (2016)
- [Multiaccuracy: Black-Box Post-Processing for Fairness in Classification](https://mlsanity.com/paper/1805.12317/) (2018)
- [Avoiding Discrimination through Causal Reasoning](https://mlsanity.com/paper/1706.02744/) (2017)
- [Fairness of Exposure in Rankings](https://mlsanity.com/paper/1802.07281/) (2018)
- [Fairness in Learning: Classic and Contextual Bandits](https://mlsanity.com/paper/1605.07139/) (2016)
- [Fairness in Recommendation Ranking through Pairwise Comparisons](https://mlsanity.com/paper/1903.00780/) (2019)
- [Equity of Attention: Amortizing Individual Fairness in Rankings](https://mlsanity.com/paper/1805.01788/) (2018)
- [FA*IR: A Fair Top-k Ranking Algorithm](https://mlsanity.com/paper/1706.06368/) (2017)
- [Measuring Fairness in Ranked Outputs](https://mlsanity.com/paper/1610.08559/) (2016)
- [Ranking with Fairness Constraints](https://mlsanity.com/paper/1704.06840/) (2017)
- [Achieving Fairness in the Stochastic Multi-armed Bandit Problem](https://mlsanity.com/paper/1907.10516/) (2019)
- [Policy Learning for Fairness in Ranking](https://mlsanity.com/paper/1902.04056/) (2019)
- [Controlling Fairness and Bias in Dynamic Learning-to-Rank](https://mlsanity.com/paper/2005.14713/) (2020)
- [Operationalizing Individual Fairness with Pairwise Fair Representations](https://mlsanity.com/paper/1907.01439/) (2019)
- [Pairwise Fairness for Ranking and Regression](https://mlsanity.com/paper/1906.05330/) (2019)
- [Evaluating Stochastic Rankings with Expected Exposure](https://mlsanity.com/paper/2004.13157/) (2020)
- [On the relation between accuracy and fairness in binary classification](https://mlsanity.com/paper/1505.05723/) (2015)
- [The Fairness of Risk Scores Beyond Classification: Bipartite Ranking and the xAUC Metric](https://mlsanity.com/paper/1902.05826/) (2019)
- [Designing Fair Ranking Schemes](https://mlsanity.com/paper/1712.09752/) (2017)
- [A statistical framework for fair predictive algorithms](https://mlsanity.com/paper/1610.08077/) (2016)
- [Selection Problems in the Presence of Implicit Bias](https://mlsanity.com/paper/1801.03533/) (2018)
- [Mitigating Bias in Set Selection with Noisy Protected Attributes](https://mlsanity.com/paper/2011.04219/) (2020)
- [Interventions for Ranking in the Presence of Implicit Bias](https://mlsanity.com/paper/2001.08767/) (2020)
- [On the Calibration and Uncertainty of Neural Learning to Rank Models](https://mlsanity.com/paper/2101.04356/) (2021)
- [FairSearch: A Tool For Fairness in Ranked Search Results](https://mlsanity.com/paper/1905.13134/) (2019)
- [When Fair Ranking Meets Uncertain Inference](https://mlsanity.com/paper/2105.02091/) (2021)

## Built on by (most cited first, 27 of 27)

- [Fair Ranking with Noisy Protected Attributes](https://mlsanity.com/paper/2211.17067/) (2022)
- [Calibrating Multimodal Learning](https://mlsanity.com/paper/2306.01265/) (2023)
- [Fairness through Aleatoric Uncertainty](https://mlsanity.com/paper/2304.03646/) (2023)
- [Fair Ranking as Fair Division: Impact-Based Individual Fairness in Ranking](https://mlsanity.com/paper/2206.07247/) (2022)
- [Introducing the Expohedron for Efficient Pareto-optimal Fairness-Utility Amortizations in Repeated Rankings](https://mlsanity.com/paper/2202.03237/) (2022)
- [What Is Fairness? On the Role of Protected Attributes and Fictitious Worlds](https://mlsanity.com/paper/2205.09622/) (2022)
- [Fairness in Matching under Uncertainty](https://mlsanity.com/paper/2302.03810/) (2023)
- [A Theoretical Approach to Characterize the Accuracy-Fairness Trade-off Pareto Frontier](https://mlsanity.com/paper/2310.12785/) (2023)
- [Stability and Multigroup Fairness in Ranking with Uncertain Predictions](https://mlsanity.com/paper/2402.09326/) (2024)
- [Interpolating Item and User Fairness in Multi-Sided Recommendations](https://mlsanity.com/paper/2306.10050/) (2023)
- [Assumption-free stability for ranking problems](https://mlsanity.com/paper/2506.02257/) (2025)
- [Sampling Individually-Fair Rankings that are Always Group Fair](https://mlsanity.com/paper/2306.11964/) (2023)
- [Calibrating Explore-Exploit Trade-off for Fair Online Learning to Rank](https://mlsanity.com/paper/2111.00735/) (2021)
- [Recent Advances in the Foundations and Applications of Unbiased Learning to Rank](https://mlsanity.com/paper/2305.02914/) (2023)
- [A Note on Bias to Complete](https://mlsanity.com/paper/2402.11710/) (2024)
- [Intuitions of Compromise: Utilitarianism vs. Contractualism](https://mlsanity.com/paper/2410.05496/) (2024)
- [The Hidden Cost of Waiting for Accurate Predictions](https://mlsanity.com/paper/2503.00650/) (2025)
- [Sampling Ex-Post Group-Fair Rankings](https://mlsanity.com/paper/2203.00887/) (2022)
- [Individual Fairness under Varied Notions of Group Fairness in Bipartite Matching - One Framework to Approximate Them All](https://mlsanity.com/paper/2208.09951/) (2022)
- [Learning to Re-rank with Constrained Meta-Optimal Transport](https://mlsanity.com/paper/2305.00319/) (2023)
- [Unfair Utilities and First Steps Towards Improving Them](https://mlsanity.com/paper/2306.00636/) (2023)
- [Ranking with Slot Constraints](https://mlsanity.com/paper/2310.17870/) (2023)
- [Fair Active Ranking from Pairwise Preferences](https://mlsanity.com/paper/2402.03252/) (2024)
- [(Un)certainty of (Un)fairness: Preference-Based Selection of Certainly Fair Decision-Makers](https://mlsanity.com/paper/2409.12677/) (2024)
- [Context-Aware Counterfactual Data Augmentation for Gender Bias Mitigation in Language Models](https://mlsanity.com/paper/2602.09590/) (2026)
- [Representation Curriculum: Stagewise Training for Robust Ranking and Allocation](https://mlsanity.com/paper/2606.09891/) (2026)
- [The Role of Uncertainty in Assessing the Fairness of Machine Learning Models](https://mlsanity.com/paper/2609.07959/) (2026)

## Abstract (arXiv)

Fairness has emerged as an important consideration in algorithmic decision-making. Unfairness occurs when an agent with higher merit obtains a worse outcome than an agent with lower merit. Our central point is that a primary cause of unfairness is uncertainty. A principal or algorithm making decisions never has access to the agents' true merit, and instead uses proxy features that only imperfectly predict merit (e.g., GPA, star ratings, recommendation letters). None of these ever fully capture an agent's merit; yet existing approaches have mostly been defining fairness notions directly based on observed features and outcomes. Our primary point is that it is more principled to acknowledge and model the uncertainty explicitly. The role of observed features is to give rise to a posterior distribution of the agents' merits. We use this viewpoint to define a notion of approximate fairness in ranking. We call an algorithm φ-fair (for φ ∈ [0,1]) if it has the following property for all agents x and all k: if agent x is among the top k agents with respect to merit with probability at least ρ (according to the posterior merit distribution), then the algorithm places the agent among the top k agents in its ranking with probability at least φ ρ. We show how to compute rankings that optimally trade off approximate fairness against utility to the principal. In addition to the theoretical characterization, we present an empirical analysis of the potential impact of the approach in simulation studies. For real-world validation, we applied the approach in the context of a paper recommendation system that we built and fielded at the KDD 2020 conference.