# Fairness in Matching under Uncertainty

arXiv: https://arxiv.org/abs/2302.03810 · HTML: https://mlsanity.com/paper/2302.03810/

## Key facts

- Cited by 5 papers in the map (data through 14 Oct 2026).
- Builds on 33 of its 71 references that are in the map.
- First posted on arXiv 8 Feb 2023.

## Builds on (most cited first, 30 of 33)

- [Equality of Opportunity in Supervised Learning](https://mlsanity.com/paper/1610.02413/) (2016)
- [Inherent Trade-Offs in the Fair Determination of Risk Scores](https://mlsanity.com/paper/1609.05807/) (2016)
- [Preventing Fairness Gerrymandering: Auditing and Learning for Subgroup Fairness](https://mlsanity.com/paper/1711.05144/) (2017)
- [Fairness of Exposure in Rankings](https://mlsanity.com/paper/1802.07281/) (2018)
- [Unbiased Learning to Rank with Unbiased Propensity Estimation](https://mlsanity.com/paper/1804.05938/) (2018)
- [Fairness Through Computationally-Bounded Awareness](https://mlsanity.com/paper/1803.03239/) (2018)
- [Learning Equilibria in Matching Markets from Bandit Feedback](https://mlsanity.com/paper/2108.08843/) (2021)
- [Supply-Side Equilibria in Recommender Systems](https://mlsanity.com/paper/2206.13489/) (2022)
- [Two-sided fairness in rankings via Lorenz dominance](https://mlsanity.com/paper/2110.15781/) (2021)
- [Interventions for Ranking in the Presence of Implicit Bias](https://mlsanity.com/paper/2001.08767/) (2020)
- [Fairness in Ranking under Uncertainty](https://mlsanity.com/paper/2107.06720/) (2021)
- [User Fairness, Item Fairness, and Diversity for Rankings in Two-Sided Markets](https://mlsanity.com/paper/2010.01470/) (2020)
- [When Fair Ranking Meets Uncertain Inference](https://mlsanity.com/paper/2105.02091/) (2021)
- [Fair ranking: a critical review, challenges, and future directions](https://mlsanity.com/paper/2201.12662/) (2022)
- [Learn to Match with No Regret: Reinforcement Learning in Markov Matching Markets](https://mlsanity.com/paper/2203.03684/) (2022)
- [Preference-Informed Fairness](https://mlsanity.com/paper/1904.01793/) (2019)
- [On Fair Selection in the Presence of Implicit Variance](https://mlsanity.com/paper/2006.13699/) (2020)
- [Optimizing generalized Gini indices for fairness in rankings](https://mlsanity.com/paper/2204.06521/) (2022)
- [Optimizing Rankings for Recommendation in Matching Markets](https://mlsanity.com/paper/2106.01941/) (2021)
- [Introducing the Expohedron for Efficient Pareto-optimal Fairness-Utility Amortizations in Repeated Rankings](https://mlsanity.com/paper/2202.03237/) (2022)
- [Individually Fair Ranking](https://mlsanity.com/paper/2103.11023/) (2021)
- [Rawlsian Fairness in Online Bipartite Matching: Two-sided, Group, and Individual](https://mlsanity.com/paper/2201.06021/) (2022)
- [Stable Matching with Uncertain Linear Preferences](https://mlsanity.com/paper/1607.02917/) (2016)
- [A Framework for Fairness in Two-Sided Marketplaces](https://mlsanity.com/paper/2006.12756/) (2020)
- [Individual Fairness in Advertising Auctions through Inverse Proportionality](https://mlsanity.com/paper/2003.13966/) (2020)
- [Two-Sided Matching Meets Fair Division](https://mlsanity.com/paper/2107.07404/) (2021)
- [On Fairness and Stability in Two-Sided Matchings](https://mlsanity.com/paper/2111.10885/) (2021)
- [Fair Division of Indivisible Goods: A Survey](https://mlsanity.com/paper/2202.07551/) (2022)
- [Fair Division with Two-Sided Preferences](https://mlsanity.com/paper/2206.05879/) (2022)
- [Bernoulli Factories and Black-Box Reductions in Mechanism Design](https://mlsanity.com/paper/1703.04143/) (2017)

## Built on by (most cited first, 5 of 5)

- [Stability and Multigroup Fairness in Ranking with Uncertain Predictions](https://mlsanity.com/paper/2402.09326/) (2024)
- [Sampling Individually-Fair Rankings that are Always Group Fair](https://mlsanity.com/paper/2306.11964/) (2023)
- [Fair and Welfare-Efficient Constrained Multi-matchings under Uncertainty](https://mlsanity.com/paper/2411.02654/) (2024)
- [Optimal Transport under Group Fairness Constraints](https://mlsanity.com/paper/2601.07144/) (2026)
- [Beyond Match Maximization and Fairness: Retention-Optimized Two-Sided Matching](https://mlsanity.com/paper/2602.15752/) (2026)

## Abstract (arXiv)

The prevalence and importance of algorithmic two-sided marketplaces has drawn attention to the issue of fairness in such settings. Algorithmic decisions are used in assigning students to schools, users to advertisers, and applicants to job interviews. These decisions should heed the preferences of individuals, and simultaneously be fair with respect to their merits (synonymous with fit, future performance, or need). Merits conditioned on observable features are always uncertain, a fact that is exacerbated by the widespread use of machine learning algorithms to infer merit from the observables. As our key contribution, we carefully axiomatize a notion of individual fairness in the two-sided marketplace setting which respects the uncertainty in the merits; indeed, it simultaneously recognizes uncertainty as the primary potential cause of unfairness and an approach to address it. We design a linear programming framework to find fair utility-maximizing distributions over allocations, and we show that the linear program is robust to perturbations in the estimated parameters of the uncertain merit distributions, a key property in combining the approach with machine learning techniques.