# Fairness Under Composition

arXiv: https://arxiv.org/abs/1806.06122 · HTML: https://mlsanity.com/paper/1806.06122/

## Key facts

- Cited by 43 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 15 Jun 2018.

## Built on by (most cited first, 30 of 43)

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- [Justice in Misinformation Detection Systems: An Analysis of Algorithms, Stakeholders, and Potential Harms](https://mlsanity.com/paper/2204.13568/) (2022)
- [Pareto Efficient Fairness in Supervised Learning: From Extraction to Tracing](https://mlsanity.com/paper/2104.01634/) (2021)
- [Doubly Constrained Fair Clustering](https://mlsanity.com/paper/2305.19475/) (2023)
- [Tiny, always-on and fragile: Bias propagation through design choices in on-device machine learning workflows](https://mlsanity.com/paper/2201.07677/) (2022)
- [Multi Stage Screening: Enforcing Fairness and Maximizing Efficiency in a Pre-Existing Pipeline](https://mlsanity.com/paper/2203.07513/) (2022)
- [Sequential Strategic Screening](https://mlsanity.com/paper/2301.13397/) (2023)
- [FFPDG: Fast, Fair and Private Data Generation](https://mlsanity.com/paper/2307.00161/) (2023)
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- [Precarity: Modeling the Long Term Effects of Compounded Decisions on Individual Instability](https://mlsanity.com/paper/2104.12037/) (2021)
- [Simpson's Paradox in Recommender Fairness: Reconciling differences between per-user and aggregated evaluations](https://mlsanity.com/paper/2210.07755/) (2022)
- [Achieving Fairness Across Local and Global Models in Federated Learning](https://mlsanity.com/paper/2406.17102/) (2024)
- [A Unifying Post-Processing Framework for Multi-Objective Learn-to-Defer Problems](https://mlsanity.com/paper/2407.12710/) (2024)
- [Towards Trustworthy AI-Empowered Real-Time Bidding for Online Advertisement Auctioning](https://mlsanity.com/paper/2210.07770/) (2022)
- [Striking a Balance in Fairness for Dynamic Systems Through Reinforcement Learning](https://mlsanity.com/paper/2401.06318/) (2024)
- [Long-Term Fairness Inquiries and Pursuits in Machine Learning: A Survey of Notions, Methods, and Challenges](https://mlsanity.com/paper/2406.06736/) (2024)
- [Improving Fairness with Ensemble Combination: Margin-Dependent Bounds](https://mlsanity.com/paper/2301.10813/) (2023)
- [The Equity Framework: Fairness Beyond Equalized Predictive Outcomes](https://mlsanity.com/paper/2205.01072/) (2022)

## Abstract (arXiv)

Algorithmic fairness, and in particular the fairness of scoring and classification algorithms, has become a topic of increasing social concern and has recently witnessed an explosion of research in theoretical computer science, machine learning, statistics, the social sciences, and law. Much of the literature considers the case of a single classifier (or scoring function) used once, in isolation. In this work, we initiate the study of the fairness properties of systems composed of algorithms that are fair in isolation; that is, we study fairness under composition. We identify pitfalls of naive composition and give general constructions for fair composition, demonstrating both that classifiers that are fair in isolation do not necessarily compose into fair systems and also that seemingly unfair components may be carefully combined to construct fair systems. We focus primarily on the individual fairness setting proposed in [Dwork, Hardt, Pitassi, Reingold, Zemel, 2011], but also extend our results to a large class of group fairness definitions popular in the recent literature, exhibiting several cases in which group fairness definitions give misleading signals under composition.