# On the (In)Compatibility between Group Fairness and Individual Fairness

arXiv: https://arxiv.org/abs/2401.07174 · HTML: https://mlsanity.com/paper/2401.07174/

## Key facts

- Cited by 6 papers in the map (data through 14 Oct 2026).
- Builds on 12 of its 36 references that are in the map.
- First posted on arXiv 13 Jan 2024.

## Builds on (most cited first, 12 of 12)

- [Equality of Opportunity in Supervised Learning](https://mlsanity.com/paper/1610.02413/) (2016)
- [Preventing Fairness Gerrymandering: Auditing and Learning for Subgroup Fairness](https://mlsanity.com/paper/1711.05144/) (2017)
- [Fairness Beyond Disparate Treatment & Disparate Impact: Learning Classification without Disparate Mistreatment](https://mlsanity.com/paper/1610.08452/) (2016)
- [Fairness in Learning: Classic and Contextual Bandits](https://mlsanity.com/paper/1605.07139/) (2016)
- [A Convex Framework for Fair Regression](https://mlsanity.com/paper/1706.02409/) (2017)
- [Inherent Tradeoffs in Learning Fair Representations](https://mlsanity.com/paper/1906.08386/) (2019)
- [The Frontiers of Fairness in Machine Learning](https://mlsanity.com/paper/1810.08810/) (2018)
- [Wasserstein Fair Classification](https://mlsanity.com/paper/1907.12059/) (2019)
- [On the Apparent Conflict Between Individual and Group Fairness](https://mlsanity.com/paper/1912.06883/) (2019)
- [Minimum Width for Universal Approximation](https://mlsanity.com/paper/2006.08859/) (2020)
- [Bias Mitigation Post-processing for Individual and Group Fairness](https://mlsanity.com/paper/1812.06135/) (2018)
- [Fair Data Representation for Machine Learning at the Pareto Frontier](https://mlsanity.com/paper/2201.00292/) (2022)

## Built on by (most cited first, 6 of 6)

- [What is Fair? Defining Fairness in Machine Learning for Health](https://mlsanity.com/paper/2406.09307/) (2024)
- [Counterfactual Fairness Evaluation of Machine Learning Models on Educational Datasets](https://mlsanity.com/paper/2504.11504/) (2025)
- [Fair Recourse for All: Ensuring Individual and Group Fairness in Counterfactual Explanations](https://mlsanity.com/paper/2601.20449/) (2026)
- [Analyzing Fairness of Computer Vision and Natural Language Processing Models](https://mlsanity.com/paper/2412.09900/) (2024)
- [Trade-offs Between Individual and Group Fairness in Machine Learning: A Comprehensive Review](https://mlsanity.com/paper/2602.00094/) (2026)
- [Fairness in multi-class multi-group classification problems via contextial coherent risk measures](https://mlsanity.com/paper/2608.30223/) (2026)

## Abstract (arXiv)

We study the compatibility between the optimal statistical parity solutions and individual fairness. While individual fairness seeks to treat similar individuals similarly, optimal statistical parity aims to provide similar treatment to individuals who share relative similarity within their respective sensitive groups. The two fairness perspectives, while both desirable from a fairness perspective, often come into conflict in applications. Our goal in this work is to analyze the existence of this conflict and its potential solution. In particular, we establish sufficient (sharp) conditions for the compatibility between the optimal (post-processing) statistical parity L2 learning and the (K-Lipschitz or (ε,δ)) individual fairness requirements. Furthermore, when there exists a conflict between the two, we first relax the former to the Pareto frontier (or equivalently the optimal trade-off) between L2 error and statistical disparity, and then analyze the compatibility between the frontier and the individual fairness requirements. Our analysis identifies regions along the Pareto frontier that satisfy individual fairness requirements. (Lastly, we provide individual fairness guarantees for the composition of a trained model and the optimal post-processing step so that one can determine the compatibility of the post-processed model.) This provides practitioners with a valuable approach to attain Pareto optimality for statistical parity while adhering to the constraints of individual fairness.