# Maximal Fairness

arXiv: https://arxiv.org/abs/2304.06057 · HTML: https://mlsanity.com/paper/2304.06057/

## Key facts

- Cited by 6 papers in the map (data through 14 Oct 2026).
- Builds on 7 of its 12 references that are in the map.
- First posted on arXiv 12 Apr 2023.

## Builds on (most cited first, 7 of 7)

- [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)
- [Fair prediction with disparate impact: A study of bias in recidivism prediction instruments](https://mlsanity.com/paper/1610.07524/) (2016)
- [Inherent Trade-Offs in the Fair Determination of Risk Scores](https://mlsanity.com/paper/1609.05807/) (2016)
- [Algorithmic decision making and the cost of fairness](https://mlsanity.com/paper/1701.08230/) (2017)
- [Fairness in Criminal Justice Risk Assessments: The State of the Art](https://mlsanity.com/paper/1703.09207/) (2017)
- [Towards the Right Kind of Fairness in AI](https://mlsanity.com/paper/2102.08453/) (2021)

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

- [ABCFair: an Adaptable Benchmark approach for Comparing Fairness Methods](https://mlsanity.com/paper/2409.16965/) (2024)
- [Fairness Certification for Natural Language Processing and Large Language Models](https://mlsanity.com/paper/2401.01262/) (2024)
- [Legally Binding but Unfair? Towards Assessing Fairness of Privacy Policies](https://mlsanity.com/paper/2403.08115/) (2024)
- [Mapping the Potential of Explainable AI for Fairness Along the AI Lifecycle](https://mlsanity.com/paper/2404.18736/) (2024)
- [Revisiting Technical Bias Mitigation Strategies](https://mlsanity.com/paper/2410.17433/) (2024)
- [A Critical Review of Predominant Bias in Neural Networks](https://mlsanity.com/paper/2502.11031/) (2025)

## Abstract (arXiv)

Fairness in AI has garnered quite some attention in research, and increasingly also in society. The so-called "Impossibility Theorem" has been one of the more striking research results with both theoretical and practical consequences, as it states that satisfying a certain combination of fairness measures is impossible. To date, this negative result has not yet been complemented with a positive one: a characterization of which combinations of fairness notions are possible. This work aims to fill this gap by identifying maximal sets of commonly used fairness measures that can be simultaneously satisfied. The fairness measures used are demographic parity, equal opportunity, false positive parity, predictive parity, predictive equality, overall accuracy equality and treatment equality. We conclude that in total 12 maximal sets of these fairness measures are possible, among which seven combinations of two measures, and five combinations of three measures. Our work raises interest questions regarding the practical relevance of each of these 12 maximal fairness notions in various scenarios.