# Gradual (In)Compatibility of Fairness Criteria

arXiv: https://arxiv.org/abs/2109.04399 · HTML: https://mlsanity.com/paper/2109.04399/

## Key facts

- Cited by 8 papers in the map (data through 14 Oct 2026).
- Builds on 18 of its 43 references that are in the map.
- First posted on arXiv 9 Sep 2021.

## Builds on (most cited first, 18 of 18)

- [Equality of Opportunity in Supervised Learning](https://mlsanity.com/paper/1610.02413/) (2016)
- [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)
- [On Fairness and Calibration](https://mlsanity.com/paper/1709.02012/) (2017)
- [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)
- [Measurement and Fairness](https://mlsanity.com/paper/1912.05511/) (2019)
- [A comparative study of fairness-enhancing interventions in machine learning](https://mlsanity.com/paper/1802.04422/) (2018)
- [Why Is My Classifier Discriminatory?](https://mlsanity.com/paper/1805.12002/) (2018)
- [Fair Mixup: Fairness via Interpolation](https://mlsanity.com/paper/2103.06503/) (2021)
- [It's COMPASlicated: The Messy Relationship between RAI Datasets and Algorithmic Fairness Benchmarks](https://mlsanity.com/paper/2106.05498/) (2021)
- [A Moral Framework for Understanding of Fair ML through Economic Models of Equality of Opportunity](https://mlsanity.com/paper/1809.03400/) (2018)
- [FNNC: Achieving Fairness through Neural Networks](https://mlsanity.com/paper/1811.00247/) (2018)
- [Emergent Unfairness in Algorithmic Fairness-Accuracy Trade-Off Research](https://mlsanity.com/paper/2102.01203/) (2021)
- [Group Fairness: Independence Revisited](https://mlsanity.com/paper/2101.02968/) (2021)
- [Fairness in Supervised Learning: An Information Theoretic Approach](https://mlsanity.com/paper/1801.04378/) (2018)
- [Fast Fair Regression via Efficient Approximations of Mutual Information](https://mlsanity.com/paper/2002.06200/) (2020)
- [Fairness criteria through the lens of directed acyclic graphical models](https://mlsanity.com/paper/1906.11333/) (2019)

## Built on by (most cited first, 8 of 8)

- [The European AI Liability Directives -- Critique of a Half-Hearted Approach and Lessons for the Future](https://mlsanity.com/paper/2211.13960/) (2022)
- [Why Fair Labels Can Yield Unfair Predictions: Graphical Conditions for Introduced Unfairness](https://mlsanity.com/paper/2202.10816/) (2022)
- [Towards Substantive Conceptions of Algorithmic Fairness: Normative Guidance from Equal Opportunity Doctrines](https://mlsanity.com/paper/2207.02912/) (2022)
- [A Unified View of Group Fairness Tradeoffs Using Partial Information Decomposition](https://mlsanity.com/paper/2406.04562/) (2024)
- [Best Practices for Responsible Machine Learning in Credit Scoring](https://mlsanity.com/paper/2409.20536/) (2024)
- [Reliability Gaps Between Groups in COMPAS Dataset](https://mlsanity.com/paper/2308.15243/) (2023)
- [A Note on Bias to Complete](https://mlsanity.com/paper/2402.11710/) (2024)
- [Unbiased Decisions Reduce Regret: Adversarial Domain Adaptation for the Bank Loan Problem](https://mlsanity.com/paper/2308.08051/) (2023)

## Abstract (arXiv)

Impossibility results show that important fairness measures (independence, separation, sufficiency) cannot be satisfied at the same time under reasonable assumptions. This paper explores whether we can satisfy and/or improve these fairness measures simultaneously to a certain degree. We introduce information-theoretic formulations of the fairness measures and define degrees of fairness based on these formulations. The information-theoretic formulations suggest unexplored theoretical relations between the three fairness measures. In the experimental part, we use the information-theoretic expressions as regularizers to obtain fairness-regularized predictors for three standard datasets. Our experiments show that a) fairness regularization directly increases fairness measures, in line with existing work, and b) some fairness regularizations indirectly increase other fairness measures, as suggested by our theoretical findings. This establishes that it is possible to increase the degree to which some fairness measures are satisfied at the same time -- some fairness measures are gradually compatible.