# Fairness Under Feature Exemptions: Counterfactual and Observational Measures

arXiv: https://arxiv.org/abs/2006.07986 · HTML: https://mlsanity.com/paper/2006.07986/

## Key facts

- Cited by 15 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 14 Jun 2020.

## Built on by (most cited first, 15 of 15)

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- [Quantifying Knowledge Distillation Using Partial Information Decomposition](https://mlsanity.com/paper/2411.07483/) (2024)
- [Bottlenecks CLUB: Unifying Information-Theoretic Trade-offs Among Complexity, Leakage, and Utility](https://mlsanity.com/paper/2207.04895/) (2022)
- [Learning Counterfactually Invariant Predictors](https://mlsanity.com/paper/2207.09768/) (2022)
- [Demystifying Local and Global Fairness Trade-offs in Federated Learning Using Partial Information Decomposition](https://mlsanity.com/paper/2307.11333/) (2023)
- [Can Querying for Bias Leak Protected Attributes? Achieving Privacy With Smooth Sensitivity](https://mlsanity.com/paper/2211.02139/) (2022)
- [Can Information Flows Suggest Targets for Interventions in Neural Circuits?](https://mlsanity.com/paper/2111.05299/) (2021)
- [Towards Formalizing Spuriousness of Biased Datasets Using Partial Information Decomposition](https://mlsanity.com/paper/2407.00482/) (2024)
- [Promises and Challenges of Causality for Ethical Machine Learning](https://mlsanity.com/paper/2201.10683/) (2022)
- [A Unified View of Group Fairness Tradeoffs Using Partial Information Decomposition](https://mlsanity.com/paper/2406.04562/) (2024)
- [Quantifying Feature Contributions to Overall Disparity Using Information Theory](https://mlsanity.com/paper/2206.08454/) (2022)
- [Mutatis Mutandis: Revisiting the Comparator in Discrimination Testing](https://mlsanity.com/paper/2405.13693/) (2024)
- [REFRESH: Responsible and Efficient Feature Reselection Guided by SHAP Values](https://mlsanity.com/paper/2403.08880/) (2024)
- [Learning Invariant Graph Representations Through Redundant Information](https://mlsanity.com/paper/2512.06154/) (2025)
- [Interpreting Reasoning of Large Language Models via Partial Information Decomposition](https://mlsanity.com/paper/2610.00571/) (2026)

## Abstract (arXiv)

With the growing use of ML in highly consequential domains, quantifying disparity with respect to protected attributes, e.g., gender, race, etc., is important. While quantifying disparity is essential, sometimes the needs of an occupation may require the use of certain features that are critical in a way that any disparity that can be explained by them might need to be exempted. E.g., in hiring a software engineer for a safety-critical application, coding-skills may be weighed strongly, whereas name, zip code, or reference letters may be used only to the extent that they do not add disparity. In this work, we propose an information-theoretic decomposition of the total disparity (a quantification inspired from counterfactual fairness) into two components: a non-exempt component which quantifies the part that cannot be accounted for by the critical features, and an exempt component that quantifies the remaining disparity. This decomposition allows one to check if the disparity arose purely due to the critical features (inspired from the business necessity defense of disparate impact law) and also enables selective removal of the non-exempt component if desired. We arrive at this decomposition through canonical examples that lead to a set of desirable properties (axioms) that a measure of non-exempt disparity should satisfy. Our proposed measure satisfies all of them. Our quantification bridges ideas of causality, Simpson's paradox, and a body of work from information theory called Partial Information Decomposition. We also obtain an impossibility result showing that no observational measure can satisfy all the desirable properties, leading us to relax our goals and examine observational measures that satisfy only some of them. We perform case studies to show how one can audit/train models while reducing non-exempt disparity.