# MESD: A Risk-Sensitive Metric for Explanation Fairness Across Intersectional Subgroups

arXiv: https://arxiv.org/abs/2603.13452 · HTML: https://mlsanity.com/paper/2603.13452/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 17 of its 45 references that are in the map.
- First posted on arXiv 13 Mar 2026.

## Builds on (most cited first, 17 of 17)

- [A Unified Approach to Interpreting Model Predictions](https://mlsanity.com/paper/1705.07874/) (2017)
- ["Why Should I Trust You?": Explaining the Predictions of Any Classifier](https://mlsanity.com/paper/1602.04938/) (2016)
- [Equality of Opportunity in Supervised Learning](https://mlsanity.com/paper/1610.02413/) (2016)
- [Mitigating Unwanted Biases with Adversarial Learning](https://mlsanity.com/paper/1801.07593/) (2018)
- [Fooling LIME and SHAP: Adversarial Attacks on Post hoc Explanation Methods](https://mlsanity.com/paper/1911.02508/) (2019)
- [Preventing Fairness Gerrymandering: Auditing and Learning for Subgroup Fairness](https://mlsanity.com/paper/1711.05144/) (2017)
- [Evaluating and Aggregating Feature-based Model Explanations](https://mlsanity.com/paper/2005.00631/) (2020)
- [Fairness in Machine Learning: Lessons from Political Philosophy](https://mlsanity.com/paper/1712.03586/) (2017)
- [Identifying and Correcting Label Bias in Machine Learning](https://mlsanity.com/paper/1901.04966/) (2019)
- [FastSHAP: Real-Time Shapley Value Estimation](https://mlsanity.com/paper/2107.07436/) (2021)
- [In Pursuit of Interpretable, Fair and Accurate Machine Learning for Criminal Recidivism Prediction](https://mlsanity.com/paper/2005.04176/) (2020)
- [The Road to Explainability is Paved with Bias: Measuring the Fairness of Explanations](https://mlsanity.com/paper/2205.03295/) (2022)
- [Explainability for fair machine learning](https://mlsanity.com/paper/2010.07389/) (2020)
- [On the Moral Justification of Statistical Parity](https://mlsanity.com/paper/2011.02079/) (2020)
- [Fairness and Explainability: Bridging the Gap Towards Fair Model Explanations](https://mlsanity.com/paper/2212.03840/) (2022)
- [The Intersectionality Problem for Algorithmic Fairness](https://mlsanity.com/paper/2411.02569/) (2024)
- [What's Distributive Justice Got to Do with It? Rethinking Algorithmic Fairness from the Perspective of Approximate Justice](https://mlsanity.com/paper/2407.12488/) (2024)

## Built on by (most cited first, 1 of 1)

- [Fairness of Explanations in Artificial Intelligence (AI): A Unifying Framework, Axioms, and Future Direction toward Responsible AI](https://mlsanity.com/paper/2605.09852/) (2026)

## Abstract (arXiv)

Fairness in machine learning is predominantly evaluated through outcome-oriented metrics, such as Demographic parity, which measure whether predictions are statistically consistent across protected groups. However, these metrics cannot detect whether a model uses systematically different reasoning for different demographic groups, which violates procedural fairness principles. This problem is compounded by intersectionality, where models may appear fair on individual attributes (e.g., race) while exhibiting significant disparities for intersectional subgroups (e.g., race × gender), a phenomenon known as fairness gerrymandering. In this work, we introduce Multi-category Explanation Stability Disparity (MESD), a procedural fairness metric that quantifies disparities in explanation quality across intersectional subgroups formed by the Cartesian product of multiple protected attributes. MESD integrates three components, which are label-aware aggregation aligned with outcome-conditional fairness, empirical-Bayes shrinkage to stabilize estimates for small intersectional groups, and Conditional Value-at-Risk (CVaR) weighting to emphasize worst-case subgroup disparities. We integrate MESD within a multi-objective optimization framework (UEF) that jointly optimizes utility, outcome fairness, and procedural fairness using NSGA-II. We evaluated MESD and UEF on three benchmark datasets along with four state-of-the-art methods in several experiments, and we demonstrate that MESD reveals procedural disparities invisible to outcome metrics alone. We position our contribution within procedural justice theory and discuss implications for regulatory compliance and intersectional equity.