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.
Figures & tables
Figure 1: Motivating example of procedural unfairness. Two applicants with nearly identical non-protected financial profiles receive the same decision (approved), yet the model assigns substantially different reasoning. The model uses income and credit history for Applicant A, but relies on zip code and debt ratio for Applicant B. Outcome-oriented fairness metrics detect no disparity, while our metric is designed to quantify such explanation disparities across protected and intersectional groups.
Dataset
Method
AUC ↑
F1 ↑
DP ↓
EOD ↓
MESD ↓
Adult Income
ERM
0.900 ± 0.004
0.652 ± 0.018
0.305 ± 0.021
0.772 ± 0.210
0.0012 ± 0.0002
RW
0.886 ± 0.004
0.573 ± 0.024
0.165 ± 0.020
0.715 ± 0.183
0.0013 ± 0.0001
RD
0.669 ± 0.009
0.501 ± 0.017
0.064 ± 0.007
0.735 ± 0.150
0.0043 ± 0.0017
ADL
0.889 ± 0.009
0.628 ± 0.016
0.245 ± 0.013
0.637 ± 0.100
0.0016 ± 0.0005
UEF
0.906 ± 0.002
0.722 ± 0.037
0.127 ± 0.069
0.526 ± 0.294
0.0006 ± 0.0005
Recidivism
ERM
0.998 ± 0.001
0.988 ± 0.002
0.260 ± 0.042
0.042 ± 0.040
0.0156 ± 0.0293
Table 1: Comparative evaluation across three datasets using 5-fold stratified cross-validation (mean ± std). ↑ higher is better, ↓ lower is better. Bold indicates best performance per metric per dataset.
Figure 2: Performance of each algorithm on each dataset
Method
Recidivism
German
Adult
Total (/15)
UEF
4
3
5
12
ADL
3
5
0
8
ERM
5
2
0
7
RW
5
2
0
7
RD
2
1
0
3
Table 2: Number of non-dominated solutions (out of 5 folds) per method and dataset.
Group
UEF
RW
RD
ADL
ERM
1,0
0.89
0.74
0.73
0.74
0.73
1,1
0.91
0.85
0.88
0.86
0.85
0,0
0.91
0.87
0.84
0.87
0.88
0,1
0.92
0.89
0.89
0.88
0.88
Table 3: Stability of each algorithm on the Recidivism dataset
Figure 3: MESD variants from each algorithm on the Recidivism Dataset
Figure 4: Effect of Empirical-Bayes Shrinkage on Stability of Recidivism
Figure 5: Baseline Perturbation
Figure 6: MESD sensitivity on Hyperparameter Choices on Adult Income Dataset
Algorithmic fairness studies how automated decisions distribute errors, opportunities, and harms across groups, and how to measure and reduce disparities.
Machine learning (ML) algorithms are increasingly deployed in high-stakes decision-making domains such as loan approvals, hiring, and recidivism predictions. While existing fairness metrics (e.g., statistical parity, equal opportunity) effectively quantify outcome-oriented disparities, they offer limited insight into the procedure or explanation behind biased decisions. To address this gap, we propose Group-level Explanation Stability Disparity (GESD), a procedural-oriented fairness metric that measures disparities in the stability, robustness, and sensitivity of model explanations across different subgroups in a protected category. %GESD is explainer-agnostic, model-agnostic, and extends the scope of fairness analyses to the level of explainability. We further integrate GESD into a multi-objective optimization framework that jointly optimizes for utility, outcome-based fairness, and explanation-based fairness called FEU (Fairness--Explainability--Utility). Empirical results on multiple benchmark datasets show that GESD effectively captures group-wise discrepancies in explanation quality, and that FEU improves both utility and fairness over state-of-the-art methods. By bridging outcome-based and explanation-based fairness, GESD offers a comprehensive tool for diagnosing and mitigating bias in predictive modeling. Our code and datasets are available on GitHub {\hyperlink{https://github.com/horlahsunbo/GESD}{https://github.com/horlahsunbo/GESD}}
Fairness in machine learning research has largely focused on outcome-oriented fairness criteria such as Equalized Odds, while comparatively less attention has been given to procedural-oriented fairness, which addresses how a model arrives at its predictions. Neglecting procedural fairness means it is possible for a model to generate different explanations for different protected groups, thereby eroding trust. In this work, we introduce Group Counterfactual Integrated Gradients (GCIG), an in-processing regularization framework that enforces explanation invariance across groups, conditioned on the true label. For each input, GCIG computes explanations relative to multiple Group Conditional baselines and penalizes cross-group variation in these attributions during training. GCIG formalizes procedural fairness as Group Counterfactual explanation stability and complements existing fairness objectives that constrain predictions alone. We compared GCIG empirically against six state-of-the-art methods, and the results show that GCIG substantially reduces cross-group explanation disparity while maintaining competitive predictive performance and accuracy-fairness trade-offs. Our results also show that aligning model reasoning across groups offers a principled and practical avenue for advancing fairness beyond outcome parity.
Gideon Popoola, John Sheppard
Gianforte School of Computing, Montana State University, Bozeman, MT, USA
Machine learning algorithms in socially sensitive domains (e.g., credit decisions) often focus on equalizing predictive outcomes. However, satisfying these metrics does not guarantee that models use the same reasoning for different groups. We show that existing outcome-fair models can still apply fundamentally different reasoning to individuals, a hidden procedural bias'' missed by standard fairness metrics and algorithms. We propose Counterfactual Explanation Consistency (CEC), a framework that detects and mitigates this bias by aligning feature attributions between individuals and their counterfactual counterparts. Key contributions include a nearest-neighbor counterfactual generation method, a modified baseline for integrated gradient comparisons, an individual-level procedural fairness metric, and a corresponding training loss. We introduce a taxonomy identifying Regime B'' (same outcome, different reasoning) as a critical blind spot. Experiments on synthetic data, German Credit, Adult Income, and HMDA mortgage data demonstrate that outcome-fair baselines exhibit substantial hidden bias, while CEC substantially reduces it with modest utility cost.
Gideon Popoola, John Sheppard
Gianforte School of Computing Montana State University Bozeman, MT, USA, 59715