# A Rank Graduation metric for Algorithmic fairness

arXiv: https://arxiv.org/abs/2609.39025 · HTML: https://mlsanity.com/paper/2609.39025/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 12 of its 25 references that are in the map.
- First posted on arXiv 30 Sep 2026.

## Builds on (most cited first, 12 of 12)

- [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)
- [Counterfactual Explanations without Opening the Black Box: Automated Decisions and the GDPR](https://mlsanity.com/paper/1711.00399/) (2017)
- [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)
- [Fairness in Credit Scoring: Assessment, Implementation and Profit Implications](https://mlsanity.com/paper/2103.01907/) (2021)
- [Fairness Metrics: A Comparative Analysis](https://mlsanity.com/paper/2001.07864/) (2020)
- [The Fairness of Credit Scoring Models](https://mlsanity.com/paper/2205.10200/) (2022)
- [Properties of fairness measures in the context of varying class imbalance and protected group ratios](https://mlsanity.com/paper/2411.08425/) (2024)
- [On Rank Graduation Metrics for High Dimensional Ordinal Data](https://mlsanity.com/paper/2511.23100/) (2025)
- [A rank-based Cram'er-von-Mises-type test for two samples](https://mlsanity.com/paper/1802.06332/) (2018)

## Abstract (arXiv)

Fairness assessment in algorithmic decisions that affect individuals, such as credit scoring, often relies on parity measures calculated at the aggregate group level. Such measures may not reveal which individuals experience unfairness or which explanatory factors contribute to it. In this paper, we propose a rank-based framework that evaluates fairness through the distribution of model prediction errors, thereby linking fairness assessment with predictive accuracy and explainability. The framework combines Rank Graduation Fairness (RGF), its integrated measure AURGF, a centered Cramer--von Mises permutation test, and a feature removal procedure for fairness explainability. We evaluate the methodology using logistic regression, random forest, gradient boosting, and a multilayer perceptron. The simulation study shows that protected-group imbalance can reverse descriptive fairness comparisons, whereas the proposed inferential procedure correctly distinguishes fair from unfair mechanisms. Its application to HMDA mortgage data produces model rankings that differ from those obtained with classical fairness criteria. Tree-based models, rather than logistic regression, provide the strongest combination of predictive accuracy and rank-based fairness, while the fairness null hypothesis is rejected for all four models. The persistence of disparity across statistical, bagging, boosting, and neural network specifications, together with the feature removal results, indicates that the observed unfairness is not specific to a single algorithm or predictor, but is associated with group differences embedded in the characteristics of the lending data. These findings support a broader approach to trustworthy artificial intelligence that combines predictive accuracy, fairness measurement, statistical inference, and explainability.