# Fairness and Sparsity within Rashomon sets: Enumeration-Free Exploration and Characterization

arXiv: https://arxiv.org/abs/2502.05286 · HTML: https://mlsanity.com/paper/2502.05286/

## Key facts

- Cited by 4 papers in the map (data through 14 Oct 2026).
- Builds on 25 of its 40 references that are in the map.
- First posted on arXiv 7 Feb 2025.

## Builds on (most cited first, 25 of 25)

- [Equality of Opportunity in Supervised Learning](https://mlsanity.com/paper/1610.02413/) (2016)
- [A Survey on Bias and Fairness in Machine Learning](https://mlsanity.com/paper/1908.09635/) (2019)
- [Towards A Rigorous Science of Interpretable Machine Learning](https://mlsanity.com/paper/1702.08608/) (2017)
- [A Survey Of Methods For Explaining Black Box Models](https://mlsanity.com/paper/1802.01933/) (2018)
- [Certifying and removing disparate impact](https://mlsanity.com/paper/1412.3756/) (2014)
- [Fooling LIME and SHAP: Adversarial Attacks on Post hoc Explanation Methods](https://mlsanity.com/paper/1911.02508/) (2019)
- [All Models are Wrong, but Many are Useful: Learning a Variable's Importance by Studying an Entire Class of Prediction Models Simultaneously](https://mlsanity.com/paper/1801.01489/) (2018)
- [Interpretable Machine Learning: Fundamental Principles and 10 Grand Challenges](https://mlsanity.com/paper/2103.11251/) (2021)
- [Predictive Multiplicity in Classification](https://mlsanity.com/paper/1909.06677/) (2019)
- [Fairwashing: the risk of rationalization](https://mlsanity.com/paper/1901.09749/) (2019)
- [Exploring the Whole Rashomon Set of Sparse Decision Trees](https://mlsanity.com/paper/2209.08040/) (2022)
- [Characterizing Fairness Over the Set of Good Models Under Selective Labels](https://mlsanity.com/paper/2101.00352/) (2021)
- [Rashomon Capacity: A Metric for Predictive Multiplicity in Classification](https://mlsanity.com/paper/2206.01295/) (2022)
- [Arbitrariness and Social Prediction: The Confounding Role of Variance in Fair Classification](https://mlsanity.com/paper/2301.11562/) (2023)
- [On The Impact of Machine Learning Randomness on Group Fairness](https://mlsanity.com/paper/2307.04138/) (2023)
- [Enforcing Interpretability and its Statistical Impacts: Trade-offs between Accuracy and Interpretability](https://mlsanity.com/paper/2010.13764/) (2020)
- [A Theory of Statistical Inference for Ensuring the Robustness of Scientific Results](https://mlsanity.com/paper/1804.08646/) (2018)
- [Computing the Collection of Good Models for Rule Lists](https://mlsanity.com/paper/2204.11285/) (2022)
- [One Model Many Scores: Using Multiverse Analysis to Prevent Fairness Hacking and Evaluate the Influence of Model Design Decisions](https://mlsanity.com/paper/2308.16681/) (2023)
- [Efficient Exploration of the Rashomon Set of Rule Set Models](https://mlsanity.com/paper/2406.03059/) (2024)
- [Be Intentional About Fairness!: Fairness, Size, and Multiplicity in the Rashomon Set](https://mlsanity.com/paper/2501.15634/) (2025)
- [Optimal Kidney Exchange with Immunosuppressants](https://mlsanity.com/paper/2103.02253/) (2021)
- [Supersparse Linear Integer Models for Interpretable Classification](https://mlsanity.com/paper/1306.6677/) (2013)
- [The Legal Duty to Search for Less Discriminatory Algorithms](https://mlsanity.com/paper/2406.06817/) (2024)
- [Hiring Fairly in the Age of Algorithms](https://mlsanity.com/paper/2004.07132/) (2020)

## Built on by (most cited first, 4 of 4)

- [ElliCE: Efficient and Provably Robust Algorithmic Recourse via the Rashomon Sets](https://mlsanity.com/paper/2602.07674/) (2026)
- [The Double-Edged Nature of the Rashomon Set for Trustworthy Machine Learning](https://mlsanity.com/paper/2511.21799/) (2025)
- [When Interpretability Is Unequally Distributed: Fairness in Hybrid Interpretable Models](https://mlsanity.com/paper/2605.28626/) (2026)
- [Model Multiplicity and Predictive Arbitrariness in Recidivism Risk Assessment](https://mlsanity.com/paper/2606.02198/) (2026)

## Abstract (arXiv)

We introduce an enumeration-free method based on mathematical programming to precisely characterize various properties such as fairness or sparsity within the set of "good models", known as Rashomon set. This approach is generically applicable to any hypothesis class, provided that a mathematical formulation of the model learning task exists. It offers a structured framework to define the notion of business necessity and evaluate how fairness can be improved or degraded towards a specific protected group, while remaining within the Rashomon set and maintaining any desired sparsity level. We apply our approach to two hypothesis classes: scoring systems and decision diagrams, leveraging recent mathematical programming formulations for training such models. As seen in our experiments, the method comprehensively and certifiably quantifies trade-offs between predictive performance, sparsity, and fairness. We observe that a wide range of fairness values are attainable, ranging from highly favorable to significantly unfavorable for a protected group, while staying within less than 1% of the best possible training accuracy for the hypothesis class. Additionally, we observe that sparsity constraints limit these trade-offs and may disproportionately harm specific subgroups. As we evidenced, thoroughly characterizing the tensions between these key aspects is critical for an informed and accountable selection of models.