# Characterizing Fairness Over the Set of Good Models Under Selective Labels

arXiv: https://arxiv.org/abs/2101.00352 · HTML: https://mlsanity.com/paper/2101.00352/

## Key facts

- Cited by 65 papers in the map (data through 14 Oct 2026).
- Builds on 21 of its 63 references that are in the map.
- First posted on arXiv 2 Jan 2021.

## Builds on (most cited first, 21 of 21)

- [Equality of Opportunity in Supervised Learning](https://mlsanity.com/paper/1610.02413/) (2016)
- [Certifying and removing disparate impact](https://mlsanity.com/paper/1412.3756/) (2014)
- [A Reductions Approach to Fair Classification](https://mlsanity.com/paper/1803.02453/) (2018)
- [On Fairness and Calibration](https://mlsanity.com/paper/1709.02012/) (2017)
- [Algorithmic decision making and the cost of fairness](https://mlsanity.com/paper/1701.08230/) (2017)
- [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)
- [Improving fairness in machine learning systems: What do industry practitioners need?](https://mlsanity.com/paper/1812.05239/) (2018)
- [Empirical Risk Minimization under Fairness Constraints](https://mlsanity.com/paper/1802.08626/) (2018)
- [Multiaccuracy: Black-Box Post-Processing for Fairness in Classification](https://mlsanity.com/paper/1805.12317/) (2018)
- [Doctor AI: Predicting Clinical Events via Recurrent Neural Networks](https://mlsanity.com/paper/1511.05942/) (2015)
- [Mitigating Bias in Algorithmic Hiring: Evaluating Claims and Practices](https://mlsanity.com/paper/1906.09208/) (2019)
- [Fair Regression: Quantitative Definitions and Reduction-based Algorithms](https://mlsanity.com/paper/1905.12843/) (2019)
- [Predictive Multiplicity in Classification](https://mlsanity.com/paper/1909.06677/) (2019)
- [Counterfactual Risk Assessments, Evaluation, and Fairness](https://mlsanity.com/paper/1909.00066/) (2019)
- [Two-Player Games for Efficient Non-Convex Constrained Optimization](https://mlsanity.com/paper/1804.06500/) (2018)
- [The age of secrecy and unfairness in recidivism prediction](https://mlsanity.com/paper/1811.00731/) (2018)
- [Residual Unfairness in Fair Machine Learning from Prejudiced Data](https://mlsanity.com/paper/1806.02887/) (2018)
- [Equal Opportunity in Online Classification with Partial Feedback](https://mlsanity.com/paper/1902.02242/) (2019)
- [Variable Importance Clouds: A Way to Explore Variable Importance for the Set of Good Models](https://mlsanity.com/paper/1901.03209/) (2019)
- [Fairer and more accurate, but for whom?](https://mlsanity.com/paper/1707.00046/) (2017)
- [Deep Generative Models for Reject Inference in Credit Scoring](https://mlsanity.com/paper/1904.11376/) (2019)

## Built on by (most cited first, 30 of 65)

- [Interpretable Machine Learning: Fundamental Principles and 10 Grand Challenges](https://mlsanity.com/paper/2103.11251/) (2021)
- [Amazing Things Come From Having Many Good Models](https://mlsanity.com/paper/2407.04846/) (2024)
- [Rashomon Capacity: A Metric for Predictive Multiplicity in Classification](https://mlsanity.com/paper/2206.01295/) (2022)
- [Predictive Multiplicity in Probabilistic Classification](https://mlsanity.com/paper/2206.01131/) (2022)
- [A Path to Simpler Models Starts With Noise](https://mlsanity.com/paper/2310.19726/) (2023)
- [A Validity Perspective on Evaluating the Justified Use of Data-driven Decision-making Algorithms](https://mlsanity.com/paper/2206.14983/) (2022)
- [Robust Counterfactual Explanations in Machine Learning: A Survey](https://mlsanity.com/paper/2402.01928/) (2024)
- [Characterizing the risk of fairwashing](https://mlsanity.com/paper/2106.07504/) (2021)
- [Rank List Sensitivity of Recommender Systems to Interaction Perturbations](https://mlsanity.com/paper/2201.12686/) (2022)
- [Arbitrary Decisions are a Hidden Cost of Differentially Private Training](https://mlsanity.com/paper/2302.14517/) (2023)
- [Dropout-Based Rashomon Set Exploration for Efficient Predictive Multiplicity Estimation](https://mlsanity.com/paper/2402.00728/) (2024)
- [The Dataset Multiplicity Problem: How Unreliable Data Impacts Predictions](https://mlsanity.com/paper/2304.10655/) (2023)
- [Systemizing Multiplicity: The Curious Case of Arbitrariness in Machine Learning](https://mlsanity.com/paper/2501.14959/) (2025)
- [What's the Harm? Sharp Bounds on the Fraction Negatively Affected by Treatment](https://mlsanity.com/paper/2205.10327/) (2022)
- [Recourse under Model Multiplicity via Argumentative Ensembling (Technical Report)](https://mlsanity.com/paper/2312.15097/) (2023)
- [Predictive Churn with the Set of Good Models](https://mlsanity.com/paper/2402.07745/) (2024)
- [FADE: FAir Double Ensemble Learning for Observable and Counterfactual Outcomes](https://mlsanity.com/paper/2109.00173/) (2021)
- [The Impact of Algorithmic Risk Assessments on Human Predictions and its Analysis via Crowdsourcing Studies](https://mlsanity.com/paper/2109.01443/) (2021)
- [TimberTrek: Exploring and Curating Sparse Decision Trees with Interactive Visualization](https://mlsanity.com/paper/2209.09227/) (2022)
- [Algorithmic Arbitrariness in Content Moderation](https://mlsanity.com/paper/2402.16979/) (2024)
- [Computing the Collection of Good Models for Rule Lists](https://mlsanity.com/paper/2204.11285/) (2022)
- [Multi-Target Multiplicity: Flexibility and Fairness in Target Specification under Resource Constraints](https://mlsanity.com/paper/2306.13738/) (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)
- [Equalizing Credit Opportunity in Algorithms: Aligning Algorithmic Fairness Research with U.S. Fair Lending Regulation](https://mlsanity.com/paper/2210.02516/) (2022)
- [Robust Design and Evaluation of Predictive Algorithms under Unobserved Confounding](https://mlsanity.com/paper/2212.09844/) (2022)
- [The Fragility of Fairness: Causal Sensitivity Analysis for Fair Machine Learning](https://mlsanity.com/paper/2410.09600/) (2024)
- [What Constitutes a Less Discriminatory Algorithm?](https://mlsanity.com/paper/2412.18138/) (2024)
- [Perspectives on Incorporating Expert Feedback into Model Updates](https://mlsanity.com/paper/2205.06905/) (2022)
- [Toward Operationalizing Pipeline-aware ML Fairness: A Research Agenda for Developing Practical Guidelines and Tools](https://mlsanity.com/paper/2309.17337/) (2023)

## Abstract (arXiv)

Algorithmic risk assessments are used to inform decisions in a wide variety of high-stakes settings. Often multiple predictive models deliver similar overall performance but differ markedly in their predictions for individual cases, an empirical phenomenon known as the "Rashomon Effect." These models may have different properties over various groups, and therefore have different predictive fairness properties. We develop a framework for characterizing predictive fairness properties over the set of models that deliver similar overall performance, or "the set of good models." Our framework addresses the empirically relevant challenge of selectively labelled data in the setting where the selection decision and outcome are unconfounded given the observed data features. Our framework can be used to 1) replace an existing model with one that has better fairness properties; or 2) audit for predictive bias. We illustrate these uses cases on a real-world credit-scoring task and a recidivism prediction task.