# Prediction without Preclusion: Recourse Verification with Reachable Sets

arXiv: https://arxiv.org/abs/2308.12820 · HTML: https://mlsanity.com/paper/2308.12820/

## Key facts

- Cited by 4 papers in the map (data through 14 Oct 2026).
- Builds on 54 of its 98 references that are in the map.
- First posted on arXiv 24 Aug 2023.

## Builds on (most cited first, 30 of 54)

- [Counterfactual Explanations without Opening the Black Box: Automated Decisions and the GDPR](https://mlsanity.com/paper/1711.00399/) (2017)
- [Explaining Machine Learning Classifiers through Diverse Counterfactual Explanations](https://mlsanity.com/paper/1905.07697/) (2019)
- [Actionable Recourse in Linear Classification](https://mlsanity.com/paper/1809.06514/) (2018)
- [Strategic Classification](https://mlsanity.com/paper/1506.06980/) (2015)
- [Algorithmic Recourse: from Counterfactual Explanations to Interventions](https://mlsanity.com/paper/2002.06278/) (2020)
- [FACE: Feasible and Actionable Counterfactual Explanations](https://mlsanity.com/paper/1909.09369/) (2019)
- [Model-Agnostic Counterfactual Explanations for Consequential Decisions](https://mlsanity.com/paper/1905.11190/) (2019)
- [Formal Guarantees on the Robustness of a Classifier against Adversarial Manipulation](https://mlsanity.com/paper/1705.08475/) (2017)
- [Mitigating Bias in Algorithmic Hiring: Evaluating Claims and Practices](https://mlsanity.com/paper/1906.09208/) (2019)
- [Counterfactual Explanations and Algorithmic Recourses for Machine Learning: A Review](https://mlsanity.com/paper/2010.10596/) (2020)
- [Preserving Causal Constraints in Counterfactual Explanations for Machine Learning Classifiers](https://mlsanity.com/paper/1912.03277/) (2019)
- [Algorithmic recourse under imperfect causal knowledge: a probabilistic approach](https://mlsanity.com/paper/2006.06831/) (2020)
- [Towards Realistic Individual Recourse and Actionable Explanations in Black-Box Decision Making Systems](https://mlsanity.com/paper/1907.09615/) (2019)
- [Strategic Classification from Revealed Preferences](https://mlsanity.com/paper/1710.07887/) (2017)
- [A survey of algorithmic recourse: definitions, formulations, solutions, and prospects](https://mlsanity.com/paper/2010.04050/) (2020)
- [The Hidden Assumptions Behind Counterfactual Explanations and Principal Reasons](https://mlsanity.com/paper/1912.04930/) (2019)
- [Efficient Search for Diverse Coherent Explanations](https://mlsanity.com/paper/1901.04909/) (2019)
- [The Social Cost of Strategic Classification](https://mlsanity.com/paper/1808.08460/) (2018)
- [Towards Robust and Reliable Algorithmic Recourse](https://mlsanity.com/paper/2102.13620/) (2021)
- [Strategic Classification is Causal Modeling in Disguise](https://mlsanity.com/paper/1910.10362/) (2019)
- [How Do Classifiers Induce Agents To Invest Effort Strategically?](https://mlsanity.com/paper/1807.05307/) (2018)
- [Counterfactual Invariance to Spurious Correlations: Why and How to Pass Stress Tests](https://mlsanity.com/paper/2106.00545/) (2021)
- [Interpretable Predictions of Tree-based Ensembles via Actionable Feature Tweaking](https://mlsanity.com/paper/1706.06691/) (2017)
- [On the Fairness of Causal Algorithmic Recourse](https://mlsanity.com/paper/2010.06529/) (2020)
- [Strategic Classification in the Dark](https://mlsanity.com/paper/2102.11592/) (2021)
- [Causal Strategic Linear Regression](https://mlsanity.com/paper/2002.10066/) (2020)
- [Strategic Classification Made Practical](https://mlsanity.com/paper/2103.01826/) (2021)
- [On the Adversarial Robustness of Causal Algorithmic Recourse](https://mlsanity.com/paper/2112.11313/) (2021)
- [Equalizing Recourse across Groups](https://mlsanity.com/paper/1909.03166/) (2019)
- [Causally motivated Shortcut Removal Using Auxiliary Labels](https://mlsanity.com/paper/2105.06422/) (2021)

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

- [Feature Responsiveness Scores: Model-Agnostic Explanations for Recourse](https://mlsanity.com/paper/2410.22598/) (2024)
- [Understanding Fixed Predictions via Confined Regions](https://mlsanity.com/paper/2502.16380/) (2025)
- [Regretful Decisions under Label Noise](https://mlsanity.com/paper/2504.09330/) (2025)
- [Responsiveness Verification: Will Predictions Change? How Much? How Often?](https://mlsanity.com/paper/2507.02169/) (2025)

## Abstract (arXiv)

Machine learning models are often used to decide who receives a loan, a job interview, or a public benefit. Models in such settings use features without considering their actionability. As a result, they can assign predictions that are fixed - meaning that individuals who are denied loans and interviews are, in fact, precluded from access to credit and employment. In this work, we introduce a procedure called recourse verification to test if a model assigns fixed predictions to its decision subjects. We propose a model-agnostic approach for recourse verification with reachable sets - i.e., the set of all points that a person can reach through their actions in feature space. We develop methods to construct reachable sets for discrete feature spaces, which can certify the responsiveness of any model by simply querying its predictions. We conduct a comprehensive empirical study on the infeasibility of recourse on datasets from consumer finance. Our results highlight how models can inadvertently preclude access by assigning fixed predictions and underscore the need to account for actionability in model development.