# Decisions, Counterfactual Explanations and Strategic Behavior

arXiv: https://arxiv.org/abs/2002.04333 · HTML: https://mlsanity.com/paper/2002.04333/

## Key facts

- Cited by 44 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 11 Feb 2020.

## Built on by (most cited first, 30 of 44)

- [Counterfactual Explanations Can Be Manipulated](https://mlsanity.com/paper/2106.02666/) (2021)
- [Outside the Echo Chamber: Optimizing the Performative Risk](https://mlsanity.com/paper/2102.08570/) (2021)
- [Information Discrepancy in Strategic Learning](https://mlsanity.com/paper/2103.01028/) (2021)
- [Alternative Microfoundations for Strategic Classification](https://mlsanity.com/paper/2106.12705/) (2021)
- [Counterfactual Explanations in Sequential Decision Making Under Uncertainty](https://mlsanity.com/paper/2107.02776/) (2021)
- [Anticipating Performativity by Predicting from Predictions](https://mlsanity.com/paper/2208.07331/) (2022)
- [Causal Strategic Classification: A Tale of Two Shifts](https://mlsanity.com/paper/2302.06280/) (2023)
- [Counterfactual Explanations for Arbitrary Regression Models](https://mlsanity.com/paper/2106.15212/) (2021)
- [Learning Losses for Strategic Classification](https://mlsanity.com/paper/2203.13421/) (2022)
- [Improvement-Focused Causal Recourse (ICR)](https://mlsanity.com/paper/2210.15709/) (2022)
- [Improving Screening Processes via Calibrated Subset Selection](https://mlsanity.com/paper/2202.01147/) (2022)
- [Directive Explanations for Actionable Explainability in Machine Learning Applications](https://mlsanity.com/paper/2102.02671/) (2021)
- [Bayesian Persuasion for Algorithmic Recourse](https://mlsanity.com/paper/2112.06283/) (2021)
- [A Review of the Role of Causality in Developing Trustworthy AI Systems](https://mlsanity.com/paper/2302.06975/) (2023)
- [Finding Counterfactually Optimal Action Sequences in Continuous State Spaces](https://mlsanity.com/paper/2306.03929/) (2023)
- [Achieving Diversity in Counterfactual Explanations: a Review and Discussion](https://mlsanity.com/paper/2305.05840/) (2023)
- [Can LLMs Explain Themselves Counterfactually?](https://mlsanity.com/paper/2502.18156/) (2025)
- [Personalized Algorithmic Recourse with Preference Elicitation](https://mlsanity.com/paper/2205.13743/) (2022)
- [GAM Coach: Towards Interactive and User-centered Algorithmic Recourse](https://mlsanity.com/paper/2302.14165/) (2023)
- [Synthesizing explainable counterfactual policies for algorithmic recourse with program synthesis](https://mlsanity.com/paper/2201.07135/) (2022)
- [Optimizing the Performative Risk under Weak Convexity Assumptions](https://mlsanity.com/paper/2209.00771/) (2022)
- [Incentive-Aware Machine Learning; Robustness, Fairness, Improvement & Causality](https://mlsanity.com/paper/2505.05211/) (2025)
- [Should Decision-Makers Reveal Classifiers in Online Strategic Classification?](https://mlsanity.com/paper/2506.01936/) (2025)
- [Beyond Fairness Metrics: Roadblocks and Challenges for Ethical AI in Practice](https://mlsanity.com/paper/2108.06217/) (2021)
- [On the Current and Emerging Challenges of Developing Fair and Ethical AI Solutions in Financial Services](https://mlsanity.com/paper/2111.01306/) (2021)
- [Margin-distancing for safe model explanation](https://mlsanity.com/paper/2202.11266/) (2022)
- [Causal Modeling of Policy Interventions From Sequences of Treatments and Outcomes](https://mlsanity.com/paper/2209.04142/) (2022)
- [Towards Regulatable AI Systems: Technical Gaps and Policy Opportunities](https://mlsanity.com/paper/2306.12609/) (2023)
- [Flexible Counterfactual Explanations with Generative Models](https://mlsanity.com/paper/2502.17613/) (2025)
- [DiCoFlex: Model-agnostic diverse counterfactuals with flexible control](https://mlsanity.com/paper/2505.23700/) (2025)

## Abstract (arXiv)

As data-driven predictive models are increasingly used to inform decisions, it has been argued that decision makers should provide explanations that help individuals understand what would have to change for these decisions to be beneficial ones. However, there has been little discussion on the possibility that individuals may use the above counterfactual explanations to invest effort strategically and maximize their chances of receiving a beneficial decision. In this paper, our goal is to find policies and counterfactual explanations that are optimal in terms of utility in such a strategic setting. We first show that, given a pre-defined policy, the problem of finding the optimal set of counterfactual explanations is NP-hard. Then, we show that the corresponding objective is nondecreasing and satisfies submodularity and this allows a standard greedy algorithm to enjoy approximation guarantees. In addition, we further show that the problem of jointly finding both the optimal policy and set of counterfactual explanations reduces to maximizing a non-monotone submodular function. As a result, we can use a recent randomized algorithm to solve the problem, which also offers approximation guarantees. Finally, we demonstrate that, by incorporating a matroid constraint into the problem formulation, we can increase the diversity of the optimal set of counterfactual explanations and incentivize individuals across the whole spectrum of the population to self improve. Experiments on synthetic and real lending and credit card data illustrate our theoretical findings and show that the counterfactual explanations and decision policies found by our algorithms achieve higher utility than several competitive baselines.