# On Counterfactual Explanations under Predictive Multiplicity

arXiv: https://arxiv.org/abs/2006.13132 · HTML: https://mlsanity.com/paper/2006.13132/

## Key facts

- Cited by 74 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 23 Jun 2020.

## Built on by (most cited first, 30 of 74)

- [Deep Neural Networks and Tabular Data: A Survey](https://mlsanity.com/paper/2110.01889/) (2021)
- [Counterfactual Explanations Can Be Manipulated](https://mlsanity.com/paper/2106.02666/) (2021)
- [Towards Robust and Reliable Algorithmic Recourse](https://mlsanity.com/paper/2102.13620/) (2021)
- [CARLA: A Python Library to Benchmark Algorithmic Recourse and Counterfactual Explanation Algorithms](https://mlsanity.com/paper/2108.00783/) (2021)
- [If Only We Had Better Counterfactual Explanations: Five Key Deficits to Rectify in the Evaluation of Counterfactual XAI Techniques](https://mlsanity.com/paper/2103.01035/) (2021)
- [NICE: An Algorithm for Nearest Instance Counterfactual Explanations](https://mlsanity.com/paper/2104.07411/) (2021)
- [Counterfactuals and Causability in Explainable Artificial Intelligence: Theory, Algorithms, and Applications](https://mlsanity.com/paper/2103.04244/) (2021)
- [On the Adversarial Robustness of Causal Algorithmic Recourse](https://mlsanity.com/paper/2112.11313/) (2021)
- [Directional Bias Amplification](https://mlsanity.com/paper/2102.12594/) (2021)
- [Exploring Counterfactual Explanations Through the Lens of Adversarial Examples: A Theoretical and Empirical Analysis](https://mlsanity.com/paper/2106.09992/) (2021)
- [Robust Counterfactual Explanations for Tree-Based Ensembles](https://mlsanity.com/paper/2207.02739/) (2022)
- [Rashomon Capacity: A Metric for Predictive Multiplicity in Classification](https://mlsanity.com/paper/2206.01295/) (2022)
- [Robust Counterfactual Explanations for Neural Networks With Probabilistic Guarantees](https://mlsanity.com/paper/2305.11997/) (2023)
- [Predictive Multiplicity in Probabilistic Classification](https://mlsanity.com/paper/2206.01131/) (2022)
- [Fast Diffusion-Based Counterfactuals for Shortcut Removal and Generation](https://mlsanity.com/paper/2312.14223/) (2023)
- [Probabilistically Robust Recourse: Navigating the Trade-offs between Costs and Robustness in Algorithmic Recourse](https://mlsanity.com/paper/2203.06768/) (2022)
- [Consistent Counterfactuals for Deep Models](https://mlsanity.com/paper/2110.03109/) (2021)
- [A Path to Simpler Models Starts With Noise](https://mlsanity.com/paper/2310.19726/) (2023)
- [On the Robustness of Sparse Counterfactual Explanations to Adverse Perturbations](https://mlsanity.com/paper/2201.09051/) (2022)
- [Robust Counterfactual Explanations in Machine Learning: A Survey](https://mlsanity.com/paper/2402.01928/) (2024)
- [Counterfactual Explanations for Arbitrary Regression Models](https://mlsanity.com/paper/2106.15212/) (2021)
- [Rank List Sensitivity of Recommender Systems to Interaction Perturbations](https://mlsanity.com/paper/2201.12686/) (2022)
- [On the Trade-Off between Actionable Explanations and the Right to be Forgotten](https://mlsanity.com/paper/2208.14137/) (2022)
- [The privacy issue of counterfactual explanations: explanation linkage attacks](https://mlsanity.com/paper/2210.12051/) (2022)
- [Improvement-Focused Causal Recourse (ICR)](https://mlsanity.com/paper/2210.15709/) (2022)
- [Provably Robust and Plausible Counterfactual Explanations for Neural Networks via Robust Optimisation](https://mlsanity.com/paper/2309.12545/) (2023)
- [Diverse, Global and Amortised Counterfactual Explanations for Uncertainty Estimates](https://mlsanity.com/paper/2112.02646/) (2021)
- [Counterfactual Plans under Distributional Ambiguity](https://mlsanity.com/paper/2201.12487/) (2022)
- [Loss-Aversively Fair Classification](https://mlsanity.com/paper/2105.04273/) (2021)
- [Robust Bayesian Recourse](https://mlsanity.com/paper/2206.10833/) (2022)

## Abstract (arXiv)

Counterfactual explanations are usually obtained by identifying the smallest change made to an input to change a prediction made by a fixed model (hereafter called sparse methods). Recent work, however, has revitalized an old insight: there often does not exist one superior solution to a prediction problem with respect to commonly used measures of interest (e.g. error rate). In fact, often multiple different classifiers give almost equal solutions. This phenomenon is known as predictive multiplicity (Breiman, 2001; Marx et al., 2019). In this work, we derive a general upper bound for the costs of counterfactual explanations under predictive multiplicity. Most notably, it depends on a discrepancy notion between two classifiers, which describes how differently they treat negatively predicted individuals. We then compare sparse and data support approaches empirically on real-world data. The results show that data support methods are more robust to multiplicity of different models. At the same time, we show that those methods have provably higher cost of generating counterfactual explanations under one fixed model. In summary, our theoretical and empiricaln results challenge the commonly held view that counterfactual recommendations should be sparse in general.