# A Refutation of Shapley Values for Explainability

arXiv: https://arxiv.org/abs/2309.03041 · HTML: https://mlsanity.com/paper/2309.03041/

## Key facts

- Cited by 4 papers in the map (data through 14 Oct 2026).
- Builds on 28 of its 81 references that are in the map.
- First posted on arXiv 6 Sep 2023.

## Builds on (most cited first, 28 of 28)

- [A Unified Approach to Interpreting Model Predictions](https://mlsanity.com/paper/1705.07874/) (2017)
- ["Why Should I Trust You?": Explaining the Predictions of Any Classifier](https://mlsanity.com/paper/1602.04938/) (2016)
- [Explanation in Artificial Intelligence: Insights from the Social Sciences](https://mlsanity.com/paper/1706.07269/) (2017)
- [The many Shapley values for model explanation](https://mlsanity.com/paper/1908.08474/) (2019)
- [Problems with Shapley-value-based explanations as feature importance measures](https://mlsanity.com/paper/2002.11097/) (2020)
- [Abduction-Based Explanations for Machine Learning Models](https://mlsanity.com/paper/1811.10656/) (2018)
- [Improving KernelSHAP: Practical Shapley Value Estimation via Linear Regression](https://mlsanity.com/paper/2012.01536/) (2020)
- [A Symbolic Approach to Explaining Bayesian Network Classifiers](https://mlsanity.com/paper/1805.03364/) (2018)
- [Reliable Post hoc Explanations: Modeling Uncertainty in Explainability](https://mlsanity.com/paper/2008.05030/) (2020)
- [FastSHAP: Real-Time Shapley Value Estimation](https://mlsanity.com/paper/2107.07436/) (2021)
- [Asymmetric Shapley values: incorporating causal knowledge into model-agnostic explainability](https://mlsanity.com/paper/1910.06358/) (2019)
- [L-Shapley and C-Shapley: Efficient Model Interpretation for Structured Data](https://mlsanity.com/paper/1808.02610/) (2018)
- [On the Tractability of SHAP Explanations](https://mlsanity.com/paper/2009.08634/) (2020)
- [Shapley explainability on the data manifold](https://mlsanity.com/paper/2006.01272/) (2020)
- [Towards Unifying Feature Attribution and Counterfactual Explanations: Different Means to the Same End](https://mlsanity.com/paper/2011.04917/) (2020)
- [Shapley values for feature selection: The good, the bad, and the axioms](https://mlsanity.com/paper/2102.10936/) (2021)
- [Logic-Based Explainability in Machine Learning](https://mlsanity.com/paper/2211.00541/) (2022)
- [Local Explanations via Necessity and Sufficiency: Unifying Theory and Practice](https://mlsanity.com/paper/2103.14651/) (2021)
- [On Efficiently Explaining Graph-Based Classifiers](https://mlsanity.com/paper/2106.01350/) (2021)
- [On the Complexity of SHAP-Score-Based Explanations: Tractability via Knowledge Compilation and Non-Approximability Results](https://mlsanity.com/paper/2104.08015/) (2021)
- [The Inadequacy of Shapley Values for Explainability](https://mlsanity.com/paper/2302.08160/) (2023)
- [Feature Necessity & Relevancy in ML Classifier Explanations](https://mlsanity.com/paper/2210.15675/) (2022)
- [Explainability is NOT a Game](https://mlsanity.com/paper/2307.07514/) (2023)
- [Counterfactual Shapley Additive Explanations](https://mlsanity.com/paper/2110.14270/) (2021)
- [Rational Shapley Values](https://mlsanity.com/paper/2106.10191/) (2021)
- [XOmiVAE: an interpretable deep learning model for cancer classification using high-dimensional omics data](https://mlsanity.com/paper/2105.12807/) (2021)
- [Towards Rigorous Interpretations: a Formalisation of Feature Attribution](https://mlsanity.com/paper/2104.12437/) (2021)
- [Exact Shapley Values for Local and Model-True Explanations of Decision Tree Ensembles](https://mlsanity.com/paper/2112.10592/) (2021)

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

- [Refutation of Shapley Values for XAI -- Additional Evidence](https://mlsanity.com/paper/2310.00416/) (2023)
- [Logic-Based Explainability: Past, Present & Future](https://mlsanity.com/paper/2406.11873/) (2024)
- [Binary Spiking Neural Networks as Causal Models](https://mlsanity.com/paper/2604.27007/) (2026)
- [Towards Rigorous Explainability by Feature Attribution](https://mlsanity.com/paper/2604.15898/) (2026)

## Abstract (arXiv)

Recent work demonstrated the existence of Boolean functions for which Shapley values provide misleading information about the relative importance of features in rule-based explanations. Such misleading information was broadly categorized into a number of possible issues. Each of those issues relates with features being relevant or irrelevant for a prediction, and all are significant regarding the inadequacy of Shapley values for rule-based explainability. This earlier work devised a brute-force approach to identify Boolean functions, defined on small numbers of features, and also associated instances, which displayed such inadequacy-revealing issues, and so served as evidence to the inadequacy of Shapley values for rule-based explainability. However, an outstanding question is how frequently such inadequacy-revealing issues can occur for Boolean functions with arbitrary large numbers of features. It is plain that a brute-force approach would be unlikely to provide insights on how to tackle this question. This paper answers the above question by proving that, for any number of features, there exist Boolean functions that exhibit one or more inadequacy-revealing issues, thereby contributing decisive arguments against the use of Shapley values as the theoretical underpinning of feature-attribution methods in explainability.