# Rational Shapley Values

arXiv: https://arxiv.org/abs/2106.10191 · HTML: https://mlsanity.com/paper/2106.10191/

## Key facts

- Cited by 18 papers in the map (data through 14 Oct 2026).
- Builds on 24 of its 51 references that are in the map.
- First posted on arXiv 18 Jun 2021.

## Builds on (most cited first, 24 of 24)

- [A Unified Approach to Interpreting Model Predictions](https://mlsanity.com/paper/1705.07874/) (2017)
- [Explanation in Artificial Intelligence: Insights from the Social Sciences](https://mlsanity.com/paper/1706.07269/) (2017)
- [Counterfactual Explanations without Opening the Black Box: Automated Decisions and the GDPR](https://mlsanity.com/paper/1711.00399/) (2017)
- [A Survey Of Methods For Explaining Black Box Models](https://mlsanity.com/paper/1802.01933/) (2018)
- [Explaining Machine Learning Classifiers through Diverse Counterfactual Explanations](https://mlsanity.com/paper/1905.07697/) (2019)
- [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)
- [The many Shapley values for model explanation](https://mlsanity.com/paper/1908.08474/) (2019)
- [Actionable Recourse in Linear Classification](https://mlsanity.com/paper/1809.06514/) (2018)
- [Interpretable machine learning: definitions, methods, and applications](https://mlsanity.com/paper/1901.04592/) (2019)
- [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)
- [Explaining individual predictions when features are dependent: More accurate approximations to Shapley values](https://mlsanity.com/paper/1903.10464/) (2019)
- [The What-If Tool: Interactive Probing of Machine Learning Models](https://mlsanity.com/paper/1907.04135/) (2019)
- [Problems with Shapley-value-based explanations as feature importance measures](https://mlsanity.com/paper/2002.11097/) (2020)
- [Feature relevance quantification in explainable AI: A causal problem](https://mlsanity.com/paper/1910.13413/) (2019)
- [Preserving Causal Constraints in Counterfactual Explanations for Machine Learning Classifiers](https://mlsanity.com/paper/1912.03277/) (2019)
- [Reliable Post hoc Explanations: Modeling Uncertainty in Explainability](https://mlsanity.com/paper/2008.05030/) (2020)
- [A survey of algorithmic recourse: definitions, formulations, solutions, and prospects](https://mlsanity.com/paper/2010.04050/) (2020)
- [Asymmetric Shapley values: incorporating causal knowledge into model-agnostic explainability](https://mlsanity.com/paper/1910.06358/) (2019)
- [Efficient Search for Diverse Coherent Explanations](https://mlsanity.com/paper/1901.04909/) (2019)
- [Causal Shapley Values: Exploiting Causal Knowledge to Explain Individual Predictions of Complex Models](https://mlsanity.com/paper/2011.01625/) (2020)
- [The age of secrecy and unfairness in recidivism prediction](https://mlsanity.com/paper/1811.00731/) (2018)
- [Local Explanations via Necessity and Sufficiency: Unifying Theory and Practice](https://mlsanity.com/paper/2103.14651/) (2021)
- [Statistical Causality from a Decision-Theoretic Perspective](https://mlsanity.com/paper/1405.2292/) (2014)

## Built on by (most cited first, 18 of 18)

- [The Inadequacy of Shapley Values for Explainability](https://mlsanity.com/paper/2302.08160/) (2023)
- [Explainability is NOT a Game](https://mlsanity.com/paper/2307.07514/) (2023)
- [Counterfactual Shapley Additive Explanations](https://mlsanity.com/paper/2110.14270/) (2021)
- [The role of causality in explainable artificial intelligence](https://mlsanity.com/paper/2309.09901/) (2023)
- [Disproving XAI Myths with Formal Methods -- Initial Results](https://mlsanity.com/paper/2306.01744/) (2023)
- [Bayesian Hierarchical Models for Counterfactual Estimation](https://mlsanity.com/paper/2301.08833/) (2023)
- [Explainability of Machine Learning Models under Missing Data](https://mlsanity.com/paper/2407.00411/) (2024)
- [A Refutation of Shapley Values for Explainability](https://mlsanity.com/paper/2309.03041/) (2023)
- [SHAP-based Explanations are Sensitive to Feature Representation](https://mlsanity.com/paper/2505.08345/) (2025)
- [Causal Dependence Plots](https://mlsanity.com/paper/2303.04209/) (2023)
- [Can Global XAI Methods Reveal Injected Behaviours in LLMs? SHAP vs Rule Extraction vs RuleSHAP](https://mlsanity.com/paper/2505.11189/) (2025)
- [Attribution Explanations for Deep Neural Networks: A Theoretical Perspective](https://mlsanity.com/paper/2508.07636/) (2025)
- [Error Analysis of Shapley Value-Based Model Explanations: An Informative Perspective](https://mlsanity.com/paper/2404.13522/) (2024)
- [Detect & Score: Privacy-Preserving Misbehaviour Detection and Contribution Evaluation in Federated Learning](https://mlsanity.com/paper/2506.23583/) (2025)
- [Explainable Machine Learning for Categorical and Mixed Data with Lossless Visualization](https://mlsanity.com/paper/2305.18437/) (2023)
- [Suboptimal Shapley Value Explanations](https://mlsanity.com/paper/2502.12209/) (2025)
- [TaylorPODA: A Taylor Expansion-Based Method to Improve Post-Hoc Attributions for Opaque Models](https://mlsanity.com/paper/2507.10643/) (2025)
- [Rigorous Feature Importance Scores based on Shapley Value and Banzhaf Index](https://mlsanity.com/paper/2508.11959/) (2025)

## Abstract (arXiv)

Explaining the predictions of opaque machine learning algorithms is an important and challenging task, especially as complex models are increasingly used to assist in high-stakes decisions such as those arising in healthcare and finance. Most popular tools for post-hoc explainable artificial intelligence (XAI) are either insensitive to context (e.g., feature attributions) or difficult to summarize (e.g., counterfactuals). In this paper, I introduce textitrational Shapley values, a novel XAI method that synthesizes and extends these seemingly incompatible approaches in a rigorous, flexible manner. I leverage tools from decision theory and causal modeling to formalize and implement a pragmatic approach that resolves a number of known challenges in XAI. By pairing the distribution of random variables with the appropriate reference class for a given explanation task, I illustrate through theory and experiments how user goals and knowledge can inform and constrain the solution set in an iterative fashion. The method compares favorably to state of the art XAI tools in a range of quantitative and qualitative comparisons.