# Generalized Priority-Aware Shapley Value

arXiv: https://arxiv.org/abs/2605.15018 · HTML: https://mlsanity.com/paper/2605.15018/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 18 of its 45 references that are in the map.
- First posted on arXiv 14 May 2026.

## Builds on (most cited first, 18 of 18)

- [Judging LLM-as-a-Judge with MT-Bench and Chatbot Arena](https://mlsanity.com/paper/2306.05685/) (2023)
- [A Unified Approach to Interpreting Model Predictions](https://mlsanity.com/paper/1705.07874/) (2017)
- [Efficient Memory Management for Large Language Model Serving with PagedAttention](https://mlsanity.com/paper/2309.06180/) (2023)
- [Chatbot Arena: An Open Platform for Evaluating LLMs by Human Preference](https://mlsanity.com/paper/2403.04132/) (2024)
- [Data Shapley: Equitable Valuation of Data for Machine Learning](https://mlsanity.com/paper/1904.02868/) (2019)
- [Beta Shapley: a Unified and Noise-reduced Data Valuation Framework for Machine Learning](https://mlsanity.com/paper/2110.14049/) (2021)
- [Data Banzhaf: A Robust Data Valuation Framework for Machine Learning](https://mlsanity.com/paper/2205.15466/) (2022)
- [Asymmetric Shapley values: incorporating causal knowledge into model-agnostic explainability](https://mlsanity.com/paper/1910.06358/) (2019)
- [Investigating Non-Transitivity in LLM-as-a-Judge](https://mlsanity.com/paper/2502.14074/) (2025)
- [Statistical Impossibility and Possibility of Aligning LLMs with Human Preferences: From Condorcet Paradox to Nash Equilibrium](https://mlsanity.com/paper/2503.10990/) (2025)
- [Regression-adjusted Monte Carlo Estimators for Shapley Values and Probabilistic Values](https://mlsanity.com/paper/2506.11849/) (2025)
- [One Sample Fits All: Approximating All Probabilistic Values Simultaneously and Efficiently](https://mlsanity.com/paper/2410.23808/) (2024)
- [PolySHAP: Extending KernelSHAP with Interaction-Informed Polynomial Regression](https://mlsanity.com/paper/2601.18608/) (2026)
- [An Odd Estimator for Shapley Values](https://mlsanity.com/paper/2602.01399/) (2026)
- [Belief propagation for permutations, rankings, and partial orders](https://mlsanity.com/paper/2110.00513/) (2021)
- [Rethinking Data Value: Asymmetric Data Shapley for Structure-Aware Valuation in Data Markets and Machine Learning Pipelines](https://mlsanity.com/paper/2511.12863/) (2025)
- [Priority-Aware Shapley Value](https://mlsanity.com/paper/2602.09326/) (2026)
- [First-Order Efficiency for Probabilistic Value Estimation via A Statistical Viewpoint](https://mlsanity.com/paper/2605.02827/) (2026)

## Abstract (arXiv)

Shapley value and its priority-aware extensions are widely used for valuation in machine learning, but existing methods require pairwise priority to be binary and acyclic, a restriction spectacularly violated in real-data examples such as aggregated human preferences and multi-criterion comparisons. We introduce the generalized priority-aware Shapley value (GPASV), a random order value defined on arbitrary directed weighted priority graphs, in which pairwise edges penalize rather than forbid order violations. GPASV covers a range of classical models as boundary cases. We establish GPASV through an axiomatic characterization, develop the associated computational methods, and introduce a priority sweeping diagnostic extending PASV's. We apply GPASV to LLM ensemble valuation on the cyclic Chatbot Arena preference graph, illustrating that priority-aware valuation is not a one-button operation: different balances of pairwise graph priority versus individual soft priority produce substantively different valuations of the same data.