Priority-Aware Shapley Value

Shapley values are widely used for model-agnostic data valuation and feature attribution, yet they implicitly assume contributors are interchangeable. This can be problematic when contributors are dependent (e.g., reused/augmented data or causal feature orderings) or when contributions should be adjusted by factors such as trust or risk. We propose Priority-Aware Shapley Value (PASV), which incorporates both hard precedence constraints and soft, contributor-specific priority weights. PASV is applicable to general precedence structures, recovers precedence-only and weight-only Shapley variants as special cases, and is uniquely characterized by natural axioms. We develop an efficient adjacent-swap Metropolis–Hastings sampler for scalable Monte Carlo estimation and analyze limiting regimes induced by extreme priority weights. Experiments on data valuation (MNIST/CIFAR10) and feature attribution (Census Income) demonstrate more structure-faithful allocations and a practical sensitivity analysis via our proposed ``priority sweeping".

How should credit be fairly split among contributors? This is a central question for data markets serving modern AI's development, where the Shapley value has become a popular tool. But existing methods typically ignore natural priorities between contributors — both hard precedence (one contributor's work builds on another's) and soft priority (some contributors tend to be more original or trustworthy than others). We introduce Priority-Aware Shapley Value (PASV), a single valuation method that handles both kinds of priority at once. Beyond producing a single allocation, PASV gives users a sensitivity diagnostic tool called priority sweeping: by systematically varying each priority assumption, they can see which assumptions actually change the answer and which ones do not. We demonstrate PASV on two real-world settings: a data marketplace where some sources copy or derive from others' training data, and a feature attribution task where domain knowledge dictates causal relations among variables. This makes credit allocation more trustworthy, protecting original contributors from being undercut by copies, and ensuring that domain knowledge shapes how AI predictions are attributed.