🤖 AI Summary
This work formalizes the independence of utility within causal structures, establishing a systematic link between causal inference and decision theory. It introduces the value causal Markov condition (v-CMC) along with its local, global, and factorization forms, and proves their equivalence. A v-separation criterion is defined and shown to be complete. The Bellman recursion is generalized to arbitrary causal directed acyclic graphs (DAGs). Leveraging a probability–utility duality, the paper develops a comprehensive causal utility framework that enables modular representation, inference, and transfer of utilities across causal contexts. Furthermore, it proposes a structured utility heuristic and an automated method for constructing influence diagrams, offering efficient tools for decision modeling.
📝 Abstract
This paper proposes a causal independence principle for value -- the value Causal Markov Condition (v-CMC) -- and develops the conceptual and mathematical foundations of a "causal value theory" linking causality and utility. After motivating a local formulation of the v-CMC, we introduce a probability-value duality that translates standard causal-inference results into the value setting. In particular, we formulate local, global, and decomposition versions of the v-CMC and prove their equivalence. We also define v-separation and show that it is sound and complete for conditional value independence. Furthermore, we derive a Bellman-type recursion as a special case of the v-CMC, thereby generalizing standard Bellman recursion from linear chains to causal DAGs. Finally, we show how the v-CMC supports modular transfer and updating of utility information across causal contexts and develop algorithms for causally structured utility elicitation and canonical influence-diagram construction.