A Causal Markov Condition for Value
Olav Benjamin Vassend
stat.ML, cs.AI, cs.LG
Submitted: 2026-07-18
Comments: Accepted at UAI 2026
License: http://creativecommons.org/licenses/by/4.0/
The gist: 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"
Terminology
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.
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