# A Causal Markov Condition for Value

arXiv: https://arxiv.org/abs/2607.16717 · HTML: https://mlsanity.com/paper/2607.16717/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 7 of its 34 references that are in the map.
- First posted on arXiv 18 Jul 2026.

## Builds on (most cited first, 7 of 7)

- [A Survey of Inverse Reinforcement Learning: Challenges, Methods and Progress](https://mlsanity.com/paper/1806.06877/) (2018)
- [Agent Incentives: A Causal Perspective](https://mlsanity.com/paper/2102.01685/) (2021)
- [Strong Completeness and Faithfulness in Bayesian Networks](https://mlsanity.com/paper/1302.4973/) (2013)
- [Graphical Models for Preference and Utility](https://mlsanity.com/paper/1302.4928/) (2013)
- [UCP-Networks: A Directed Graphical Representation of Conditional Utilities](https://mlsanity.com/paper/1301.2259/) (2013)
- [Expected Utility Networks](https://mlsanity.com/paper/1301.6714/) (2013)
- [Directed expected utility networks](https://mlsanity.com/paper/1608.00810/) (2016)

## Abstract (arXiv)

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.