# A Complete Criterion for Value of Information in Soluble Influence Diagrams

arXiv: https://arxiv.org/abs/2202.11629 · HTML: https://mlsanity.com/paper/2202.11629/

## Key facts

- Cited by 5 papers in the map (data through 14 Oct 2026).
- Builds on 16 of its 45 references that are in the map.
- First posted on arXiv 23 Feb 2022.

## Builds on (most cited first, 16 of 16)

- [Counterfactual Fairness](https://mlsanity.com/paper/1703.06856/) (2017)
- [Cooperative Inverse Reinforcement Learning](https://mlsanity.com/paper/1606.03137/) (2016)
- [Reward Tampering Problems and Solutions in Reinforcement Learning: A Causal Influence Diagram Perspective](https://mlsanity.com/paper/1908.04734/) (2019)
- [Causal Networks: Semantics and Expressiveness](https://mlsanity.com/paper/1304.2379/) (2013)
- [Agent Incentives: A Causal Perspective](https://mlsanity.com/paper/2102.01685/) (2021)
- [User Tampering in Reinforcement Learning Recommender Systems](https://mlsanity.com/paper/2109.04083/) (2021)
- [Should Robots be Obedient?](https://mlsanity.com/paper/1705.09990/) (2017)
- [Bayes-Ball: The Rational Pastime (for Determining Irrelevance and Requisite Information in Belief Networks and Influence Diagrams)](https://mlsanity.com/paper/1301.7412/) (2013)
- [How RL Agents Behave When Their Actions Are Modified](https://mlsanity.com/paper/2102.07716/) (2021)
- [Why Fair Labels Can Yield Unfair Predictions: Graphical Conditions for Introduced Unfairness](https://mlsanity.com/paper/2202.10816/) (2022)
- [Equilibrium Refinements for Multi-Agent Influence Diagrams: Theory and Practice](https://mlsanity.com/paper/2102.05008/) (2021)
- [Modeling AGI Safety Frameworks with Causal Influence Diagrams](https://mlsanity.com/paper/1906.08663/) (2019)
- [AGI Agent Safety by Iteratively Improving the Utility Function](https://mlsanity.com/paper/2007.05411/) (2020)
- [Asymptotically Unambitious Artificial General Intelligence](https://mlsanity.com/paper/1905.12186/) (2019)
- [Evaluating Influence Diagrams using LIMIDs](https://mlsanity.com/paper/1301.3881/) (2013)
- [Welldefined Decision Scenarios](https://mlsanity.com/paper/1301.6729/) (2013)

## Built on by (most cited first, 5 of 5)

- [Towards Guaranteed Safe AI: A Framework for Ensuring Robust and Reliable AI Systems](https://mlsanity.com/paper/2405.06624/) (2024)
- [The Reasons that Agents Act: Intention and Instrumental Goals](https://mlsanity.com/paper/2402.07221/) (2024)
- [On Imperfect Recall in Multi-Agent Influence Diagrams](https://mlsanity.com/paper/2307.05059/) (2023)
- [Unfair Utilities and First Steps Towards Improving Them](https://mlsanity.com/paper/2306.00636/) (2023)
- [The Design and Composition of Structural Causal Decision Processes](https://mlsanity.com/paper/2605.02681/) (2026)

## Abstract (arXiv)

Influence diagrams have recently been used to analyse the safety and fairness properties of AI systems. A key building block for this analysis is a graphical criterion for value of information (VoI). This paper establishes the first complete graphical criterion for VoI in influence diagrams with multiple decisions. Along the way, we establish two important techniques for proving properties of multi-decision influence diagrams: ID homomorphisms are structure-preserving transformations of influence diagrams, while a Tree of Systems is collection of paths that captures how information and control can flow in an influence diagram.