Complete criterion for materiality in insoluble decision problems

Develop a complete graphical criterion for materiality in insoluble decision problems—construct a criterion that determines, based solely on the scoped graph, when a context variable is material for a decision across insoluble cases, thereby matching the completeness achieved for soluble graphs.

Background

The authors extend materiality analysis beyond soluble graphs and show new obstacles to proving completeness in the insoluble setting. While they establish necessity for one condition and suggest approaches for others, they conclude that achieving a complete criterion in insoluble settings remains unresolved.

A complete criterion for materiality in insoluble graphs would enable rigorous, graph‑only evaluation of value of information, supporting stronger guarantees in AI safety, fairness, and decision‑analytic efficiency for more general multi‑decision causal structures.