Completeness of Lee–Bareinboim (2020, Thm. 2) immateriality criterion for insoluble graphs

Determine whether Theorem 2 of Lee and Bareinboim (2020), which provides a criterion for identifying immaterial decisions in insoluble multi‑decision scoped graphs, is complete—specifically, ascertain whether the criterion can establish immateriality in every case where immateriality is derivable solely from the scoped graph’s structure.

Background

The paper studies graphical criteria for determining when an observation (context) is material for a decision within a causal decision problem. For soluble graphs, a complete criterion exists; for insoluble graphs, Lee and Bareinboim (2020, Thm. 2) propose a more potent criterion that can identify immaterial decisions. However, the authors note that it is currently unresolved whether this criterion is complete—i.e., whether it can capture all cases of immateriality inferable from the graph.

Establishing completeness would require proving that the criterion’s assumptions are not only sufficient but also necessary. This would strengthen the theoretical foundations for value‑of‑information analysis in insoluble decision problems and broaden the applicability of safety, fairness, and efficiency analyses discussed in the paper.