  In a decision problem, observations are said to be material if they must be
taken into account to perform optimally. Decision problems have an underlying
(graphical) causal structure, which may sometimes be used to evaluate certain
observations as immaterial. For soluble graphs - ones where important past
observations are remembered - there is a complete graphical criterion; one that
rules out materiality whenever this can be done on the basis of the graphical
structure alone. In this work, we analyse a proposed criterion for insoluble
graphs. In particular, we prove that some of the conditions used to prove
immateriality are necessary; when they are not satisfied, materiality is
possible. We discuss possible avenues and obstacles to proving necessity of the
remaining conditions.
