Toward a Complete Criterion for Value of Information in Insoluble Decision Problems

TL;DR

This paper investigates criteria for determining the materiality of observations in decision problems with complex causal structures, aiming to establish a complete graphical criterion for insoluble graphs.

Contribution

It analyzes a proposed criterion for insoluble graphs, proving some conditions are necessary for immateriality and discussing challenges in establishing a complete criterion.

Findings

Some conditions for immateriality are proven necessary.

Materiality can occur when certain conditions are not met.

Discussion of future directions for complete criteria.

Abstract

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.