A Graph-Theoretic Analysis of Information Value

TL;DR

This paper uses graph theory to analyze how the structure of decision models influences the informational importance of variables, enabling non-numerical ordering of variables by relevance.

Contribution

It introduces a method to determine the informational relevance of variables based on influence diagram topology, without relying on numerical calculations.

Findings

Identifies dominance relations for expected information value based on diagram structure

Provides qualitative procedures for ordering variables by relevance

Enhances decision analysis with topology-based relevance assessment

Abstract

We derive qualitative relationships about the informational relevance of variables in graphical decision models based on a consideration of the topology of the models. Specifically, we identify dominance relations for the expected value of information on chance variables in terms of their position and relationships in influence diagrams. The qualitative relationships can be harnessed to generate nonnumerical procedures for ordering uncertain variables in a decision model by their informational relevance.