Ignorant Influence Diagrams

Abstract

Influence Diagrams (IDs) are a graphic formalism able to provide a compact representation of decision problems. IDs are based on the axioms of probability and decision theory, and they define a normative framework to model decision making. Unfortunately, IDs require a large amount of information that is not always available to the decision maker. This paper introduces a new class of IDs, called Ignorant Influence Diagrams (liDs), able to reason on the basis of incomplete information and to improve the accuracy of their decisions as a monotonically increasing function of the available information. liDs represent a net gain with respect to the traditional IDs, since they are able to explicitly represent lack of information, without loosing any capability of traditional IDs when the required information is available. Furthermore, liDs provide a new method to assess the reliability of the decisions by replacing the traditional sensitivity analysis with a single analytical measure.