Handbook of Decision Analysis

Appendix B

Influence Diagrams

STEVEN N. TANI and GREGORY S. PARNELL

B.1 Introduction

B.2 Influence Diagram Elements

B.3 Influence Diagram Rules

B.3.1 Rule 1: No Loops

B.3.2 Rule 2: One Value Measure

B.3.3 Rule 3: No Forgetting

B.4 Summary

References

B.1 Introduction

The purpose of this appendix is to provide an introduction to influence diagrams (ID) and pointers to some of the foundational references. An influence diagram is a compact graphical representation of a decision. Howard and Matheson published the seminal paper on influence diagrams in 1980. The paper was republished in Decision Analysis to be more broadly available (Howard & Matheson, 2005). They developed influence diagrams as a decision problem representation that could be understood by both computers and people. Currently, Howard (Howard, 2004) uses the term “relevance diagram” to describe an influence diagram that contains only uncertainties and “decision diagram” for one that also includes decisions and values. Howard prefers “relevance” to “influence” since an arrow in an ID means that knowledge of one uncertain event is relevant to knowledge of a second uncertain event and not that one event “influences” the outcome of another event.

Shachter developed computation algorithms for influence diagrams that are equivalent to the decision tree algorithm (Shachter, 1986, and Shachter, 1988). This research put influence diagrams on a sound theoretical foundation. Influence diagrams were originally developed for decisions ...