Decisions and Dependence in Influence Diagrams

The concept of dependence among variables in a Bayesian belief network is well understood, but what does it mean in an influence diagram where some of those variables are decisions? There are three quite different answers to this question that take the familiar concepts for uncertain variables and extend them to decisions. First is responsiveness, whether the choice for a decision affects another variable. Second is materiality, whether observing other variables before making a decision affects the choice for the decision and thus improves its quality. Third is the usual notion of dependence, assuming that all of the decisions are made optimally given the information available at the time of the decisions. There are some subtleties involved, but all three types of decision dependence can be quite useful for understanding a decision model.