Directed Expected Utility Networks

Abstract

A variety of statistical graphical models have been defined to represent the con-ditional independences underlying a random vector of interest. Similarly, many differentgraphs embedding various types of preferential independences, such as, for example, con-ditional utility independence and generalized additive independence, have more recentlystarted to appear. In this paper, we define a new graphical model, called a directedexpected utility network, whose edges depict both probabilistic and utility conditionalindependences. These embed a very flexible class of utility models, much larger thanthose usually conceived in standard influence diagrams. Our graphical representation andvarious transformations of the original graph into a tree structure are then used to guidefast routines for the computation of a decision problem’s expected utilities. We show thatour routines generalize those usually utilized in standard influence diagrams’ evalua-tions under much more restrictive conditions. We then proceed with the construction of adirected expected utility network to support decision makers in the domain of householdfood security.