Decision Theory

3Utility

Broadly defined, the goal of decision theory is to help choose among actions whose consequences cannot be completely anticipated, typically because they depend on some future or unknown state of the world. Expected utility theory handles this choice by assigning a quantitative utility to each consequence, a probability to each state of the world, and then selecting an action that maximizes the expected value of the resulting utility. This simple and powerful idea has proven to be a widely applicable description of rational behavior.

In this chapter, we begin our exploration of the relationship between acting rationally and ranking actions based on their expected utility. For now, probabilities of unknown states of the world will be fixed. In the chapter about coherence we began to examine the relationship between acting rationally and reasoning about uncertainty using the laws of probability, but utilities were fixed and relegated to the background. So, in this chapter, we will take a complementary perspective.

The pivotal contribution to this chapter is the work of von Neumann and Morgenstern. The earliest version of their theory (here NM theory) is included in the appendix of their book Theory of Games and Economic Behavior. The goal of the book was the construction of a theory of games that would serve as the foundation for studying the economic behavior of individuals. But the theory of utility that they constructed in the process is a formidable contribution in its ...