Decision Theory

4Utility in action

The von Neumann and Morgenstern (NM) theory is an axiomatization of the expected utility principle, but its logic also provides the basis for measuring an individual decision maker’s utilities for outcomes. In this chapter, we discuss how NM utility theory is typically applied to utility elicitation in practical decision problems. In Section 4.1 we discuss a general utility elicitation approach, and then review basic applications in economics and medicine.

In Section 4.2, we apply NM utility theory to situations where the set of rewards consists of alternative sums of money. An important question in this scenario is how attitudes towards future uncertainties change as current wealth changes. The key concept in this regard is risk aversion. We review some intuitive results which describe risk aversion mathematically and characterize properties of utility functions for money. Much of our discussion is based on Keeney et al. (1976) and Kreps (1988).

In Section 4.3, we discuss how the lottery approach can be used to elicit patients’ preferences when the outcomes are related to future health. The main issue we will consider is the trade-off between length and quality of life. We also introduce the concept of a quality-adjusted life year (QALY), which is defined as the period of time in good health that a patient says is equivalent to a year in ill health, and commonly used in medical decision-making applications. We discuss its relationship with utility theory, and ...