The important financial decisions in our life concern large stakes, and then the maximization of expected value may not be reasonable. Most of our decisions concern nonquantitative outcomes such as health states. Then expected value cannot be used because it cannot even be defined. For these reasons, a more general theory is warranted. We now turn to such a theory – expected utility. For simplicity, we consider only the case where probabilities are known in this chapter. This case is called decision under risk. The general case of both unknown probabilities and unknown utility is more complex, and will be dealt with in later chapters. Whereas Chapter 1 showed how to read the minds (beliefs, i.e. subjective probabilities) of people, this chapter will show how to read their hearts (happiness, i.e. utility).

Decision under risk as a special case of decision under uncertainty

Probabilities can be (un)known to many degrees, all covered by the general term uncertainty. Decision under risk is the special, limiting case where probabilities are objectively given, known, and commonly agreed upon. Risk is often treated separately from uncertainty in the literature. It is more efficient, and conceptually more appropriate, to treat risk as a special case of uncertainty. I will discuss this point in some detail in this and the following sections. This point will be especially important in the study of ambiguity in Part III. Machina (2004) provided a formal model supporting this point.