Expected Utility Theory with Bounded Probability Nets∗

This paper develops an extension of expected utility theory by introducing various restrictions; e.g., probabilities have only decimal (or binary) fractions of finite depths not greater than a given constant, the preference relation in question may be incomplete. The basic idea is separation between measurement of utility for pure alternatives and extension to lotteries involving more risks such as plans for future events. These are formulated in an axiomatic manner. When no depth restrictions are given on permissible probabilities, the axioms determine a complete preference relation uniquely, which may be regarded as the classical EU theory. When a finite restriction is given, there are multiple preference relations compatible with the axioms, including incomparability on some lotteries. We exemplify the Alleis-Kahneman-Tversky anomaly within our theory. We also connect the measurement process in our theory to the satisficing/aspiration argument due to H. Simon. JEL Classification Numbers: C72, C79, C91