### Weak* Axiom of Independence and the Non-Expected Utility Theory

#### Abstract

The axiomatic foundation of the expected utility theory (which states that given a set of uncertain prospects individuals pick up the prospect which yields the highest expected utility) was first laid down by Von Neumann and Morgenstern (1947). This axiom has come under severe criticisms in recent years. A large number of experiments have shown that in making decisions involving uncertain prospects people frequently violate the independence axiom. In this paper we shall consider the problem of choice under uncertainty from a wider point of view and we shall examine the nature of the restriction imposed by the axiom of independence. We shall use the mean-variance utility function to prove our point. Then we shall consider a weak version of the independence axiom namely the weak* axiom of independence. This is the point of departure from the expected utility theory to the realm of the non-expected utility theory. The weak* axiom allows aversion to pure uncertainty and, in the context of the mean-variance utility theory, it is compatible with utility being an increasing function of expected returns at all levels.