A discussion of the present state of utility theory (FUR II, Venice, 1984)

✍ Scribed by Georges Bernard

• Publisher: Springer US
• Year: 1986
• Tongue: English
• Weight: 780 KB
• Volume: 20
• Category: Article
• ISSN: 0040-5833
• DOI: 10.1007/bf00135091

✦ Synopsis

The present state of the utility theory can be summarized by four propositions:

1. The utility function u(x) derived from the vNM(von Neumann and Morgenstern) axiomatics is not the cardinal utility of the certain outcome x; this last utility is a different function v(x).

2. The relation between u and v expresses the utility of uncertainty. If u = v, as assumed in [14], the expected utility, as a preference functional among uncertain prospects, expresses a risk neutral behavior.

3. The axioms of vNM shall be dropped. In particular, single stage and multiple equivalent bets are not indifferent, i.e., of equal utility. This proposition, which requires the abandonment of the independence axiom as expressed by axiom 3:C:b of vNM and by the formulations of Samuelson [2] and Malinvaud [3], is necessary in order to be able to establish a general utility function of uncertain prospects such that it covers the intrinsic utility of uncertainty.

4. Such a general utility function is non-linear in probabilities.

At present three schools are offered. The firs't, represented among others by the three authors quoted in Section 2 of this paper, tries to formulate and empirically verify the points 1 and 2 of this conclusion. The second, represented among others by the three authors quoted in Section 3 of this paper, tries to prove conclusions 3 and 4. My proposal of 1966-74 [19-25] assumes all four conclusions. But it lacks formal proof and is also critized as it can lead to violations of the principle of dominance. It is shown in [22] and recalled here that such violations are in fact fruitful explanations of possible behaviors and can be considered as rational.