A General Criterion of Choice, with Discussion of Borch Paradox

Abstract

The author resumes a proposal by Frosini of a criterion of choice between probability prospects, which realizes a suggestion by Allais of taking account, beside the expected utility of the dispersion or variability of utilities. The suggested criterion is unidimensional, and is increasing with expected utility, and decreasing, for most people, who are risk averse, with the absolute deviation of utilities; a parameter multiplying this dispersion measure allows for risk-averse or risk-prone behaviour, according to its sign, and also for more or less departure from a certain prospect. This composite criterion shares practically all desirable conditions of rationality, and allows explaining all popular paradoxes in the literature about utility theory. Then the author deals with an apparent, but really false paradox, raised by Borch in connection with the representation of probability prospects in a Markowitz-type plot. This kind of analysis is modified from the traditional reference to points of type (mean, standard deviation) to the reference which replaces the standard deviation with the mean absolute deviation; no essential change is involved. The paper closes with some numerical examples which show the correctness of the suggested criterion, as compared to unaccettable conclusions of the expected utility approach.