PROPOSTA DI UNA FUNZIONE UTILITÀ DIPENDENTE DALL’UTILITÀ ATTESA E DALLA DISPERSIONE DELLE UTILITÀ

The author develops the properties and implications of a proposal, concerning a summary statistic of the random prospect of utilities. Following a suggestion of Maurice Allais, such a statistic is increasing with expected utility, and decreasing – for most people, who are risk averse – with the mean 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. It is demonstrated that this statistic (a) satisfies the first stochastic dominance, (b) satisfies the independence condition, (c) satisfies the so called “problem of probabilistic insurance”, (d) resolves the paradoxes of Allais, Ellsberg and Kahneman-Tversky (paradox of the substitution axiom), (e) the mean absolute deviation from the mean cannot be replaced by the standard deviation.