Security level, potential level, expected utility: a three-criteria decision model under risk.

*(English)*Zbl 0770.90004Summary: Among the violations of expected utility (E.U.) theory which have been observed by experimenters, the violations of its independence axiom is, by far, the most common. It seems that, in many cases, these inconsistencies can be ascribed to the desire for security — called the security factor by L. Lopes (1986) — which “makes people attach special importance to the worst outcomes of risky decisions” as well as to the sole outcomes of riskless decisions (certainty effect). J.-Y. Jaffray [Theory Decis. 24, No. 2, 169–200 (1988; Zbl 0631.90005)] has proposed a model which generalizes E.U. theory by taking into account this factor and is then able to account for certain violations. However, especially in experiments on choice involving prospective losses, violations of the von Neumann-Morgenstern independence axiom cannot be explained by the security factor alone and have to be partially ascribed to the potential factor (L. Lopes, 1986) which “reflects heightened attention to the best outcomes of decisions”, especially when the best outcome is the status quo.

In this paper, we construct an axiomatic model for subjects taking into account simultaneously or alternatively the security factor and the potential factor. For this, as in Jaffray’s model, it has been necessary to weaken not only the standard independence axiom but also the continuity axiom and, in the same time, to reinforce the dominance axiom. In the resulting model, choices are partially determined by the mere comparison of the (security level, potential level) (i.e. the (worst outcome, best outcome)) pairs offered, and completed by the maximization of an affine function of the expected utility, the coefficients of which depend on both the security level and potential level. In this model, a decision maker who (i) has constant marginal utility for money, (ii) is sensitive to the security factor alone in the domain of gains, (iii) is sensitive to the potential factor alone in the domain of losses, behaves as a risk averter for gains and a risk seeker for losses.

In this paper, we construct an axiomatic model for subjects taking into account simultaneously or alternatively the security factor and the potential factor. For this, as in Jaffray’s model, it has been necessary to weaken not only the standard independence axiom but also the continuity axiom and, in the same time, to reinforce the dominance axiom. In the resulting model, choices are partially determined by the mere comparison of the (security level, potential level) (i.e. the (worst outcome, best outcome)) pairs offered, and completed by the maximization of an affine function of the expected utility, the coefficients of which depend on both the security level and potential level. In this model, a decision maker who (i) has constant marginal utility for money, (ii) is sensitive to the security factor alone in the domain of gains, (iii) is sensitive to the potential factor alone in the domain of losses, behaves as a risk averter for gains and a risk seeker for losses.

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