The general theory of random choices in relation to the invariant cardinal utility function and the specific probability function. The (U,\(\theta\) ) model. A general overview.

*(English)*Zbl 0676.90005
Risk, decision and rationality, Sel. Pap. 3rd Int. Conf. Found. Appl. Utility, Risk Dec. Theories, FUR-3, Theory Decis. Libr., Ser. B 9, 231-289 (1988).

[For the entire collection see Zbl 0658.00021.]

The purpose of this paper is to specify and illustrate Allais’ general theory of random choice which is based on the consideration of the invariant cardinal utility function and the whole distribution of cardinal utilities and on the general preference for security in the neighbourhood of certainty when large sums are at stake. A hypothesis used for this purpose is the linearity of cardinal utility of a random prospect with respect to the component cardinal utilities. This is applied to the case of discrete random prospects of order three. Qualitative and quantitative discussions of the conditions necessary for the Allais Paradox are presented. It is shown that it is possible to analyze and predict the behaviour of a given subject with respect to this Paradox. As an illustration, this method is applied to four respondents to the 1952 Questionnaire (de Finetti, Malinvaud, Saint-Guilhem and Jacquelin) whose psychology differ. In the case of discrete random choice of order three, indifference lines of the fields of choice of the above subjects are computed and drawn with a triangular representation as a function of probabilities for given values of cardinal utilities. Their answers to questions relating to the Allais Paradox are predicted from the consideration of their cardinal utility of random prospects.

The purpose of this paper is to specify and illustrate Allais’ general theory of random choice which is based on the consideration of the invariant cardinal utility function and the whole distribution of cardinal utilities and on the general preference for security in the neighbourhood of certainty when large sums are at stake. A hypothesis used for this purpose is the linearity of cardinal utility of a random prospect with respect to the component cardinal utilities. This is applied to the case of discrete random prospects of order three. Qualitative and quantitative discussions of the conditions necessary for the Allais Paradox are presented. It is shown that it is possible to analyze and predict the behaviour of a given subject with respect to this Paradox. As an illustration, this method is applied to four respondents to the 1952 Questionnaire (de Finetti, Malinvaud, Saint-Guilhem and Jacquelin) whose psychology differ. In the case of discrete random choice of order three, indifference lines of the fields of choice of the above subjects are computed and drawn with a triangular representation as a function of probabilities for given values of cardinal utilities. Their answers to questions relating to the Allais Paradox are predicted from the consideration of their cardinal utility of random prospects.

Reviewer: A.Mukherji