The Generalized Means Model (GMM) for non-deterministic decision making: Its normative and descriptive power, including sketch of the representation theorem

Two schools of thought have been arguing during the last thirty years about the foundations of the theory of choice under uncertainty, namely: The neo-Bernoullian or American school defending an Expected Utility Model (EUM); and the Allais or French school proposing a model based on the moments of the probability distribution over psychological values (MM).In this paper we present a unified theory: the Generalized Means Model (GMM). By using the well known concept of the generalized mean it is possible to derive both contesting models from the same core of axioms, that — surprisingly enough — includes an extended form of the hotly debated Substitution Principle.It can be seen that the differences between the two models occur at the beginning and at the end of their axiomatic derivation, as follows: the EUM starts from a probability distribution function over consequences whereas the MM begins with a probability distribution over psychological values. The EUM finishes with an early introduction of a behavioural axiom on the existance of utility, whereas the MM uses first the properties of the distribution function, and then introduces the behavioural assumptions.The simplest MM consistent with all axioms of the GMM is the model proposed by the author some years ago. It is suggested that a reduced version, the Three Moments Model (TMM), is sufficient for practical applications.The second part of the paper demonstrates how the TMM solves in a very natural way the Allais Paradox, the certainty effect, the reflection effect, and several other behavioural observations.