Determination of Cardinal Utility According to an Intrinsic Invariant Model

Abstract

The purpose of the Paper is to show that it is possible to represent all the empirical data of the 1952 Experiment (19 subjects) and of the 1975 Experiment (8 subjects) by only one model, the same whatever the subjects considered.

An invariant formulation is presented of the generating function X=f(A) corresponding to the condition S (U_o+X)=2S (U_o+A) where S (U_o + X) represents cardinal utility of a given subject, and U_o his psychological assets, that is his psychological estimate of his assets.

The function of cardinal utility of anyone subject can be deduced from the knowledge of his generating function. The function of cardinal utility is invariant from one subject to the next once one considers the ratio X/μ, in which μ represents the index of a subject with respect to a reference subject.

All the empirical data can be validly represented by the same generating function and a single function of cardinal utility which together constitute the intrinsic invariant model. This agreement is the more remarkable in that the intrinsic invariant model was deduced from the analysis of the empirical data of the 1952 Experiment alone, and it applies itself as well to the empirical data of the 1975 Experiment.

Not only the preceding analysis gave undeniable evidence of the existence of cardinal utility, but its expression appears effectively to be invariant from one subject to the next both at a given moment and over time, at least as a first approximation.

This conclusion is the more significant in that the expression of cardinal utility as a function of variable X shows a very striking similarity to the expression for psychophysiological sensation as a function of luminous stimulus determined by Weber’s and Fechner’s successors.