The Beginning of a New Paradigm: From D. Bernouilli to M. Allais

Abstract

To represent the interaction of the human being with his environment and letting him express it, therefore blending the subject with the object and completing what was missing from Quantum theory. In our polynomial the subjective factor Xo shows up in the numerator and leads to an objective valuation since of a finite degree. Study also revives an approach to elicit human preferences based on the stimuli-response procedure long forgotten. Fifty years ago a new theory, Elementary Catastrophe Theory,(E.C.T.), unfolding a unique Potential in our brain, provided the underlying dynamics needed to fulfill all the desiderata of the so-called school of Psycho-Physics (Weber-Fechner, 1860), seeking to make mathematical sense of the procedure above. The axiomatization of a self-measurement process removes any "a priori" assumptions about human motivation from the explanation of the empirical data. This 5th degree symmetric polynomial exhibits a characteristic (Negative Schwarz' Derivative) that goes a long way to resolve disputes and remove obstacles in the development of Portfolio Theory in addition to meeting the major landmark criteria in the fields of Value and Utility.  Given that chaos theory has the divergence of Newton's Method as a paradigm, we have brought order to a potentially chaotic process because our algorithm ensures local and global convergence through the careful selection of initial points. The possibility of expanding the approach to the complex field is encouraged by the expression of the Schwarz derivative's invariance to the Mobius transformation.