Arrow and Pratt Revisited: The Case for a Polynomial Representation

Abstract

This study revives an approach to elicit human preferences based on the stimuli-response procedure long forgotten. The so-called school of Psycho-Physics (Weber-Fechner, 1860) [1], sought to make mathematical sense of the procedure above. Fifty years ago a new theory, Elementary Catastrophe Theory, (E.C.T.) [2], unfolding a unique Potential in our brain, provided the underlying dynamics needed to fulfill all the desiderata then missing. This axiomatization of a self-measurement process brings a rationale to the empirical data away from any “a priori” assumption about human purpose. Besides fitting the major landmark criteria in the fields of Value and Utility, like Arrow Impossibility result, this 5th degree symmetric polynomial exhibit a characteristic (Negative Schwarz’ Derivative) [3] going a long way to solve controversies and remove roadblocks in the progress of Portfolio Theory [4]. In the Annex we reproduce a long needed extension to Pratt’s [5]. Finally with this newly-found Human Scale (Cardinal) [6], grounded solely on the axiom of Non-Satiation, Free Energy could dislodge Entropy as a paradigm in this field [7].