William M Saade



Arrow and Pratt revisited

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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), sought to make mathematical sense of the procedure above. 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 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, Arrow Impossibility result and Arrow-Pratt premium, this 5th degree symmetric polynomial exhibit a characteristic (Negative Schwarz’ Derivative) going a long way to solve controversies and remove roadblocks in the progress of Portfolio Theory. In the Annex we reproduce a long needed extension to Pratt’s. Finally with this newly-found Human Scale (Cardinal), grounded solely on the axiom of Non-Satiation, Free Energy could dislodge Entropy as a paradigm in this field.



Arrow Impossibility, E.C.T, Weber-Fechner, Negative Schwarz’ derivative, Skewness, Morphic resonance, Poincare – Dulac, Synapses, Cardinality.



[1] André Orléan: L’empire de la valeur, Points, Économie 2013 Ed. du seuil

[2] D.W.Griesinger: The Physics of Motivation and Choice. IEEE Transactions on Systems, Man and Cybernetics, vol.SMC-8, n°12, Dec.1978.

[3] Francois Jacob: La logique du vivant, Gallimard,Paris 1970.

[4] G.L. Schackle : Decision, order and time/ Epistemics and Economics, Cambridge 1972.

[5] G.Menges: Information, Inference and Decision. (Theory and Decision Library, vol. 1) Dordrecht, Boston 1974.

[6] Guy Orban:La Vision, mission du cerveau, le consinaugurales du College de France 2007.

[7] Henry P. Stapp: Mindful Universe, Quantum Mechanics and the participating observer, Springer, 2014.

[8] J.M. Grandmont :On endogeneous business cycles.IMSSS Tech. Report # 438.1983

[9] Jean Petitot : Logos et Theorie des Catastrophes, Colloque de Cerisy sur l’oeuvre de R.Thom, Ed. Patino, 1988.

[10] Jean Petitot: in “Issues in contemporary Phenomenology and Cognitive Science” Stanford University Press 1999.

[11] Jean Petitot: in Mathématiques et Sciences Humaines Numéro Spécial linguistique et Mathématiques – III, 1982.

[12] Jose Rodrigues Dos Santos : La clé de Salomon, Ed. Herve Chopin, 2014.

[13] Joseph Delboeuf : Etude critique de la loi psychophysique de Fechner, l’Harmattan, 2006.

[14] K. Pribram: Languages of the Brain. Englewood Cliffs, N.J.Prentice Hall, '70

[15] Keen Steve, Fullbrook Edward, “Improbable, incorrect or imposible? The persuasive but flawed mathematics of icroeconomics”, in A guide to what’s wrong with Economics, London, Anthem Press, p.209-222. 2004

[16] Keeney Ralph: Value-focused thinking. Harvard U.Press,Cambridge, Massachusetts. London, England 1992

[17] L.C. Jeffrey: The logic of decision. 2 nd Ed. University of Chicago Press 1983

[18] Leinfellner W. & Booth E.: The naturalistic versus the intuitionistic school of values in Allais & Hagen op.cit. 303-332, 1979.

[19] Lujo Brentano,”Die Entwickelung der Wertlehre” in Sitzungsberichte der Koniglich Bayerischen Akademie der Wissenschaften.Philossophisch-philologische und historische Klasse, Band XXIV, 3. 1908

[20] M. Allais and O. Hagen: Expected Utility Hypothesisand Allais Paradox. (Theory and Decision Library, Vol. 21) Dordrecht, Reidel 1979.

[21] Paul Davies: The mind of God. Penguin Book,1993

[22] Philip Kitcher: The nature of mathematical knowledge.Oxford University Press, 1984.

[23] Pierre Buser:Neurophilosophie de l’Esprit, Odile Jacob, 2013.

[24] R.Thom :Structural stability and Morphogenesis, Addison-Wesley.1989

[25] R.Thom: Esquisse d’une Semiophysique, InterEditions, 1991.

[26] Roger Penrose : Les cycles du temps, une nouvelle vision de l’univers. Odile Jacob, 2013.

[27] Roger Penrose : Les ombres de l’Esprit.A la recherche d’une science de la conscience, InterEditions.1995.

[28] Rupert Sheldrake: The Science Delusion Coronet 2013.

[29] S.C. Tsiang:”The rationale of mean-standard deviation analysis,skewness preference & the demand for money. A.E.R. p:354-371, june1972

[30] S.Ross: Some Stronger Measures of Risk Aversion in the Small and the Large with Applications, Series n°39. Yale University 1979.

[31] W.M. Saade:’From D. Bernouilli to M. Allais: a new paradigm in the making?, WSEAS conference MACISE 2017-128, London Oct. 27-29, 2017.

[32] W. M. Saade:”A synthetic approach to value as a standard of reference”, in Proceedings of FTC conference. London july 18-20, 2017

[33] W. M. Saade:”Toward a convergence between utility and value through a polynomial representation”, Proceedings of FTC conference in San Francisco, dec 2016. http:ieeexplore.ieee.org/xpl/most Recentissue.jsp?punumber7802033

[34] W.M.Saade:”An alternative vision to Weber- Fechner Psycho-Physics, WSEAS, NAUM joint conference ICANCM, Malta..SLIEMA, August 2015.

[35] W. M. Saade:” The identification of Negative Schwarz’ derivative with systematic risk aversion”, same publication as following reference below.

[36] W.M.Saade:”A Phenomenological approach to Value”, Post conference proceedings of the 18th World Multi-Conference on Systemics, Cybernetics and Informatics, Orlando, Florida, 2014.

[37] W.M. Saade:”An Engineering-Economy”, presented at Oslo First international Conference on the Foundation of Utility and Risk Theory” July 1982.

[38] Weibull J.W.: A dual to the Von-Neumann- Morgenstern theorem. Journal of mathematical Psychology 26 :191-203, 1982

[39] Y. Balasko (1978): Economie et Théorie des Catastrophes, in Cahiers du Séminaire d’Econométrie, #19.

Cite this paper

William M Saade. (2017) Arrow and Pratt revisited. International Journal of Mathematical and Computational Methods, 2, 249-264


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