Abstract
1.-The Impossibility Theorem rests on five fundamental properties. On each of them Machina has confirmed his agreement over and over again between 1984 and 1986. The proof of the Impossibility Theorem is mathematically and rigorously correct.
2.- The alleged Machina's demonstration of the Allais' two errorsis indeed only grounded on a series of errors and it isin total contradiction with the interpretationsexplicitly given by Machina from 1982 to 1986 of his local utility theory in the discrete case, especially in his letters.
3.1 In fact one cannot but ask if Machina really understands the meaning and the implications of his formulation of the local utility, and what is really in question.
In any case it would he without any doubt eminently desirable that before hastily concluding that the others are making mistakes, Machina should begin by seriously asking himself if he is not himself into error.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
References
ALLAIS Maurice 1952Fondements d'une Théorie Positive des Choix comportant un Risque et Critique des Postulats et Axiomes de l'Ecole Américaine Colloques Internationaux, Centre National de la Recherche Scientifique,Econométrie, Vol. XL, Paris, 1953, p. 257–332.
ALLAIS Maurice 1952*The Foundations of a Positive Theory of Choice Involving Risk and Criticism of the Postulates and Axioms of the American School English translation of 1952, in Allais and Hagen 1979, p. 27–145.
ALLAIS Maurice 1983The Foundations of the Theory of Utility and Risk in O. Hagen and F. Wenstop,Progress in Decision Theory, p. 3–131, Reidel, Dordrecht 1984, 279 p.
ALLAIS Maurice 1984 cSur la Signification et la Portée de la Théorie de l'Utilité locale de Mark Machina — Contribution à la Théorie générale des Choix Aléatoires. Centre d'Analyse Economique, Oct. 1984, 95 p.
ALLAIS Maurice 1986 aOn the Determination of a Discrete Distribution of order n from 2n−1 Successive Moments Centre d'Analyse Economique, March 1986, C-4369, 15 p.
ALLAIS Maurice 1986 bImpossibility of the Validity of Machina's Function of Local Utility in any Finite Domain Centre d'Analyse Economique, March 1986, C-4368, 17 p.
ALLAIS Maurice 1986 cMachina's Local Utility and the Allais Impossibility Theorem — Additional Comments Centre d'Analyse Economique, April 19, 1986, C-4384, 20 p.
ALLAIS Maurice 1986 dMachina's Fundamentally Wrong Statements on the Allais Impossibility Theorem Centre d'Analyse Economique, April 20, 1986, C-4385, 12 p.
ALLAIS Maurice 1986 hThe General Theory of Random Choices in Relation to the Invariant Cardinal Utility Function and the Specific Probability Function. The (u, θ) Model. A General Overview. Dans l'ouvrage collectif“Risk, Decision and Rationality”, Bertrand Munier edit., D. Reidel Publishing Company, Dordrecht, 1987, p. 231–289.
ALLAIS Maurice 1986iCritical Analysis of the Local Utility Theory. Working Paper for the Debate Machina/Allais Third International Conference on the Foundations and Applications of Utility, Risk and Decision Theories, Aix-en-Provence, June 1986, 28 p.
ALLAIS Maurice 1986 jA New Neo-Bernoullian Theory: The Machina Theory — A Critical Analysis with aPostscript in “Risk, Decision and Rationality”, 1987, id., p. 345–403.
ALLAIS Maurice 1987Some Remarkable Properties of the Determination of a Continuous Distribution by its Moments Dans l'ouvrage collectif “Risk, Decision and Rationality”, Bertrand Munier, édit., D. Reidel Publishing Company, 1987, p. 557–561.
ALLAIS Maurice 1994An Outline of my Main Contributions to Risk and Utility Theory — Theory, Experience, and Applications — General Overview Dans l'ouvrage collectif“Models and Experiments in Risk and Rationality, Bertrand Munier and Mark Machina édit., Kluwer Academic Publishers, p. 173–221.
ALLAIS Maurice and HAGEN Ole 1979Expected Utility Hypotheses and the Allais Paradox ; Contemporary Discussions and Rational Decisions under Uncertainty with Allais' Rejoinder Reidel, Dordrecht, 1979, 715 p.
MACHINA Mark 1981Rational Decision Making Versus Rational Decision Modelling? Review of Allais and Hagen 1979,Journal of Mathematical Psychology, p. 163–175.
MACHINA Mark 1982Expected Utility Without the Independence Axiom Econometrica, Vol. 50, no 2, March 1982, p. 277–323
MACHINA Mark 1983The Economic Theory of Individual Behavior toward Risk. Theory, Evidence and new Directions. University of California, Technical Report, no 433, Oct. 1983, 151 p.
MACHINA Mark 1987Cardinal Properties of “Local Utility Functions” inRisk, Decision and Rationality, 1987, id., p. 339–344.
MACHINA Mark 1987Choice under Uncertainty: Problems Solved and Unsolved Economic Perspectives, p. 121–154.
MACHINA Mark 1987Expected Utility Hypotheses The New Palgrave.A Dictionary of Economics, Vol. 1, p. 232–239.
MACHINA Mark 1994Two Errors in the “Allais Impossibility Theorem” Theory and Decision, 1995.
POPE Robin 1985Machina's Decision Model: An Empty Box? University of New South Wales, Australia, 1985, 30 p.
Rights and permissions
About this article
Cite this article
Allais, M. The real foundations of the alleged errors in Allais' Impossibility Theorem: Unceasingly repeated errors or contradictions of mark machina. Theor Decis 38, 251–299 (1995). https://doi.org/10.1007/BF01362235
Issue Date:
DOI: https://doi.org/10.1007/BF01362235