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Le Comportement de l'Homme Rationnel devant le Risque: Critique des Postulats e

Le Comportement de l'Homme Rationnel devant le Risque: Critique des Postulats et Axiomes de l'Ecole Americaine Author(s): M. Allais Source: Econometrica, Vol. 21, No. 4 (Oct., 1953), pp. 503-546 Published by: The Econometric Society Stable URL: http://www.jstor.org/stable/1907921 . Accessed: 07/09/2011 12:07 Your use of the JSTOR archive indicates your acceptance of the Terms & Conditions of Use, available at . http://www.jstor.org/page/info/about/policies/terms.jsp JSTOR is a not-for-profit service that helps scholars, researchers, and students discover, use, and build upon a wide range of content in a trusted digital archive. We use information technology and tools to increase productivity and facilitate new forms of scholarship. For more information about JSTOR, please contact support@jstor.org. The Econometric Society is collaborating with JSTOR to digitize, preserve and extend access to Econometrica. http://www.jstor.org VOLUME 21 OCTOBER, 1953 NUMBER 4 LE COMPORTEMENT DE L'HOMME RATIONNEL DEVANT LE RISQUE: CRITIQUE DES POSTULATS ET AXIOMES DE L'ECOLE AMERICAINE1 PAR M. ALLAIS2 ENGLISH SUMMARY The most important points of this article can be summarized as follows: (1) Contrary to the apparent belief of many authors, the concept of cardinal utility, s(x), can be defined in an operational manner either by considering equivalent differences of levels of satis- faction or by use of the Weber-Fechner minimum sensible or psychological threshold. Thus one can associate a psychological value s(x) with each monetary value x. lUne premiere version de cet article a 6te donnee dans une etude plus gen6rale intitulee "Notes th6oriques sur l'incertitude de l'avenir et le ris- que" qui a ete pr6sent6e au Congres Europeen d'Econometrie en Septembre 1951. Une deuxieme version en a ete present6e sous forme d'une communication au Colloque International sur le Risque qui s'est tenu a Paris en Mai 1952. Le lecteur pourra trouver dans le m6moire que nous avons redig6 a cette occasion toutes les justifications math6matiques des r6sultats indiqu6s cidessous avec de nombreux exemples que, faute de place, nous n'avons pu faire figurer dans cet article. Nous ne saurions trop conseiller au lecteur qui s'int6resserait aux indica- tions qui suivent de se reporter a ce m6moire. EDITOR'S NOTE: The problem discussed in Professor Allais' paper is of an ex- tremely subtle sort and it seems to be difficult to reach a general agreement on the main points at issue. I had a vivid impression of these difficulties at the Paris colloquium in May, 1952. One evening when a small number of the prominent con- tributors to this field of study found themselves gathered around a table under the most pleasant exterior circumstances, it even proved to be quite a bit of a task to clear up in a satisfactory way misunderstandings in the course of the con- versation. The version of Professor Allais' paper, which is now published in ECONOMETRICA, has emerged after many informal exchanges of views, including work done by editorial referees. Hardly anything more is now to be gained by a continuation of such procedures. The paper is therefore now published as it stands on the author's responsibility. The editor is convinced that the paper will be a most valuable means of preventing inbreeding of thoughts in this important field.-R.F. 2 Nous croyons devoir remercier ici tout particulierement MM. Capoulade, de Finetti, Mathieu, Lavaill, Lesourne, Mass6, Mercier, et Morlat pour leurs observa- tions et suggestions qui nous ont et6 particulierement precieuses. 503 0504 M. ALLAIS (2) There are four considerations which must necessarily be taken into account, even in a first approximation, by every theory of risk if it is to be realistic and is to bring out what is absolutely essential to every choice involving risk. (i) The distinction between monetary and psychological values. (ii) The distortion of objective probabilities and the appearance of subjective probabilities. (iii) The mathematical expectation of psychological values (the mean of the probability distribution of psychological values). (iv) The dispersion (variance) as well as general properties of the form of the probability distribution of psychological values. Consideration (iv) seems to us to be in fact the one that is specific to the theory of risk. In many cases, it can be much more important than the other three. (3) Other considerations enter into choices involving risk, such as the expenses entailed by every gamble, the pleasure derived from the gamble per se, the magnitude of the minimum sensible, etc., but these elements can be regarded as secondary and can be neglected in a first approximation. (4) Everybody recognizes the fact that man in reality does not behave according to the principle of Bernoulli. There does exist a profound difference, however, in points of view as to how a rational man ought to behave. According to the American school, a rational man must conform to the principle of Bernoulli. In our view, this is a mistake which in fact is tantamount to neglecting the fourth specific element in the psychology of risk. (5) If rationality is to be defined as adherence to one of the systems of axioms which leads to a Bernoulli type formulation, then ob- viously no discussion is possible. Such a definition, therefore, has no interest per se. That is to say that rationality, to be interest- ing from a scientific point of view, must be defined, in our opinion, in either of two ways. First, it may be defined in the abstract by referring to a general criterion of internal consistency employed in the social sciences, that is, a criterion implying the coherence of desired ends and the use of appropriate means for attaining them. Secondly, rationality can be defined experimen- tally by observing the actions of people who can be regarded as acting in a rational manner. (6) The principle of internal consistency implies only: (a) the use of objective probabilities when they exist, and (b) the axiom of absolute preference which states that out of two situations, COMPORTEMENT RATIONNEL DEVANT LE RISQUE 505 one is certainly preferable if, for all possible outcomes, it yields a greater gain. Together these two conditions are less restrictive than the formulation of Bernoulli. Consequently, there are rational types of behavior (in the sense of rationality defined above) which do not obey the Bernoulli formulation. It cannot be said, therefore, that a rational man must behave according to the Bernoulli principle. (7) The experimental observation of the behavior of men who are considered rational by public opinion, invalidates Bernoulli's principle. Four classes of facts are particularly significant in this regard: (i) The manner in which very prudent people behave in gambling small sums. (ii) The choice of risks bordering on certainty that contradicts the independence principle of Savage. (iii) The choice of risks bordering on certainty that contradicts the substitutability principle of Samuelson. (iv) The behavior of entrepreneurs when great losses are possible. (8) Whatever their attraction might be, none of the fundamental postulates leading to the Bernoulli principle as formulated by the American school can withstand analysis. All are based on false evidence. (9) For the rational man, there does not exist in general an indicator B(x) such that the optimum situation could be defined by maximizing the expected value of B(xi). (10) In particular cases where the psychology of the rational man is such that this indicator exists, it necessarily follows that B(x) = s(x), up to a linear transformation. (11) The justification of Bernoulli's formulation, even as a first approximation, by the law of large numbers is pure illusion. (12) In the most general case, the connection between monetary values and psychological values, and the dispersion of psy- chological values are inseparably mixed and no experience bearing upon the choices involving risk could determine the function s(x). Such a function can be determined only through introspective observation of equivalent differences of levels of satisfaction and of sensible psychological thresholds. It is only in the very particular psychological case in which the indicator B(x) would be identical with the psychological value s(x) that the observation of risky choices could enable one to determine the psychological value s(x). 506 M. ALLAIS 1. LA PR?SENTE etude est essentiellement destin6e A un expos6 critique des postulats et axiomes des th6ories du risque de l'6cole am6ricaine. Pour proc6der a cet expos6 critique, le mieux nous parait de diviser notre expos6 en deux parties; dans la premiere nous essaierons de faire comprendre quelle est notre propre conception, dans la seconde nous procederons, compte tenu des indications donn6es dans la premiere partie, A une analyse critique du principe de Bernoulli et tout particu- lierement des differents axiomes de l'6cole am6ricaine. D'une mani6re g6n6rale nous essaierons de faire appel A l'intuition et d'eviter dans toute la mesure du possible un formalisme math6matique trop abstrait, qui en r6alit6 n'a que trop souvent pour effet de d6tourner l'attention des veritables difficult6s et de masquer des aspects essentiels. Les math6matiques ne sont qu'un moyen de transformation; seule compte en fait la discussion des premisses et des r6sultats.3 I. CONSIDERATIONS PRELIMINAIRES 2. Eldments psychologiques intervenant dans les choix comportant un risque. II convient de distinguer soigneusement parmi les 6l6ments qui interviennent dans les choix comportant un uploads/Geographie/ allais-rational-man-1953.pdf