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Cardinalism pp 31-64 | Cite as

Determination of Cardinal Utility According to an Intrinsic Invariant Model

Chapter
Part of the Theory and Decision Library book series (TDLA, volume 19)

Abstract

The purpose of this paper is to show that it is possible to represent all the empirical data of the 1952 Experiment (19 subjects) and of the 1975 Experiment (8 subjects) by only one model, the same whatever the subjects considered.

An invariant formulation is presented of the generating function X = f(A) corresponding to the condition s(U 0 + X) = 2s(U 0 + A) where s(U 0+X) represents cardinal utility of a given subject, and U 0 his psychological assets, that is his psychological estimate of his assets.

The function of cardinal utility of any one subject can be deduced from the knowledge of his generating function. The function of cardinal utility is invariant from one subject to the next once one considers the ratio X/μ, in which μ represents the index of a subject with respect to a reference subject.

All the empirical data can be validly represented by the same generating function and a single function of cardinal utility which together constitute the intrinsic invariant model. This agreement is the more remarkable in that the intrinsic invariant model was deduced from the analysis of the empirical data of the 1952 experiment alone, and it applies equally as well to the empirical data of the 1975 experiment.

Not only the preceding analysis gave undeniable evidence of the existence of cardinal utility, but its expression appears effectively to be invariant from one subject to the next both at a given moment and over time, at least as a first approximation.

This conclusion is the more significant in that the expression of cardinal utility as a function of variable X shows a very striking similarity to the expression for psychophysiological sensation as a function of luminous stimulus determined by Weber’s and Fechner’s successors.

Keywords

Generate Function Empirical Data Reference Subject Luminous Stimulus Vertical Asymptote 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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References

  1. Allais, Maurice (1952a) ‘Fondements d’une théorie positive des choix comportant un risque et critique des postulats et axiomes de l’Ecole Américaine’ (Foundations of a positive theory of choice involving risk, and a criticism of the postulates and axioms of the American School), Econométrie, Colloques Internationaux du Centre National de la Recherche Scientifique, Vol. XL, Paris, 1953, pp. 257–332. (See also pp. 34-35, 37-39, 40, 47-48, 151-163, 194-197 and 245-247.) This memoir was republished in Vol. 144 of the Annales des Mines, special issue, 1955, and again as a separate volume, under the same title by the Imprimerie Nationale 1955.Google Scholar
  2. Allais, Maurice (1952b) ‘Le comportement de l’homme rationnel devant le risque: Critique des postulats et axiomes de l’Ecole Américaine’ (The behavior of rational man facing risk: Criticism of the postulates and axioms of the American School) in Econometrica, 21(4), October 1953, pp. 503–546 (summarised version of the 1952 Memoir).CrossRefGoogle Scholar
  3. Allais, Maurice (1952c) ‘La psychologie de l’homme rationnel devant le risque — La théorie et l’expérience’, Journal de la Société de Statistique de Paris, January-March 1953, pp. 47-73.Google Scholar
  4. Allais, Maurice (1976) The Foundations of a Positive Theory of Choice Involving Risk and a Criticism of the Postulates and Axioms of the American School, English translation of the (1952) Memoir, in Allais and Hagen, 1979, pp. 27-145.Google Scholar
  5. Allais, Maurice (1977) ‘The so-called Allais’ paradox and rational decisions under uncertainty’, in Allais and Hagen, 1979, pp. 437-699.Google Scholar
  6. Allais, Maurice (1983) ‘The foundations of the theory of utility and risk; some central points of the discussions at the Oslo Conference’, in Hagen and Wenstop (Eds.), Progress in Decision Theory, Reidel, 1984, pp. 3-131.Google Scholar
  7. Allais, Maurice (1984), ‘The cardinal utility and its determination, hypothesis, methods and empirical results’, Theory and Decision, forthcoming.Google Scholar
  8. Allais, Maurice and Hagen, Ole (1979) Expected Utility Hypotheses and the Allais’ Paradox; Contemporary Discussions and Rational Decisions under Uncertainty with Allais’ Rejoinder, Reidel, Dordrecht, 1979, p. 715.Google Scholar
  9. Pieron, Henri (1927) Psychologie Expérimentale, A. Colin, Paris, p. 220.Google Scholar

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© Springer Science+Business Media Dordrecht 1994

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