Skip to main content
SpringerLink
Log in

Cognitive rationality and alternative belief measures

  • Published:
Journal of Risk and Uncertainty Aims and scope Submit manuscript

Abstract

In this article, we first examine the various criticisms of the probabilistic model. Then we introduce capacities in order to show that if a probability measure corresponds to anesthetizing the belief of the agent's knowledge, it is then possible to suggest another type of rationality—namely, being able to describe a wise and a rash behavior when facing risk—and therefore another model of belief under uncertainty. While trying to specify various alternative measures, possibility, necessity, and measures resulting from a triangular norm or from a triangular conorm, we finally try to define the field of application of the probabilistic model as well as a sign of the rationality choice: constraint of mass-unity for traditional rationality, and constraint of duality for the one we present.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

References

  • Abreu, D. (1988). “On the Theory of Infinitely Repeated Games with Discounting”,Econometrica 56 (2), 383–396.

    Google Scholar 

  • Abreu, D. and A. Rubinstein. (1988). “The Structure of Nash Equilibrium in Repeated Games with Finite Automata”,Econometrica 56 (6), 1259–1282.

    Google Scholar 

  • Aczel, J. (1966).Lectures on Functional Equations and their Applications. New York: Academic Press.

    Google Scholar 

  • Allais, M. (1983). Fréquence, Probabilité et Hasard”,Journal de la Société de Statistique de Paris, 70–102, 144–221.

    Google Scholar 

  • Allais, M. (1988). “The General Theory of Random Choices in Relation to the Invariant Cardinal Utility Function and the Specific Probability Function, the (U,Ø) Model: A General Overview”. In B. Munier (ed.)Risk, Decision and Rationality. Dordrecht/Boston: Reidel, pp. 231–289.

    Google Scholar 

  • Bell, D.E., H. Raiffa, and A. Tversky. (1988).Decision Making, Descriptive, Normative, and Prescriptive Interactions. Cambridge: Cambridge University Press.

    Google Scholar 

  • Billot, A. (1987).Préférence et Utilité Floues. Paris: Presses Universitaires de France.

    Google Scholar 

  • Buchanan, B.G. and E.H. Shortliffe. (1975). “A Model of Inexact Reasoning in Medicine”,Mathematical Biosciences 23, 351–379.

    Google Scholar 

  • Chateauneuf, A. and J.Y. Jaffray. (1989). “Some Characterizations of Lower Probabilities and Other Monotone Capacities through the Use of Möbius Inversion”,Mathematical Social Sciences 17, 263–283.

    Google Scholar 

  • Choquet, G. (1953). Théorie des Capacités”,Annales de l'Institut Fourier 5, 131–295.

    Google Scholar 

  • Cohen, M. and J.Y. Jaffray. (1980). “Rational Behavior under Complete Ignorance”,Econometrica 48 (5) 1281–1300.

    Google Scholar 

  • De Finetti, B. (1970).Theory of Probability. New York: Wiley.

    Google Scholar 

  • Dempster, A.P. (1967). “Upper and Lower Probabilities Induced by a Multivalued Mapping”,Annals of Mathermatical Statistics 38, 325–339.

    Google Scholar 

  • Dempster, A.P. (1988). “Probability, Evidence, and Judgment”. InDecision Making, Descriptive, Normative, and Prescriptive Interactions. Cambridge: Cambridge University Press, D.E. Bell, H. Raiffa, and A. Tversky (eds.), 284–298.

    Google Scholar 

  • Dubois, D. (1980a). “frSur les Liens entre les Notions de Possibilité et de Probabilité (Quelques Remarques)”, Table Ronde CNRS, Lyon.

    Google Scholar 

  • Dubois, D. (1980b). Un Economiste Précurseur de la Théorie des Possibilités: G.L.S. Shackle”,Busefal 2, 70–73.

    Google Scholar 

  • Dubois, D. (1983).Modèles Mathématiques de l'Imprécis et de l'Incertain en Vue d'Applications aux Techniques d'aide à la Décision, Thèse de Doctorat es Sciences, Université de Grenoble.

  • Dubois, D. and H. Prade. (1981). “Unfair Coins and Necessity Measures.” In E.P. Klement (ed.),Proceedings of the Third International Seminar on Fuzzy Set Theory, 223–231.

  • Dubois, D. and H. Prade. (1982). “A Class of Fuzzy Measures Based on Triangular Norms”,International Journal of General Systems 8, 43–61.

    Google Scholar 

  • Favereau, O. (1988). “Probability and Uncertainty: After All, Keynes Was Right”,Economies et Sociétés 10, 133–168.

    Google Scholar 

  • Favereau, O. (1989). “Marchés Internes, Marchés Externes,” Doc de Travail ERMES no88-07 publié dans laRevue Economique.

  • Fine, T. (1973).Theories of Probability. New York: Academic Press.

    Google Scholar 

  • Höhle, H. (1982). “A Mathematical Theory of Uncertainty”. In R.R. Yager (ed.),Fuzzy Set and Possibility Theory: Recent Developments. New York: Pergamon Press, 344–356.

    Google Scholar 

  • Jaffray, J.Y. (1988). “An Axiomatic Model of Choice Under Risk Which is Compatible with the Certainty Effect”. In B. Munier (ed.),Risk, Decision and Rationality. Dordrecht/Boston: Reidel, pp. 313–325.

    Google Scholar 

  • Jaffray, J.Y. (1989a). “Linear Utility Theory for Belief Functions”,Operations Research Letters 8, 107–112.

    Google Scholar 

  • Jaffray, J.Y. (1989b). “Coherents Bets under Partially Resolving Uncertainty and Belief Functions”.Theory and Decision 26, 99–105.

    Google Scholar 

  • Kahneman, D. and A. Tversky. (1979). “Prospect Theory: An Analysis of Decision Under Risk”,Econometrica 47, 263–291.

    Google Scholar 

  • Katzner, D.W. (1986). “Potential Surprise, Potential Confirmation and Probability”,Journal of Post Keynesian Economics 9(1), 58–78.

    Google Scholar 

  • Katzner, D.W. (1987). “More on the Distinction between Potential Confirmation and Probability”,Journal of Post Keynesian Economics 10(1), 65–83.

    Google Scholar 

  • Keynes, J.M. (1921).A Treatise on Probability. MacMillan.

  • Knight, F. (1921).Risk, Uncertainty and Profit. Houghton Mifflin.

  • Lawson, T., F.J. Cardim de Carvalho, and R.J. Rotheim. (1988). “Symposium on Probability and Uncertainty”,Journal of Post Keynesian Economics 11(1), 38–99.

    Google Scholar 

  • Ling, C.H. (1965). “Representation of Associative Functions”,Publ. Math. Debrecen 12, 189–212. Cited in Prade, H. (1982).Modèles Mathématiques de l'Imprécis et de l'Incertain en vue d'Applications au Raisonnement Nature, Thèse de Doctorat es Science, Université de Toulouse.

    Google Scholar 

  • Loomes, G. and R. Sugden. (1982). “Regret Theory: An Alternative of Rational Choice Under Uncertainty”,Economic Journal 92, 805–824.

    Google Scholar 

  • Luce, R.D. (1968). “On the Numerical Representation of Qualitative Conditional Probability”,Annals of Mathematical Statistics 39, 481–491.

    Google Scholar 

  • March, J.G. (1988). “Bounded Rationality, Ambiguity, and the Engineering of Choice”. In D.E. Bell, H. Raiffa, and A. Tversky,Decision Making, Descriptive, Normative, and Prescriptive Interactions. Cambridge: Cambridge University Press, pp. 33–57.

    Google Scholar 

  • Menger, K. (1942). “Statistical Metrics”,Proceedings of the National Academy of Sciences USA 28, 535–537. Cited in Prade, H. (1982).Modèles Mathématiques de l'Imprécis et de l'Incertain en vue d'Applications au Raisonnement Nature, Thèse de Doctorat es Science, Université de Toulouse.

    Google Scholar 

  • Munier, B. (1986). “Complexité et Décision Stratégique dans l'Incertain: Qué peut-on Conserver de la Théorie.” InMarchés, Capital et Incertitude, Essais en l'Honneur de Maurice Allais. Economica, 179–200.

  • Munier, B. (1989a). “Expected Utility versus Anticipated Utility: Where Do We Stand?”, Conférence au 21ème Colloque de l'Institut de Mathématiques Economiques de l'Université de Dijon, 24 Novembre 1989, 23 p. To appear in theInternational Journal of Fuzzy Sets and Systems (special issue in memoriam of C. Ponsard).

  • Munier, B. (1989b). Calcul Economique et Révision de la Théorie de la Décision en Avenir Risqué”,Revue d'Economie Politique 2, 276–306.

    Google Scholar 

  • Nguyen, H.T. (1977). “On Fuzziness and Linguistic Probabilities”,Journal of Mathematical Analysis and Applications 61, 658–671.

    Google Scholar 

  • Nguyen, H.T. (1978). “On Random Sets and Belief Functions”,Journal of Mathematical Analysis and Applications 65, 531–542.

    Google Scholar 

  • Nguyen, H.T. (1979). “Some Mathematical Tools for Linguistic Probabilities”,Fuzzy Sets and Systems 2, 53–65.

    Google Scholar 

  • Oblow, E.M. (1988). “Foundations of O-Theory: Measurements and Relation to Fuzzy Set Theory”,International Journal of General Systems 14, 357–378.

    Google Scholar 

  • Prade, H. (1982).Modèles Mathématiques de l'Imprécis et de l'Incertain en vue d'Applications au Raisonnement Naturel, Thèse de Doctorat es Sciences, Université de Toulouse.

  • Prade, H. (1983). “Notes et Commentaires”,Busefal 14, 127–128.

    Google Scholar 

  • Quiggin, J. (1982). “A Theory of Anticipated Utility”,Journal of Economic Behavior and Organization 3, 323–343.

    Google Scholar 

  • Ramsey, F.P. (1926). “Truth and Probability.” In D.H. Mellor (ed.),Foundations: Essays in Philosophy, Logic, Mathematics, and Economics, Routledge and Kegan, 178, pp. 58–100.

  • Rubinstein, A. (1988). “Finite Automata Play the Repeated Prisoner's Dilemma”,Journal of Economic Theory 39(1), 83–96.

    Google Scholar 

  • Savage, L.J. (1954).The Foundations of Statistics. New York: Wiley.

    Google Scholar 

  • Schweizer, B. and A. Sklar. (1960). “Statistical Metric Spaces”,Pacific Journal of Mathematics 10, 313–334. Cited by Dubois, D.Modèles Mathématiques de l'Imprécis et de l'Incertain en Vue d'Applications aux Techniques d'Aide à la Décision. Thèse de Doctorat es Sciences, Université de Grenoble.

    Google Scholar 

  • Shackle, G.L.S. (1961).Decision, Order, and Time in Human Affairs. Cambridge: Cambridge University Press.

    Google Scholar 

  • Shafer, G. (1976).A Mathematical Theory of Evidence. Princeton, NJ: Princeton University Press.

    Google Scholar 

  • Shafer, G. (1978). “Non-Additive Probabilities in the Works of Bernoulli and Lambert”,Archives for the History of Exact Sciences 19, 309–370.

    Google Scholar 

  • Shafer, G. (1981). “Constructive Probability”,Synthese 48, 1–59.

    Google Scholar 

  • Simon, H.A. (1978). “Rationality as Process and as Product of Thought”. In D.E. Bell, H. Raiffa, and A. Tversky (eds.),Decision Making, Descriptive, Normative, and Prescriptive Interactions. Cambridge: Cambridge University Press, pp. 58–77.

    Google Scholar 

  • Small, K.A. (1987). “A Discrete Choice Model for Ordered Alternatives”,Econometrica 55, 409–424.

    Google Scholar 

  • Smets, P. (1981). “Medical Diagnosis and Degrees of Belief”,Fuzzy Sets and Systems 5, 259–266.

    Google Scholar 

  • Smithson, M. (1989).Ignorance and Uncertainty. New York: Springer-Verlag.

    Google Scholar 

  • Sugeno, M. (1972). “Fuzzy Measures and Fuzzy Integrals”,Transactions of the Society of Instrument and Control Engineers 8, 218–226. Cited in Prade, H. (1982).Modèles Mathématiques de l'Imprécis et de l'Incertain en vue d'Applications au Raisonnement Nature Thèse de Doctorat es Science, Université de Toulouse.

    Google Scholar 

  • Suppes, P. (1974). “The Measurement of Belief”,Proceedings of the Royal Statistical Society (Series B) 36, 160–175.

    Google Scholar 

  • Suppes, P. (1981).Logique du Probable. Paris: Flammarion: Nouvelle Bibliothèque Scientifique.

    Google Scholar 

  • Thisse, J.F. and de Palma (1989). “Les Modèles de Choix Discrets”, Doc de Travail du BETA no8810, Université de Strasbourg, France.

    Google Scholar 

  • Trillas, E. (1979). Sobre Functiones de Negacion en la Teoria de Conjunctos”,Stochastica 3, 47–59.

    Google Scholar 

  • Vickers, D. (1986). “Time, Ignorance and Surprise”,Journal of Post Keynesian Economics 9(1), 48–57.

    Google Scholar 

  • Vuillemin, J. (1984).Nécessité ou Contingence: l'Aporie de Diodore. Paris: Editions de Minuit.

    Google Scholar 

  • Wakker, P. (1990). “Under Stochastic Dominance, Choquet-Expected Utility and Anticipated Utility are Identical,”Theory and Decision, forthcoming.

  • Walliser, B. (1985).Anticipations, Equilibres et Rationalité Economique. Paris: Calmann-Lévy.

    Google Scholar 

  • Walliser, B. (1989). “Instrumental Rationality and Cognitive Rationality”,Theory and Decision 27, 7–36.

    Google Scholar 

  • Yaari, M.E. (1987). “The Dual Theory of Choice Under Risk”,Econometrica 55(1), 95–116.

    Google Scholar 

  • Yager, R.R. (1980a). “On a General Class of Fuzzy Connectives”,Fuzzy Sets and Systems 4, 235–242.

    Google Scholar 

  • Yager, R.R. (1980b). “A Foundation for a Theory of Possibility”,Journal of Cybernetics 10, 177–204.

    Google Scholar 

  • Zadeh, L.A. (1975). “The Concept of a Linguistic Variable and its Application to Approximate Reasoning”,Information Sciences 8, 199–249 (I), 301–357 (II) and 9, 43–49 (III).

    Google Scholar 

  • Zadeh, L.A. (1978). “Fuzzy Sets as a Basis for a Theory of Possiblity”,Fuzzy Sets and Systems 1, 3–27.

    Google Scholar 

  • Zadeh, L.A. (1979). “On the Validity of Dempster's Rule of Combination of Evidence”,Working Paper 79/24, University of California, Berkeley.

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. GRID-Ecole Normale Supérieure, University of Paris 2, 92, rue d'Assas, 75006, Paris, France

    Antoine Billot

Authors
  1. Antoine Billot
    View author publications

    You can also search for this author in PubMed Google Scholar

Additional information

This article is a revised version of a paper presented during the FUR V Congress, Duke University, North Carolina, USA, June 10–13, 1990. I am indebted to Bertrand Munier, Alain Chateauneuf, Olivier Favereau, Jacques-François Thisse, Bernard Walliser, and Kip Viscusi for helpful comments on earlier versions of this article.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Billot, A. Cognitive rationality and alternative belief measures. J Risk Uncertainty 4, 299–324 (1991). https://doi.org/10.1007/BF00114159

Download citation

  • Issue Date:

  • DOI: https://doi.org/10.1007/BF00114159

Key words

Search

Navigation