A Quantum Cognition Analysis of the Ellsberg Paradox

  • Diederik Aerts
  • Bart D’Hooghe
  • Sandro Sozzo
Part of the Lecture Notes in Computer Science book series (LNCS, volume 7052)


The expected utility hypothesis is one of the foundations of classical approaches to economics and decision theory and Savage’s Sure-Thing Principle is a fundamental element of it. It has been put forward that real-life situations exist, illustrated by the Allais and Ellsberg paradoxes, in which the Sure-Thing Principle is violated, and where also the expected utility hypothesis does not hold. We have recently presented strong arguments for the presence of a double layer structure, a classical logical and a quantum conceptual, in human thought and that the quantum conceptual mode is responsible of the above violation. We consider in this paper the Ellsberg paradox, perform an experiment with real test subjects on the situation considered by Ellsberg, and use the collected data to elaborate a model for the conceptual landscape surrounding the decision situation of the paradox. We show that it is the overall conceptual landscape which gives rise to a violation of the Sure-Thing Principle and leads to the paradoxical situation discovered by Ellsberg.


Sure-Thing Principle Ellsberg paradox conceptual landscape quantum cognition 


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. 1.
    von Neumann, J., Morgenstern, O.: Theory of Games and Economic Behavior. Princeton University Press, Princeton (1944)MATHGoogle Scholar
  2. 2.
    Savage, L.J.: The Foundations of Statistics. Wiley, New York (1954)MATHGoogle Scholar
  3. 3.
    Allais, M.: Le Comportement de l’Homme Rationnel Devant le Risque: Critique des Postulats et Axiomes de l’École Américaine. Econometrica 21, 503–546 (1953)MathSciNetCrossRefMATHGoogle Scholar
  4. 4.
    Ellsberg, D.: Risk, Ambiguity, and the Savage Axioms. Quart. J. Econ. 75(4), 643–669 (1961)CrossRefMATHGoogle Scholar
  5. 5.
    Hampton, J.A.: Disjunction of Natural Concepts. Memory & Cognition 16, 579–591 (1988)CrossRefGoogle Scholar
  6. 6.
    Tversky, A., Shafir, E.: The Disjunction Effect in Choice Under Uncertainty. Psych. Sci. 3, 305–309 (1992)CrossRefGoogle Scholar
  7. 7.
    Gabora, L., Aerts, D.: Contextualizing Concepts Using a Mathematical Generalization of the Quantum Formalism. J. Exp. Theor. Art. Int. 14, 327–358 (2002)CrossRefMATHGoogle Scholar
  8. 8.
    Aerts, D., Gabora, L.: A Theory of Concepts and Their Combinations I: The Structure of the Sets of Contexts and Properties. Kybernetes 34, 167–191 (2005)CrossRefMATHGoogle Scholar
  9. 9.
    Aerts, D., Gabora, L.: A Theory of Concepts and Their Combinations II: A Hilbert Space Representation. Kybernetes 34, 192–221 (2005)CrossRefMATHGoogle Scholar
  10. 10.
    Aerts, D.: Quantum Structure in Cognition. J. Math. Psych. 53, 314–348 (2009)MathSciNetCrossRefMATHGoogle Scholar
  11. 11.
    Aerts, D., D’Hooghe, B.: Classical Logical Versus Quantum Conceptual Thought: Examples in Economics, Decision Theory and Concept Theory. In: Bruza, P., Sofge, D., Lawless, W., van Rijsbergen, K., Klusch, M. (eds.) QI 2009. LNCS, vol. 5494, pp. 128–142. Springer, Heidelberg (2009)CrossRefGoogle Scholar
  12. 12.
    Aerts, D.: Quantum Interference and Superposition in Cognition: Development of a Theory for the Disjunction of Concepts. In: Aerts, D., D’Hooghe, B., Note, N. (eds.) Worldviews, Science and Us: Bridging Knowledge and Its Implications for Our Perspectives of the World. World Scientific, Singapore (2011) (in print) Archive reference and link, http://arxiv.org/abs/0705.1740 (2007)Google Scholar
  13. 13.
    Aerts, D.: General Quantum Modeling of Combining Concepts: A Quantum Field Model in Fock Space (2007), Archive reference and link: http://arxiv.org/abs/0705.1740
  14. 14.
    Aerts, D., Broekaert, J., Czachor, M., D’Hooghe, B.: A Quantum-Conceptual Explanation of Violations of Expected Utility in Economics. In: Song, D., et al. (eds.) QI 2011. LNCS, vol. 7052, pp. 192–198. Springer, Heidelberg (2011)Google Scholar
  15. 15.
    Busemeyer, J.R., Wang, Z., Townsend, J.T.: Quantum Dynamics of Human Decision-Making. J. Math. Psych. 50, 220–241 (2006)MathSciNetCrossRefMATHGoogle Scholar
  16. 16.
    Franco, R.: Risk, Ambiguity and Quantum Decision Theory(2007), Archive reference and link: http://arxiv.org/abs/0711.0886
  17. 17.
    Khrennikov, A.Y., Haven, E.: Quantum Mechanics and Violations of the Sure-Thing Principle: The Use of Probability Interference and Other Concepts. J. Math. Psych. 53, 378–388 (2009)MathSciNetCrossRefMATHGoogle Scholar
  18. 18.
    Pothos, E.M., Busemeyer, J.R.: A Quantum Probability Explanation for Violations of ‘Rational’ Decision Theory. Proc. Roy. Soc. B 276, 2171–2178 (2009)CrossRefGoogle Scholar
  19. 19.
    Knight, F.H.: Risk, Uncertainty and Profit. Houghton Mifflin, Boston (1921)Google Scholar
  20. 20.
    Aerts, D., Sozzo, S.: Contextual risk and its relevance in economics. Accepted for Publication in J. Eng. Sci. Tech. Rev. (2011)Google Scholar
  21. 21.
    Aerts, D., Sozzo, J.: A contextual risk model for the Ellsberg paradox. Accepted for Publication in J. Eng. Sci. Tech. Rev. (2011)Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2011

Authors and Affiliations

  • Diederik Aerts
    • 1
  • Bart D’Hooghe
    • 1
  • Sandro Sozzo
    • 1
  1. 1.Center Leo ApostelBrussels Free UniversityBrusselsBelgium

Personalised recommendations