A Quantum-Conceptual Explanation of Violations of Expected Utility in Economics

  • Diederik Aerts
  • Jan Broekaert
  • Marek Czachor
  • Bart D’Hooghe
Part of the Lecture Notes in Computer Science book series (LNCS, volume 7052)

Abstract

The expected utility hypothesis is one of the building blocks of classical economic theory and founded on Savage’s Sure-Thing Principle. It has been put forward, e.g. by situations such as the Allais and Ellsberg paradoxes, that real-life situations can violate Savage’s Sure-Thing Principle and hence also expected utility. We analyze how this violation is connected to the presence of the ‘disjunction effect’ of decision theory and use our earlier study of this effect in concept theory to put forward an explanation of the violation of Savage’s Sure-Thing Principle, namely the presence of ‘quantum conceptual thought’ next to ‘classical logical thought’ within a double layer structure of human thought during the decision process. Quantum conceptual thought can be modeled mathematically by the quantum mechanical formalism, which we illustrate by modeling the Hawaii problem situation — a well-known example of the disjunction effect — generated by the entire conceptual landscape surrounding the decision situation.

Keywords

Expected utility disjunction effect quantum modeling quantum conceptual though ambiguity aversion concept combinations 

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References

  1. 1.
    Aerts, D.: Quantum interference and superposition in cognition: Development of a theory for the disjunction of concepts (2007a), Archive Reference and Link: http://arxiv.org/abs/0705.0975
  2. 2.
    Aerts, D.: General quantum modeling of combining concepts: A quantum field model in Fock space (2007b), Archive reference and link: http://arxiv.org/abs/0705.1740
  3. 3.
    Aerts, D.: Quantum structure in cognition. J. Math. Psy. 53, 314–348 (2009)Google Scholar
  4. 4.
    Aerts, D., Aerts, S.: Applications of quantum statistics in psychological studies of decision processes. Foundations of Science 1, 85–97 (1994)MathSciNetCrossRefMATHGoogle Scholar
  5. 5.
    Aerts, D., Apostel, L., De Moor, B., Hellemans, S., Maex, E., Van Belle, H., Van der Veken, J.: Worldviews, from Fragmentation towards Integration. VUBPress (1994)Google Scholar
  6. 6.
    Aerts, D., Broekaert, J., Gabora, L.: A case for applying an abstracted quantum formalism to cognition. New Ideas in Psychology 29, 136–146 (2010)CrossRefGoogle Scholar
  7. 7.
    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)Google 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 (2005a)CrossRefMATHGoogle Scholar
  9. 9.
    Aerts, D., Gabora, L.: A theory of concepts and their combinations II: A Hilbert space representation. Kybernetes 34, 192–221 (2005b)CrossRefMATHGoogle Scholar
  10. 10.
    Aerts, D., Van Belle, H., Van der Veken, J. (eds.): Worldviews and the Problem of Synthesis. Springer, Dordrecht (1999)Google Scholar
  11. 11.
    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
  12. 12.
    Bagassi, M., Macchi, L.: The ‘vanishing’ of the disjunction effect by sensible procrastination. Mind & Society 6, 41–52 (2007)CrossRefGoogle Scholar
  13. 13.
    Busemeyer, J.R., Wang, Z., Townsend, J.T.: Quantum dynamics of human decision-making. Journal of Mathematical Psychology 50, 220–241 (2006)MathSciNetCrossRefMATHGoogle Scholar
  14. 14.
    Busemeyer, J.R., Pothos, E., Franco, R., Trueblood, J.: A quantum theoretical explanation for probability judgment ‘errors’. Psychological Review 118(2), 193–218 (2011)CrossRefGoogle Scholar
  15. 15.
    Danilov, V.I., Lambert-Mogiliansky, A.: Measurable systems and behavioral sciences. Mathematical Social Sciences 55(3), 315–340 (2008)MathSciNetCrossRefMATHGoogle Scholar
  16. 16.
    Ellsberg, D.: Risk, ambiguity, and the Savage axioms. Quarterly Journal of Economics 75(4), 643–669 (1961)CrossRefMATHGoogle Scholar
  17. 17.
    Franco, R.: Risk, Ambiguity and Quantum Decision Theory (2007), Archive reference and link: http://arxiv.org/abs/0711.0886
  18. 18.
    Gabora, L., Aerts, D.: Contextualizing concepts using a mathematical generalization of the quantum formalism. Journal of Experimental and Theoretical Artificial Intelligence 14, 327–358 (2002)CrossRefMATHGoogle Scholar
  19. 19.
    Hampton, J.A.: Disjunction of natural concepts. Memory & Cognition 16, 579–591 (1988)CrossRefGoogle Scholar
  20. 20.
    Khrennikov, A.: Quantum-like model of cognitive decision making and information processing. Biosystems 95, 179–187 (2008)CrossRefGoogle Scholar
  21. 21.
    Pothos, E.M., Busemeyer, J.R.: A quantum probability explanation for violations of ‘rational’ decision theory. Proceedings of the Royal Society B (2009)Google Scholar
  22. 22.
    Savage, L.J.: The Foundations of Statistics. Wiley, New-York (1954)MATHGoogle Scholar
  23. 23.
    Tversky, A., Shafir, E.: The disjunction effect in choice under uncertainty. Psychological Science 3, 305–309 (1992)CrossRefGoogle Scholar
  24. 24.
    von Neumann, J., Morgenstern, O.: Theory of Games and Economic Behavior. Princeton University Press, Princeton (1944)MATHGoogle Scholar
  25. 25.
    Yukalov, V.I., Sornette, D.: Decision theory with prospect interference and entanglement. Theory and Decision 70, 283–328 (2010)MathSciNetCrossRefMATHGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2011

Authors and Affiliations

  • Diederik Aerts
    • 1
  • Jan Broekaert
    • 1
  • Marek Czachor
    • 2
  • Bart D’Hooghe
    • 1
  1. 1.Center Leo ApostelBrussels Free UniversityBrusselsBelgium
  2. 2.Katedra Fizyki Teoretycznej i Informatyki KwantowejPolitechnika GdanskaGdanskPoland

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