Skip to main content
SpringerLink
Log in

Quantum Experimental Data in Psychology and Economics

  • Published:
International Journal of Theoretical Physics Aims and scope Submit manuscript

Abstract

We prove a theorem which shows that a collection of experimental data of probabilistic weights related to decisions with respect to situations and their disjunction cannot be modeled within a classical probabilistic weight structure in case the experimental data contain the effect referred to as the ‘disjunction effect’ in psychology. We identify different experimental situations in psychology, more specifically in concept theory and in decision theory, and in economics (namely situations where Savage’s Sure-Thing Principle is violated) where the disjunction effect appears and we point out the common nature of the effect. We analyze how our theorem constitutes a no-go theorem for classical probabilistic weight structures for common experimental data when the disjunction effect is affecting the values of these data. We put forward a simple geometric criterion that reveals the non classicality of the considered probabilistic weights and we illustrate our geometrical criterion by means of experimentally measured membership weights of items with respect to pairs of concepts and their disjunctions. The violation of the classical probabilistic weight structure is very analogous to the violation of the well-known Bell inequalities studied in quantum mechanics. The no-go theorem we prove in the present article with respect to the collection of experimental data we consider has a status analogous to the well known no-go theorems for hidden variable theories in quantum mechanics with respect to experimental data obtained in quantum laboratories. Our analysis puts forward a strong argument in favor of the validity of using the quantum formalism for modeling the considered psychological experimental data as considered in this paper.

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

  1. Bruza, P.D., Gabora, L. (eds.): Special Issue: Quantum Cognition. J. Math. Psychol. 53, 303–452 (2009)

    Article  MATH  MathSciNet  Google Scholar 

  2. Bruza, P.D., Lawless, W., van Rijsbergen, C.J., Sofge, D. (eds.): Proceedings of the AAAI Spring Symposium on Quantum Interaction, March 26–28, 2007, Stanford University, SS-07-08. AAAI Press, Menlo Park (2007)

    Google Scholar 

  3. Bruza, P.D., Lawless, W., van Rijsbergen, C.J., Sofge, D., Coecke, B., Clark, S. (eds.): Proceedings of the Second Quantum Interaction Symposium, University of Oxford, March 26–28, 2008. College Publications, London (2008)

    Google Scholar 

  4. Bruza, P.D., Sofge, D., Lawless, W., van Rijsbergen, C.J., Klusch, M. (eds.): Proceedings of the Third International Symposium, QI 2009, Saarbrücken, Germany, March 25–27, 2009. Lecture Notes in Computer Science, vol. 5494. Springer, Berlin, Heidelberg (2009)

    Google Scholar 

  5. Aerts, D., Aerts, S.: Applications of quantum statistics in psychological studies of decision processes. Found. Sci. 1, 85–97 (1994). Reprinted in: B.C. van Fraassen (ed.), Topics in the Foundation of Statistics, Springer, Dordrecht

    MathSciNet  Google Scholar 

  6. Aerts, D., Broekaert, J., Smets, S.: The liar paradox in a quantum mechanical perspective. Found. Sci. 4, 115–132 (1999)

    Article  MATH  MathSciNet  Google Scholar 

  7. Aerts, D., Broekaert, J., Smets, S.: A quantum structure description of the liar paradox. Int. J. Theor. Phys. 38, 3231–3239 (1999)

    Article  MATH  MathSciNet  Google Scholar 

  8. Aerts, D., Aerts, S., Broekaert, J., Gabora, L.: The violation of Bell inequalities in the macroworld. Found. Phys. 30, 1387–1414 (2000)

    Article  MathSciNet  Google Scholar 

  9. Gabora, L., Aerts, D.: Contextualizing concepts using a mathematical generalization of the quantum formalism. J. Exp. Theor. Artif. Intell. 14, 327–358 (2002)

    Article  MATH  Google Scholar 

  10. Aerts, D., Czachor, M.: Quantum aspects of semantic analysis and symbolic artificial intelligence. J. Phys. A 37, L123–L132 (2004)

    Article  MATH  MathSciNet  ADS  Google Scholar 

  11. 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)

    Article  MATH  Google Scholar 

  12. Aerts, D., Gabora, L.: A theory of concepts and their combinations II: a Hilbert space representation. Kybernetes 34, 192–221 (2005)

    Article  MATH  Google Scholar 

  13. Broekaert, J., Aerts, D., D’Hooghe, B.: The generalised Liar Paradox: a quantum model and interpretation. Found. Sci. 11, 399–418 (2006)

    Article  MATH  MathSciNet  Google Scholar 

  14. Aerts, D.: General quantum modeling of combining concepts: a quantum field model in Fock space. Archive address and link: http://arxiv.org/abs/0705.1740 (2007)

  15. Aerts, D.: Quantum structure in cognition. J. Math. Psychol. 53, 314–348 (2009)

    Article  MATH  MathSciNet  Google Scholar 

  16. Aerts, D.: Quantum particles as conceptual entities: a possible explanatory framework for quantum theory. Found. Sci. 14, 361–411 (2009)

    Article  MATH  MathSciNet  Google Scholar 

  17. Aerts, D., Aerts, S., Gabora, L.: Experimental evidence for quantum structure in cognition. In: Bruza, P.D., Sofge, D., Lawless, W., van Rijsbergen, C.J., Klusch, M. (eds.) Proceedings of QI 2009-Third International Symposium on Quantum Interaction. Lecture Notes in Computer Science, vol. 5494, pp. 59–70. Springer, Berlin, Heidelberg (2009)

    Google Scholar 

  18. Aerts, D., D’Hooghe, B.: Classical logical versus quantum conceptual thought: examples in economics, decision theory and concept theory. In: Bruza, P.D., Sofge, D., Lawless, W., van Rijsbergen, C.J., Klusch, M. (eds.) Proceedings of QI 2009-Third International Symposium on Quantum Interaction. Lecture Notes in Computer Science, vol. 5494, pp. 128–142 Springer, Berlin, Heidelberg (2009)

    Google Scholar 

  19. 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 (2010)

    Google Scholar 

  20. Aerts, D.: Interpreting quantum particles as conceptual entities. Int. J. Theor. Phys. (2010). doi:10.1007/s10773-010-0440-0

  21. Aerts, D., Broekaert, J., Gabora, L.: A case for applying an abstracted quantum formalism to cognition. New Ideas Psychol. (2010). doi:10.1016/j.newideapsych.2010.06.002

  22. Aerts, D., D’Hooghe, B.: A quantum-conceptual explanation of violations of expected utility in economics. 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 (2010)

    Google Scholar 

  23. von Neumann, J.: Mathematische Grundlagen der Quantenmechanik. Chapter IV.1,2. Springer, Berlin. (1932)

    MATH  Google Scholar 

  24. Einstein, A., Podolsky, B., Rosen, N.: Can quantum-mechanical description of physical reality be considered complete? Phys. Rev. 47, 777–780 (1935)

    Article  MATH  ADS  Google Scholar 

  25. Bohr, N.: Can quantum-mechanical description of physical reality be considered complete? Phys. Rev. 48, 696–702 (1935)

    Article  MATH  ADS  Google Scholar 

  26. Gleason, A.M.: Measures on the closed subspaces of a Hilbert space. J. Math. Mech. 6, 885–893 (1957)

    MATH  MathSciNet  Google Scholar 

  27. Jauch, J., Piron, C.: Can hidden variables be excluded from quantum mechanics? Helv. Phys. Acta 36, 827–837 (1963)

    MATH  MathSciNet  Google Scholar 

  28. Bell, J.S.: On the Einstein Podolsky Rosen Paradox. Physics 1, 195–200 (1964)

    Google Scholar 

  29. Bohm, D., Bub, J.: A proposed solution of the measurement problem in quantum mechanics by a hidden variable theory. Rev. Mod. Phys. 38, 453–469 (1966)

    Article  MATH  MathSciNet  ADS  Google Scholar 

  30. Bell, J.S.: On the problem of hidden variables in quantum mechanics. Rev. Mod. Phys. 38, 447–452 (1966)

    Article  MATH  ADS  Google Scholar 

  31. Kochen, S., Specker, E.P.: The problem of hidden variables in quantum mechanics. J. Math. Mech. 17, 59–87 (1967)

    MATH  MathSciNet  Google Scholar 

  32. Jauch, J.M., Piron, C.: Hidden variables revisited. Rev. Mod. Phys. 40, 228–229 (1968)

    Article  ADS  Google Scholar 

  33. Gudder, S.P.: Hidden variables in quantum mechanics reconsidered. Rev. Mod. Phys. 40, 229–231 (1968)

    Article  ADS  Google Scholar 

  34. Bohm, D., Bub, J.: On hidden variables-A reply to comments by Jauch and Piron and by Gudder. Rev. Mod. Phys. 40, 235–236 (1968)

    Article  ADS  Google Scholar 

  35. Clauser, J.F., Horne, M.A., Shimony, A., Holt, R.A.: Proposed experiment to test local hidden-variable theories. Phys. Rev. Lett. 23, 880–884 (1969)

    Article  ADS  Google Scholar 

  36. Gudder, S.P.: On hidden variable theories. J. Math. Phys. 11, 431–436 (1970)

    Article  MATH  MathSciNet  ADS  Google Scholar 

  37. Clauser, J.F., Horne, M.A.: Experimental consequences of objective local theories. Phys. Rev. D 10, 526–535 (1974)

    Article  ADS  Google Scholar 

  38. Accardi, L., Fedullo, A.: On the statistical meaning of complex numbers in quantum mechanics. Lett. Nuovo Cimento 34, 161–172 (1982)

    Article  MathSciNet  Google Scholar 

  39. Aspect, A., Grangier, P., Roger, G.: Experimental realization of Einstein–Podolsky–Rosen–Bohm Gedankenexperiment: a new violation of Bell’s Inequalities. Phys. Rev. Lett. 49, 91–94 (1982)

    Article  ADS  Google Scholar 

  40. Aspect, A., Dalibard, J., Roger, G.: Experimental test of Bell’s Inequalities using time-varying analyzers. Phys. Rev. Lett. 49, 1804–1807 (1982)

    Article  MathSciNet  ADS  Google Scholar 

  41. Kolmogorov, A.N.: Foundations of the Theory of Probability. Chelsea Publishing, New York (1956)

    MATH  Google Scholar 

  42. Accardi, L.: The probabilistic roots of the quantum mechanical paradoxes. In: Diner, S., Fargue, D., Lochak, G., Selleri, F. (eds.) The Wave-Particle Dualism: A Tribute to Louis de Broglie on his 90th Birthday, pp. 297–330. Springer, Dordrecht (1984)

    Google Scholar 

  43. Aerts, D.: A possible explanation for the probabilities of quantum mechanics and a macroscopical situation that violates Bell inequalities. In: Mittelstaedt, P., Stachow, E.W. (eds.): Recent Developments in Quantum Logic, Grundlagen der Exacten Naturwissenschaften, Wissenschaftverlag, vol. 6, pp. 235–251. Bibliographisches Institut, Mannheim (1985)

    Google Scholar 

  44. Aerts, D.: A possible explanation for the probabilities of quantum mechanics. J. Math. Phys. 27, 202–210 (1986)

    Article  MathSciNet  ADS  Google Scholar 

  45. Aerts, D.: The origin of the non-classical character of the quantum probability model. In: Blanquiere, A., Diner, S., Lochak, G. (eds.) Information, Complexity, and Control in Quantum Physics, pp. 77–100. Springer, Wien-New York (1987)

    Google Scholar 

  46. Redhead, M.: Incompleteness, Nonlocality and Realism. Clarendon Press, Oxford (1987)

    MATH  Google Scholar 

  47. Pitowsky, I.: Quantum Probability, Quantum Logic. Lecture Notes in Physics, vol. 321. Springer, Heidelberg (1989)

    MATH  Google Scholar 

  48. Hampton, J.A.: Overextension of conjunctive concepts: Evidence for a unitary model for concept typicality and class inclusion. J. Exp. Psychol. Learn. Mem. Cogn. 14, 12–32 (1988)

    Article  Google Scholar 

  49. Hampton, J.A.: Inheritance of attributes in natural concept conjunctions. Mem. Cogn. 15, 55–71 (1987)

    Google Scholar 

  50. Hampton, J.A.: The combination of prototype concepts. In: Schwanenugel, P. (ed.) The Psychology of Word Meanings. Erlbaum, Hillsdale (1991)

    Google Scholar 

  51. Storms, G., De Boeck, P., Van Mechelen, I., Geeraerts, D.: Dominance and non-commutativity effects in concept conjunctions: extensional or intensional basis? Mem. Cogn. 21, 752–762 (1993)

    Google Scholar 

  52. Hampton, J.A.: Conjunctions of visually-based categories: overextension and compensation. J. Exp. Psychol. Learn. Mem. Cogn. 22, 378–396 (1996)

    Article  Google Scholar 

  53. Hampton, J.A.: Conceptual combination: conjunction and negation of natural concepts. Mem. Cogn. 25, 888–909 (1997)

    Google Scholar 

  54. Storms, G., de Boeck, P., Hampton, J.A., van Mechelen, I.: Predicting conjunction typicalities by component typicalities. Psychon. Bull. Rev. 6, 677–684 (1999)

    Google Scholar 

  55. Tversky, A., Kahneman, D.: Judgments of and by representativeness. In: Kahneman, D., Slovic, P., Tversky, A. (eds.): Judgment under Uncertainty: Heuristics and Biases. Cambridge University Press, Cambridge (1982)

    Google Scholar 

  56. Tversky, A., Kahneman, D.: Extension versus intuitive reasoning: the conjunction fallacy in probability judgment. Psychol. Rev. 90, 293–315 (1983)

    Article  Google Scholar 

  57. Hampton, J.A.: Disjunction of natural concepts. Mem. Cogn. 16, 579–591 (1988)

    Google Scholar 

  58. Carlson, B.W., Yates, J.F.: Disjunction errors in qualitative likelihood judgment. Organ. Behav. Hum. Decis. Process. 44, 368–379 (1989)

    Article  Google Scholar 

  59. Tversky, A., Shafir, E.: The disjunction effect in choice under uncertainty. Psychol. Sci. 3, 305–309 (1992)

    Article  Google Scholar 

  60. Bar-Hillel, M., Neter, E.: How alike is it versus how likely is it: a disjunction fallacy in probability judgments. J. Personal. Soc. Psychol. 65, 1119–1131 (1993)

    Article  Google Scholar 

  61. Croson, R.T.A.: The disjunction effect and reason-based choice in games. Organ. Behav. Hum. Decis. Process. 80, 118–133 (1999)

    Article  Google Scholar 

  62. Kühberger, A., Komunska, D., Perner, J.: The disjunction effect: Does it exist for two-step gambles? Organ. Behav. Hum. Decis. Process. 85, 250–264 (2001)

    Article  Google Scholar 

  63. Li, S., Taplin, J.E.: Examining whether there is a disjunction effect in prisoner’s dilemma games. Chin. J. Psychol. 44, 25–46 (2002)

    Google Scholar 

  64. van Dijk, E., Zeelenberg, M.: The discounting of ambiguous information in economic decision making. J. Behav. Decis. Mak. 16, 341–352 (2003)

    Article  Google Scholar 

  65. van Dijk, E., Zeelenberg, M.: The dampening effect of uncertainty on positive and negative emotions. J. Behav. Decis. Mak. 19, 171–176 (2006)

    Article  Google Scholar 

  66. Bauer, M.I., Johnson-Laird, P.N.: How diagrams can improve reasoning. Psychol. Sci. 4, 372–378 (2006)

    Article  Google Scholar 

  67. Lambdin, C., Burdsal, C.: The disjunction effect reexamined: relevant methodological issues and the fallacy of unspecified percentage comparisons. Organ. Behav. Hum. Decis. Process. 103, 268–276 (2007)

    Article  Google Scholar 

  68. Bagassi, M., Macchi, L.: The ‘vanishing’ of the disjunction effect by sensible procrastination. Mind & Society 6, 41–52 (2007)

    Article  Google Scholar 

  69. Hristova, E., Grinberg, M.: Disjunction effect in prisoner’s dilemma: Evidences from an eye-tracking study. In: Cogsci 2008, Proceedings, Washington, July 22–26 (2008)

  70. 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)

    Article  MATH  MathSciNet  Google Scholar 

  71. Ellsberg, D.: Risk, ambiguity, and the savage axioms. Q. J. Economics 75, 643–669 (1961)

    Article  Google Scholar 

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

    MATH  Google Scholar 

  73. von Neumann, J., Morgenstern, O.: Theory of Games and Economic Behavior. Princeton University Press, Princeton (1944)

    MATH  Google Scholar 

  74. Busemeyer, J.R., Wang, Z., Townsend, J.T.: Quantum dynamics of human decision-making. J. Math. Psychol. 50, 220–241 (2006)

    Article  MATH  MathSciNet  Google Scholar 

  75. Pothos, E.M., Busemeyer, J.R.: A quantum probability explanation for violations of ‘rational’ decision theory. Proc. R. Soc. B (2009)

  76. Khrennikov, A., Haven, E.: Quantum mechanics and violations of the sure-thing principle: the use of probability interference and other concepts. J. Math. Psychol. 53, 378–388 (2009)

    Article  MATH  MathSciNet  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Leo Apostel Center for Interdisciplinary Studies, Brussels Free University, Brussels, Belgium

    Diederik Aerts & Bart D’Hooghe

  2. School of Management, University of Leicester, Leicester, UK

    Emmanuel Haven

Authors
  1. Diederik Aerts
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Bart D’Hooghe
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Emmanuel Haven
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Emmanuel Haven.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Aerts, D., D’Hooghe, B. & Haven, E. Quantum Experimental Data in Psychology and Economics. Int J Theor Phys 49, 2971–2990 (2010). https://doi.org/10.1007/s10773-010-0477-0

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s10773-010-0477-0

Keywords

Search

Navigation