Advertisement

Modeling Human Decision-Making: An Overview of the Brussels Quantum Approach

  • Diederik Aerts
  • Massimiliano Sassoli de BianchiEmail author
  • Sandro Sozzo
  • Tomas Veloz
Article

Abstract

We present the fundamentals of the quantum theoretical approach we have developed in the last decade to model cognitive phenomena that resisted modeling by means of classical logical and probabilistic structures, like Boolean, Kolmogorovian and, more generally, set theoretical structures. We firstly sketch the operational-realistic foundations of conceptual entities, i.e. concepts, conceptual combinations, propositions, decision-making entities, etc. Then, we briefly illustrate the application of the quantum formalism in Hilbert space to represent combinations of natural concepts, discussing its success in modeling a wide range of empirical data on concepts and their conjunction, disjunction and negation. Next, we naturally extend the quantum theoretical approach to model some long-standing ‘fallacies of human reasoning’, namely, the ‘conjunction fallacy’ and the ‘disjunction effect’. Finally, we put forward an explanatory hypothesis according to which human reasoning is a defined superposition of ‘emergent reasoning’ and ‘logical reasoning’, where the former generally prevails over the latter. The quantum theoretical approach explains human fallacies as the consequence of genuine quantum structures in human reasoning, i.e. ‘contextuality’, ‘emergence’, ‘entanglement’, ‘interference’ and ‘superposition’. As such, it is alternative to the Kahneman–Tversky research programme, which instead aims to explain human fallacies in terms of ‘individual heuristics and biases’.

Keywords

Quantum structures Cognition Concept theory Decision theory Human reasoning 

References

  1. Aerts, D. (2002). Being and change: Foundations of a realistic operational formalism. In D. Aerts, M. Czachor, & T. Durt (Eds.), Probing the structure of quantum mechanics: Nonlinearity, nonlocality, probability and axiomatics (pp. 71–110). Singapore: World Scientific.CrossRefGoogle Scholar
  2. Aerts, D., & Sozzo, S. (2011). Quantum structure in cognition. Why and how concepts are entangled. Quantum Interaction. Lecture Notes in Computer Science 7052, 116–127. Berlin: Springer.Google Scholar
  3. Aerts, D., & Sozzo, S. (2016). Quantum structure in cognition: Origins, developments, successes and expectations. In Haven, E., & Khrennikov, A. (Eds.) The Palgrave handbook of quantum models in social science: Applications and grand challenges (pp. 157–193). London: Palgrave & Macmillan.Google Scholar
  4. Aerts, D., Gabora, L., & Sozzo, S. (2013). Concepts and their dynamics: A quantum-theoretic modeling of human thought. Topics in Cognitive Science, 5, 737–772.Google Scholar
  5. Aerts, D., Geriente, S., Moreira, C., & Sozzo, S. (2018). Testing ambiguity and Machina preferences within a quantum-theoretic framework for decision-making. Journal of Mathematical Economics.  https://doi.org/10.1016/j.jmateco.2017.12.002.Google Scholar
  6. Aerts, D., Sassoli de Bianchi, M., & Sozzo, S. (2016). On the foundations of the Brussels operational-realistic approach to cognition. Frontiers in Physics.  https://doi.org/10.3389/fphy.2016.00017.Google Scholar
  7. Aerts, D., Sassoli de Bianchi, M., Sozzo, S., & Veloz, T. (2018). Modeling meaning associated with documental entities: Introducing the Brussels quantum approach.Google Scholar
  8. Aerts, D., Sozzo, S., & Veloz, T. (2015). Quantum structure of negation and conjunction in human thought. Frontiers in Psychology.  https://doi.org/10.3389/fpsyg.2015.01447.Google Scholar
  9. Aerts, D. (1986). A possible explanation for the probabilities of quantum mechanics. Journal of Mathematical Physics, 27, 202–210.CrossRefGoogle Scholar
  10. Aerts, D. (1999). Foundations of quantum physics: A general realistic and operational approach. International Journal of Theoretical Physics, 38, 289–358.CrossRefGoogle Scholar
  11. Aerts, D. (2009). Quantum structure in cognition. Journal of Mathematical Psychology, 53, 314–348.CrossRefGoogle Scholar
  12. Aerts, D. (2009a). Quantum particles as conceptual entities: A possible explanatory framework for quantum theory. Foundations of Science, 14, 361–411.CrossRefGoogle Scholar
  13. Aerts, D., & Aerts, S. (1995). Applications of quantum statistics in psychological studies of decision processes. Foundations of Science, 1, 85–97.CrossRefGoogle Scholar
  14. Aerts, D., Broekaert, J., Gabora, L., & Sozzo, S. (2013). Quantum structure and human thought. Behavioral and Brain Sciences, 36, 274–276.CrossRefGoogle Scholar
  15. Aerts, D., & Gabora, L. (2005). A theory of concepts and their combinations I: The structure of the sets of contexts and properties. Kybernetes, 34, 167–191.CrossRefGoogle Scholar
  16. Aerts, D., & Gabora, L. (2005). A theory of concepts and their combinations II: A Hilbert space representation. Kybernetes, 34, 192–221.CrossRefGoogle Scholar
  17. Aerts, D., Haven, E., & Sozzo, S. (2018). A proposal to extend expected utility in a quantum probabilistic framework. Economic Theory, 65, 1079–1109.CrossRefGoogle Scholar
  18. Aerts, D., & Sozzo, S. (2014). Quantum entanglement in conceptual combinations. International Journal of Theoretical Physics, 53, 3587–3603.CrossRefGoogle Scholar
  19. Aerts, D., & Sozzo, S. (2016). From ambiguity aversion to a generalized expected utility. Modeling preferences in a quantum probabilistic framework. Journal of Mathematical Psychology, 74, 117–127.CrossRefGoogle Scholar
  20. Aerts, D., Sozzo, S., & Veloz, T. (2015). New fundamental evidence of non-classical structure in the combination of natural concepts. Philosophical Transactions of the Royal Society A, 374, 20150095.CrossRefGoogle Scholar
  21. Aerts, D., Sozzo, S., & Veloz, T. (2015). Quantum structure in cognition and the foundations of human reasoning. International Journal of Theoretical Physics, 54, 4557–4569.CrossRefGoogle Scholar
  22. Aerts, D., Sozzo, S., & Veloz, T. (2015). Quantum nature of identity in human concepts: Bose-Einstein statistics for conceptual indistinguishability. International Journal of Theoretical Physics, 54, 4430–4443.CrossRefGoogle Scholar
  23. Alxatib, S., & Pelletier, J. (2011). On the psychology of truth gaps. In R. Nouwen, R. van Rooij, U. Sauerland, & H.-C. Schmitz (Eds.), Vagueness in communication (pp. 13–36). Berlin, Heidelberg: Springer.CrossRefGoogle Scholar
  24. Bruza, P. D., Wang, Z., & Busemeyer, J. R. (2015). Quantum cognition: A new theoretical approach to psychology. Trends in Cognitive Sciences, 19, 383–393.CrossRefGoogle Scholar
  25. Busemeyer, J. R., & Bruza, P. D. (2012). Quantum models of cognition and decision. Cambridge: Cambridge University Press.CrossRefGoogle Scholar
  26. Busemeyer, J. R., Pothos, E. M., Franco, R., & Trueblood, J. S. (2011). A quantum theoretical explanation for probability judgment errors. Psychological Review, 118, 193–218.CrossRefGoogle Scholar
  27. Costello, J., & Keane, M. T. (2000). Efficient creativity: Constraint-guided conceptual combination. Cognitive Science, 24, 299–349.CrossRefGoogle Scholar
  28. Dirac, P. A. M. (1958). Quantum mechanics (4th ed.). Oxford: Oxford University Press.Google Scholar
  29. Ellsberg, D. (1961). Risk, ambiguity, and the Savage axioms. Quarterly Journal of Economic, 75, 643–669.CrossRefGoogle Scholar
  30. Fisk, J. E. (2002). Judgments under uncertainty: Representativeness or potential surprise? British Journal of Psychology, 93, 431–449.CrossRefGoogle Scholar
  31. Fisk, J. E., & Pidgeon, N. (1996). Component probabilities and the conjunction fallacy: Resolving signed summation and the low component model in a contingent approach. Acta Psychologica, 94, 1–20.CrossRefGoogle Scholar
  32. Hampton, J. A. (1988a). Overextension of conjunctive concepts: Evidence for a unitary model for concept typicality and class inclusion. Journal of Experimental Psychology: Learning, Memory, and Cognition, 14, 12–32.Google Scholar
  33. Hampton, J. A. (1988b). Disjunction of natural concepts. Memory & Cognition, 16, 579–591.CrossRefGoogle Scholar
  34. Haven, E., & Khrennikov, A. Y. (2013). Quantum social science. Cambridge: Cambridge University Press.CrossRefGoogle Scholar
  35. Haven, E., & Khrennikov, A. (2016). Statistical and subjective interpretations of probability in quantum-like models of cognition and decision making. Journal of Mathematical Psychology, 74, 82–91.CrossRefGoogle Scholar
  36. Jauch, J. M. (1968). Foundations of quantum mechanics. Reading, MA: Addison Wesley.Google Scholar
  37. Kolmogorov, A. N. (1933). Grundbegriffe der Wahrscheinlichkeitrechnung, Ergebnisse Der Mathematik; translated as Foundations of Probability (p. 1950). New York: Chelsea Publishing Company.Google Scholar
  38. Kühberger, A., Kamunska, D., & Perner, J. (2001). The disjunction effect: Does it exist for two-step gambles? Organization Behavior and Human Decision Processes, 85, 250–264.CrossRefGoogle Scholar
  39. Kvam, P. D., Pleskac, T. J., Yu, S., & Busemeyer, J. R. (2016). Interference effects of choice on confidence: Quantum characteristics of evidence accumulation. Proceedings of the National Academy of Sciences, 112, 10645–10650.CrossRefGoogle Scholar
  40. Lambdin, C., & Burdsal, C. (2007). The disjunction effect reexamined: Relevant methodological issues and the fallacy of unspecified percentage comparisons. Organization Behavior and Human Decision Processes, 103, 268–276.CrossRefGoogle Scholar
  41. Lu, Y. (2015). The conjunction and disjunction fallacies: Explanations of the Linda problem by the equate-to-differentiate model. Integrative Psychological and Behavioral Science, 1–25.Google Scholar
  42. Machina, M. J. (2009). Risk, ambiguity, and the dark-dependence axioms. American Economic Review, 99, 385–392.CrossRefGoogle Scholar
  43. Melucci, M. (2015). Introduction to information retrieval and quantum mechanics. Berlin: Springer.CrossRefGoogle Scholar
  44. Morier, D., & Borgida, E. (1984). The conjunction fallacy: A task specific phenomenon? Personality and Social Psychology Bulletin, 10, 243–252.CrossRefGoogle Scholar
  45. Moro, R. (2009). On the nature of the conjunction fallacy. Synthese, 171, 1–24.CrossRefGoogle Scholar
  46. Murphy, G. L., & Medin, D. L. (1985). The role of theories in conceptual coherence. Psychological Review, 92, 289–316.CrossRefGoogle Scholar
  47. Nosofsky, R. (1992). Exemplars, prototypes, and similarity rules. In Healy, A., Kosslyn, S., & Shiffrin, R. (Eds.), From learning theory to connectionist theory: Essays in honor of William K. Estes. Hillsdale, NJ: Erlbaum.Google Scholar
  48. Nosofsky, R. (1988). Exemplar-based accounts of relations between classification, recognition, and typicality. Journal of Experimental Psychology: Learning, Memory, and Cognition, 14, 700–708.Google Scholar
  49. Osherson, D., & Smith, E. (1981). On the adequacy of prototype theory as a theory of concepts. Cognition, 9, 35–58.CrossRefGoogle Scholar
  50. Piron, C. (1976). Foundations of quantum physics. Reading, MA: Reading.CrossRefGoogle Scholar
  51. Pitowsky, I. (1989). Quantum probability, quantum logic. Lecture Notes in Physics (vol. 321). Berlin: Springer.Google Scholar
  52. Pothos, E. M., & Busemeyer, J. R. (2013). Can quantum probability provide a new direction for cognitive modeling? Behavioral and Brain Sciences, 36, 255–274.CrossRefGoogle Scholar
  53. Pothos, E. M., Busemeyer, J. R., Shiffrin, R. M., & Yearsley, J. M. (2017). The rational status of quantum cognition. Journal of Experimental Psychology: General, 146, 968–987.CrossRefGoogle Scholar
  54. Rosch, E. (1973). Natural categories. Cognitive Psychology, 4, 328–350.CrossRefGoogle Scholar
  55. Rosch, E. (1978). Principles of categorization. In E. Rosch & B. Lloyd (Eds.), Cognition and categorization (pp. 133–179). Hillsdale, NJ: Lawrence Erlbaum.Google Scholar
  56. Rosch, E. (1983). Prototype classification and logical classification: The two systems. In E. K. Scholnick (Ed.), New trends in conceptual representation: Challenges to Piaget theory? (pp. 133–159). New Jersey: Lawrence Erlbaum.Google Scholar
  57. Rumelhart, D. E., & Norman, D. A. (1988). Representation in memory. In R. C. Atkinson, R. J. Hernsein, G. Lindzey, & R. L. Duncan (Eds.), Stevens handbook of experimental psychology. New Jersey: Wiley.Google Scholar
  58. Savage, L. (1954). The foundations of statistics. New York: Wiley.Google Scholar
  59. Shah, A. K., & Oppenheimer, D. M. (2008). Heuristics made easy: An effort-reduction framework. Psychological Bulletin, 134, 207–222.CrossRefGoogle Scholar
  60. Sozzo, S. (2014). A quantum probability explanation in Fock space for borderline contradictions. Journal of Mathematical Psychology, 58, 1–12.CrossRefGoogle Scholar
  61. Sozzo, S. (2015). Conjunction and negation of natural concepts: A quantum-theoretic modeling. Journal of Mathematical Psychology, 66, 83–102.CrossRefGoogle Scholar
  62. Thagard, P., & Stewart, T. C. (2011). The AHA! experience: Creativity through emergent binding in neural networks. Cognitive Science, 35, 1–33.CrossRefGoogle Scholar
  63. Tversky, A., & Kahneman, D. (1974). Judgment under uncertainty: Heuristics and biases. Science, 185, 1124–1131.CrossRefGoogle Scholar
  64. Tversky, A., & Kahneman, D. (1983). Extension versus intuitive reasoning: The conjunction fallacy in probability judgment. Psychological Review, 90, 293–315.CrossRefGoogle Scholar
  65. Tversky, A., & Shafir, E. (1992). The disjunction effect in choice under uncertainty. Psychological Science, 3, 305–309.CrossRefGoogle Scholar
  66. Van Dantzig, S., Raffone, A., & Hommel, B. (2011). Acquiring contextualized concepts: A connectionist approach. Cognitive Science, 35, 1162–1189.CrossRefGoogle Scholar
  67. Wang, Z., Solloway, T., Shiffrin, R. M., & Busemeyer, J. R. (2014). Context effects produced by question orders reveal quantum nature of human judgments. Proceedings of the National Academy of Sciences, 111, 9431–9436.CrossRefGoogle Scholar
  68. Wittgenstein, L. (1953/2001). Philosophical investigations. Blackwell Publishing.Google Scholar
  69. Zadeh, L. (1982). A note on prototype theory and fuzzy sets. Cognition, 12, 291–297.CrossRefGoogle Scholar

Copyright information

© Springer Nature B.V. 2018

Authors and Affiliations

  • Diederik Aerts
    • 1
  • Massimiliano Sassoli de Bianchi
    • 2
    • 3
    Email author
  • Sandro Sozzo
    • 4
  • Tomas Veloz
    • 5
    • 6
  1. 1.Department of Mathematics, Center Leo Apostel for Interdisciplinary StudiesBrussels Free UniversityBrusselsBelgium
  2. 2.Center Leo Apostel for Interdisciplinary StudiesBrussels Free UniversityBrusselsBelgium
  3. 3.Laboratorio di Autoricerca di BaseBarbengoSwitzerland
  4. 4.School of Business and Centre IQSCSUniversity of LeicesterLeicesterUK
  5. 5.Departamento Ciencias Biológicas, Facultad Ciencias de la VidaUniversidad Andres BelloSantiagoChile
  6. 6.Instituto de Filosofía y Ciencias de la ComplejidadÑuñoaChile

Personalised recommendations