Are Quantum Models for Order Effects Quantum?


The application of principles of Quantum Mechanics in areas outside of physics has been getting increasing attention in the scientific community in an emergent disciplined called Quantum Cognition. These principles have been applied to explain paradoxical situations that cannot be easily explained through classical theory. In quantum probability, events are characterised by a superposition state, which is represented by a state vector in a N-dimensional vector space. The probability of an event is given by the squared magnitude of the projection of this superposition state into the desired subspace. This geometric approach is very useful to explain paradoxical findings that involve order effects, but do we really need quantum principles for models that only involve projections? This work has two main goals. First, it is still not clear in the literature if a quantum projection model has any advantage towards a classical projection. We compared both models and concluded that the Quantum Projection model achieves the same results as its classical counterpart, because the quantum interference effects play no role in the computation of the probabilities. Second, it intends to propose an alternative relativistic interpretation for rotation parameters that are involved in both classical and quantum models. In the end, instead of interpreting these parameters as a similarity measure between questions, we propose that they emerge due to the lack of knowledge concerned with a personal basis state and also due to uncertainties towards the state of world and towards the context of the questions.

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  1. 1.

    Asano, M., Basieva, I., Khrennikov, A., Ohya, M., Tanaka, Y., Yamato, I.: Quantum-like model of diauxie in escherichia coli: operational description of precultivation effect. J. Theor. Biol. 314, 130–137 (2012)

    Article  Google Scholar 

  2. 2.

    Asano, M., Khrennikov, A., Ohya, M.: Quantum adaptative biology: From genetics to cognition. Springer (2015)

  3. 3.

    Basieva, I., Khrennikov, A., Ohya, M., Yamato, I.: Quantum-like interference effect in gene expression: glucose-lactose destructive interference. Syst. Synth. Biol. 5, 59–68 (2011)

    Article  Google Scholar 

  4. 4.

    Birnbaum, M.: New paradoxes of risky decision making. Psychol. Rev. 115, 463–501 (2008)

    Article  Google Scholar 

  5. 5.

    Bruza, P., Kitto, K., Nelson, D., McEvoy, C.: Is there something quantum-like about the human mental lexicon? J. Math. Psychol. 53, 362–377 (2009)

    Article  MATH  MathSciNet  Google Scholar 

  6. 6.

    Bruza, P., Zuccon, G., Sitbon, L.: Modelling the information seeking user by the decisions they make Proceedings of the 36th Annual ACM SIGIR Conference: Workshop on Modeling User Behavior for Information Retrieval Evaluation (MUBE 2013) (2013)

  7. 7.

    Busemeyer, J., Bruza, P.: Quantum model of cognition and decision. Cambridge University Press (2012)

  8. 8.

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

    Article  MATH  MathSciNet  Google Scholar 

  9. 9.

    Busemeyer, J., Wang, Z., Lambert-Mogiliansky, A.: Empirical comparison of markov and quantum models of decision making. J. Math. Psychol. 53, 423–433 (2009)

    Article  MATH  MathSciNet  Google Scholar 

  10. 10.

    Busemeyer, J., Wang, Z., Shiffrin, R.: Bayesian model comparison favors quantum over standard decision theory account of dynamic inconsistencies. Decision 2, 1–12 (2015)

    Article  Google Scholar 

  11. 11.

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

    Article  Google Scholar 

  12. 12.

    Haven, E., Khrennikov, A.: Quantum social science. Cambridge University Press (2013)

  13. 13.

    Khrennikov, A.: Classical and quantum-like randomness and the financial market Coping with the Complexity of Economics. Springer (2009)

  14. 14.

    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 

  15. 15.

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

    Article  Google Scholar 

  16. 16.

    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 

  17. 17.

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

    Google Scholar 

  18. 18.

    Moore, D.: Measuring new types of question-order effects: Additive and subtractive. Public Opin. Q. 66, 80–91 (2002)

    Article  Google Scholar 

  19. 19.

    Moreira, C., Wichert, A.: Exploring the relations between quantum-like bayesian networks and decision-making tasks with regard to face stimuli. J. Math. Psychol. (2016)

  20. 20.

    Moreira, C., Wichert, A.: Quantum-like bayesian networks for modeling decision making. Front. Psychol. 7(11) (2016)

  21. 21.

    Moreira, C., Wichert, A.: Quantum probabilistic models revisited: the case of disjunction effects in cognition. Front. Phys.: Interdiscip. Phys. 4, 1–26 (2016)

    Article  Google Scholar 

  22. 22.

    Pothos, E., Busemeyer, J.: A quantum probability explanation for violations of rational decision theory. Proc. R. Soc. B 276, 2171–2178 (2009)

    Article  Google Scholar 

  23. 23.

    Pothos, E., Busemeyer, J., Trueblood, J.: A quantum geometric model of similarity. Psychol. Rev. 120, 679–696 (2013)

    Article  Google Scholar 

  24. 24.

    Shafir, E., Tversky, A.: Thinking through uncertainty: nonconsequential reasoning and choice. Cogn. Psychol. 24, 449–474 (1992)

    Article  Google Scholar 

  25. 25.

    Trueblood, J., Busemeyer, J.: A quantum probability account of order of effects in inference. Cogn. Sci. 35, 1518–1552 (2011)

    Article  Google Scholar 

  26. 26.

    Trueblood, J., Pothos, E., Busemeyer, J.: Quantum probability theory as a common framework for reasoning and similarity. Front. Psychol. 5 (2014)

  27. 27.

    Tversky, A., Kahneman, D.: Judgment under uncertainty: Heuristics and biases. Science 185, 1124–1131 (1974)

    ADS  Article  Google Scholar 

  28. 28.

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

    Article  Google Scholar 

  29. 29.

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

    Article  Google Scholar 

  30. 30.

    Wang, Z., Busemeyer, J.: A quantum question order model supported by empirical tests of an apriori and precise prediction. J. Top. Cogn. Sci. 5, 689–710 (2013)

    Google Scholar 

  31. 31.

    Wang, Z., Solloway, T., Shiffrin, R., Busemeyer, J.: Context effects produced by question orders reveal quantum nature of human judgments. Proc. Natl. Acad. Sci. 111, 9431–9436 (2014)

    ADS  Article  Google Scholar 

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Corresponding author

Correspondence to Catarina Moreira.

Additional information

This work was supported by national funds through Fundação para a Ciência e a Tecnologia (FCT) with reference UID/CEC/50021/2013 and through the PhD grant SFRH/BD/92391/2013. The funders had no role in study design, data collection and analysis, decision to publish, or preparation of the manuscript.

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Moreira, C., Wichert, A. Are Quantum Models for Order Effects Quantum?. Int J Theor Phys 56, 4029–4046 (2017).

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  • Order effects
  • Quantum cognition
  • Quantum projections
  • Occam’s razor