Skip to main content
    • Aa
    • Aa

Can quantum probability provide a new direction for cognitive modeling?

  • Emmanuel M. Pothos (a1) and Jerome R. Busemeyer (a2)

Classical (Bayesian) probability (CP) theory has led to an influential research tradition for modeling cognitive processes. Cognitive scientists have been trained to work with CP principles for so long that it is hard even to imagine alternative ways to formalize probabilities. However, in physics, quantum probability (QP) theory has been the dominant probabilistic approach for nearly 100 years. Could QP theory provide us with any advantages in cognitive modeling as well? Note first that both CP and QP theory share the fundamental assumption that it is possible to model cognition on the basis of formal, probabilistic principles. But why consider a QP approach? The answers are that (1) there are many well-established empirical findings (e.g., from the influential Tversky, Kahneman research tradition) that are hard to reconcile with CP principles; and (2) these same findings have natural and straightforward explanations with quantum principles. In QP theory, probabilistic assessment is often strongly context- and order-dependent, individual states can be superposition states (that are impossible to associate with specific values), and composite systems can be entangled (they cannot be decomposed into their subsystems). All these characteristics appear perplexing from a classical perspective. However, our thesis is that they provide a more accurate and powerful account of certain cognitive processes. We first introduce QP theory and illustrate its application with psychological examples. We then review empirical findings that motivate the use of quantum theory in cognitive theory, but also discuss ways in which QP and CP theories converge. Finally, we consider the implications of a QP theory approach to cognition for human rationality.

Linked references
Hide All

This list contains references from the content that can be linked to their source. For a full set of references and notes please see the PDF or HTML where available.

D. Aerts & S. Aerts (1995) Applications of quantum statistics in psychological studies of decision processes. Foundations of Science 1:8597.

N. Anderson (1971) Integration theory and attitude change. Psychological Review 78:171206.

H. Atmanspacher & T. Filk (2010) A proposed test of temporal nonlocality in bistable perception. Journal of Mathematical Psychology 54:314–21.

H. Atmanspacher , T. Filk & H. Romer (2004) Quantum zero features of bistable perception. Biological Cybernetics 90:3340.

H. Atmanspacher , H. Römer & H. Walach (2002) Weak quantum theory: Complementarity and entanglement in physics and beyond. Foundations of Physics 32:379406.

B. E. Baaquie (2004) Quantum finance: Path integrals and Hamiltonians for options and interest rates. Cambridge University Press.

M. Bar-Hillel & E. Neter (1993) How alike is it versus how likely is it: A disjunction fallacy in probability judgments. Journal of Personality and Social Psychology 65:1119–31.

R. Barkan & J. R. Busemeyer (2003) Modeling dynamic inconsistency with a changing reference point. Journal of Behavioral Decision Making 16:235–55.

R. F. Bordley (1998) Quantum mechanical and human violations of compound probability principles: Toward a generalized Heisenberg uncertainty principle. Operations Research 46:923–26.

C. J. Brainerd & V. F. Reyna (2008) Episodic over-distribution: A signature effect of familiarity without recognition. Journal of Memory & Language 58:765–86.

C. J. Brainerd , V. F. Reyna & S. J. Ceci (2008) Developmental reversals in false memory: A review of data and theory. Psychological Bulletin 134:343–82.

P. D. Bruza , K. Kitto , D. Nelson & C. L. McEvoy (2009) Is there something quantum-like about the human mental lexicon? Journal of Mathematical Psychology 53:362–77.

J. R. Busemeyer , E. M. Pothos , R. Franco & J. S. Trueblood (2011) A quantum theoretical explanation for probability judgment errors. Psychological Review 118(2):193218.

J. R. Busemeyer , Z. Wang & J. T. Townsend (2006) Quantum dynamics of human decision-making. Journal of Mathematical Psychology 50:220–41.

B. W. Carlson & J. F. Yates (1989) Disjunction errors in qualitative likelihood judgment. Organizational Behavior and Human Decision Processes 44:368–79.

J. A. de Barros & P. Suppes (2009) Quantum mechanics, interference, and the brain. Journal of Mathematical Psychology 53:306–13.

J. M. Feldman & J. G. Lynch (1988) Self-generated validity and other effects of measurement on belief, attitude, intention, and behavior. Journal of Applied Psychology 73:421–35.

I. Gavanski & D. R. Roskos-Ewoldsen (1991) Representativeness and conjoint probability. Journal of Personality and Social Psychology 61:181–94.

T. L. Griffiths , N. Chater , C. Kemp , A. Perfors & J. B. Tenenbaum (2010) Probabilistic models of cognition: Exploring representations and inductive biases. Trends in Cognitive Sciences 14:357–64.

L. K. Grover (1997) Quantum mechanics helps in searching for a needle in a haystack. Physical Review Letters 79:325–28.

J. A. Hampton (1988a) Disjunction of natural concepts. Memory & Cognition 16:579–91.

R. M. Hogarth & H. J. Einhorn (1992) Order effects in belief updating: The belief-adjustment model. Cognitive Psychology 24:155.

M. Jibu & K. Yasue (1995) Quantum brain dynamics and consciousness. Benjamins.

D. Kahneman , P. Slovic & A. Tversky (1982) Judgment under uncertainty: Heuristics and biases. Cambridge University Press.

A. Y. Khrennikov (2010) Ubiquitous quantum structure: From psychology to finance. Springer.

J. I. Krueger , T. E. DiDonato & D. Freestone (2012) Social projection can solve social dilemmas. Psychological Inquiry 23:127.

A. Litt , C. Eliasmith , F. W. Kroon , S. Weinstein & P. Thagard (2006) Is the brain a quantum computer? Cognitive Science 30:593603.

A. B. Markman & D. Gentner (1993) Splitting the differences: A structural alignment view of similarity. Journal of Memory and Language 32:517–35.

C. R. M. McKenzie , S. M. Lee & K. K. Chen (2002) When negative evidence increases confidence: Change in belief after hearing two sides of a dispute. Journal of Behavioral Decision Making 15:118.

D. W. Moore (2002) Measuring new types of question-order effects. Public Opinion Quarterly 66:8091.

A. Perfors , J. B. Tenenbaum , T. L. Griffiths & F. Xu (2011) A tutorial introduction to Bayesian models of cognitive development. Cognition 120:302–21.

E. M. Pothos & J. R. Busemeyer (2009) A quantum probability explanation for violations of “rational” decision theory. Proceedings of the Royal Society B 276:2171–78.

V. F. Reyna (2008) A theory of medical decision making and health: Fuzzy trace theory. Medical Decision Making 28:850–65.

V. F. Reyna & C. J. Brainerd (1995) Fuzzy-trace theory: An interim synthesis. Learning and Individual Differences 7:175.

L. M. Ricciardi & H. Umezawa (1967) Brain and physics of many bodied problems. Kybernetik 4:4448.

A. N. Sanborn , T. L. Griffiths & D. J. Navarro (2010) Rational approximations to rational models: Alternative algorithms for category learning. Psychological Review 117:1144–67.

N. Schwarz (2007) Attitude construction: Evaluation in context. Social Cognition 25:638–56.

G. Shafer & A. Tversky (1985) Languages and designs for probability judgment. Cognitive Science 9:309–39.

E. Shafir & A. Tversky (1992) Thinking through uncertainty: nonconsequential reasoning and choice. Cognitive Psychology 24:449–74.

J. C. Shanteau (1970) An additive model for sequential decision making. Journal of Experimental Psychology 85:181191.

S. Sher & C. R. M. McKenzie (2008) Framing effects and rationality. In: The probabilistic mind: Prospects for Bayesian cognitive science, ed. N. Chater & M. Oaksford , pp. 7996. Oxford University Press.

S. A. Sloman (1993) Feature-based induction. Cognitive Psychology 25:231–80.

S. Stolarz-Fantino , E. Fantino , D. J. Zizzo & J. Wen (2003) The conjunction effect: New evidence for robustness. American Journal of Psychology 116(1):1534.

K. Tentori & V. Crupi (2012) On the conjunction fallacy and the meaning of and, yet again: A reply to Hertwig, Benz, and Krauss (2008). Cognition 122:123–34.

R. Tourangeau , L. J. Rips & K. A. Rasinski (2000) The psychology of survey response. Cambridge University Press.

A. Tversky & D. Kahneman (1973) Availability: A heuristic for judging frequency and probability. Cognitive Psychology 5:207–32.

A. Tversky & D. J. Koehler (1994) Support theory: A nonextensional representation of subjective probability. Psychological Review 101:547–67.

G. Vitiello (1995) Dissipation and memory capacity in the quantum brain model. International Journal of Modern Physics B9:973–89.

P. P. Wakker (2010) Prospect theory for risk and ambiguity. Cambridge University Press.

A. J. Wills & E. M. Pothos (2012) On the adequacy of current empirical evaluations of formal models of categorization. Psychological Bulletin 138:102–25.

Recommend this journal

Email your librarian or administrator to recommend adding this journal to your organisation's collection.

Behavioral and Brain Sciences
  • ISSN: 0140-525X
  • EISSN: 1469-1825
  • URL: /core/journals/behavioral-and-brain-sciences
Please enter your name
Please enter a valid email address
Who would you like to send this to? *



Altmetric attention score

Full text views

Total number of HTML views: 13
Total number of PDF views: 177 *
Loading metrics...

Abstract views

Total abstract views: 824 *
Loading metrics...

* Views captured on Cambridge Core between September 2016 - 19th September 2017. This data will be updated every 24 hours.