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## Behavioral and Brain Sciences

### Target Article

### Can quantum probability provide a new direction for cognitive modeling?

### Emmanuel M. Pothos^{a1} and Jerome R. Busemeyer^{a2}

- Behavioral and Brain Sciences / Volume 36 / Issue 03 / June 2013, pp 255- 274
- Copyright © Cambridge University Press 2013
- DOI: http://dx.doi.org/10.1017/S0140525X12001525 (About DOI), Published online: 14 May 2013

^{a1 }
Department of Psychology, City University London, London EC1V 0HB, United Kingdom. emmanuel.pothos.1@city.ac.uk
http://www.staff.city.ac.uk/~sbbh932/

^{a2 }
Department of Psychological and Brain Sciences, Indiana University, Bloomington, IN 47405. jbusemey@indiana.edu
http://mypage.iu.edu/~jbusemey/home.html

Abstract

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.

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Keywords

- category membership;
- classical probability theory;
- conjunction effect;
- decision making;
- disjunction effect;
- interference effects;
- judgment;
- quantum probability theory;
- rationality;
- similarity ratings

Emmanuel Pothos studied physics at Imperial College, during which time he obtained the Stanley Raimes Memorial prize in mathematics, and continued with a doctorate in experimental psychology at Oxford University. He has worked with a range of computational frameworks for cognitive modeling, including ones based on information theory, flexible representation spaces, Bayesian methods, and, more recently, quantum theory. He has authored approximately sixty journal articles on related topics, as well as on applications of cognitive methods to health and clinical psychology. Pothos is currently a senior lecturer in psychology at City University London.

Jerome Busemeyer received his PhD as a mathematical psychologist from University of South Carolina in 1980, and later he enjoyed a post-doctoral position at University of Illinois. For 14 years he was a faculty member at Purdue University. He moved on to Indiana University, where he is provost professor, in 1997. Busemeyer's research has been steadily funded by the National Science Foundation, National Institute of Mental Health, and National Institute on Drug Abuse, and in return he served on national grant review panels for these agencies. He has published over 100 articles in various cognitive and decision science journals, such as *Psychological Review*, as well as serving on $their editorial boards. He served as chief editor of *Journal of Mathematical Psychology* from 2005 through 2010 and he is currently an associate editor of *Psychological Review*. From 2005 through 2007, Busemeyer served as the manager of the Cognition and Decision Program at the Air Force Office of Scientific Research. He became a fellow of the Society of Experimental Psychologists in 2006. His research includes mathematical models of learning and decision making, and he formulated a dynamic theory of human decision making called decision field theory. Currently, he is working on a new theory applying quantum probability to human judgment and decision making, and he published a new book on this topic with Cambridge University Press.