Half Day Tutorial on Using Quantum Probability Theory to Model Cognition

Half Day Tutorial on Using Quantum Probability Theory to Model Cognition Emmanuel M. Pothos (Emmanuel.pothos.1@city.ac.uk) Department of Psychology, City University London, London, EC1R 0JD, UK Zheng Wang (wang.1243@osu.edu) School of Communication, Derby Hall, The Ohio State University, Columbus, OH 43210 USA. Keywords: probability theory, Bayesian probability, quantum theory, decision making, probabilistic models. General Purpose This tutorial introduces why and how to build cognitive models using quantum probability (QP) theory. In the tutorial, we will show that QP is inherently consistent with deeply rooted psychological conceptions and intuitions. It offers a fresh conceptual framework for explaining some puzzling empirical findings of cognition, and provides a rich new source of alternative formal tools, compared to classical probability (CP) theory, for cognitive modeling. CP models, including Bayesian models, have had an enormous influence in cognitive science (e.g., Griffiths et al., 2010). Such formal models are appealing for many reasons. First, CP theory provides an integrated, coherent, self-consistent set of principles, which can be flexibly applied in any inductive inference situation. Second, such approaches are more falsifiable. Core principles of CP theory are inter-dependent, and identifying an empirical violation of one principle in a setting could invalidate the applicability of CP theory as a whole in that setting. Third, CP principles are intuitive. In the words of Laplace (1816, cited in Perfors et al., 2011), “probability theory is nothing but common sense reduced to calculation. ” However, human cognition often goes against the description and prescription from CP theory. In one of the most influential empirical traditions in cognitive psychology, Kahneman, Tversky, and colleagues have reported persistent, clear violations of CP principles in decision making (e.g., Tversky & Kahneman, 1974). For example, consider the famous conjunction fallacy. Participants are told of a person, Linda, looking very much like a feminist and unlike a bank teller. Then, they are asked to judge probabilities of some events. Violating CP rules, people think the probability that Linda is a bank teller and a feminist is higher than the probability that she is just a bank teller. According to CP theory, it is a fallacy to think P(A and B)>P(A). Importantly, even when we become aware of our “fallacy,” we cannot shake off the impression that Linda is indeed more likely to be a bank teller and a feminist, than to be just a bank teller. Important findings like this have led to intense and extensive controversy about the mechanisms which guide human cognition and decision making. The inspiration for Jerome R. Busemeyer (jbusemey@indiana.edu) Psychological and Brain Sciences, Indiana University, Bloomington 47468 Indiana, USA. exploring QP theory in cognitive modeling partly arises as a way to resolve this controversy. The physical theory of quantum mechanics is a marriage between a framework for how to assign probabilities to events and assumptions regarding the nature of the physical world. We can call the former QP theory (or just quantum theory). Can it be applied outside of physics? The motivation for doing so is twofold. First, QP theory is a highly rigorous framework for probabilistic inference. It has been developed over several decades by some of the most brilliant scientists of all time (e.g., Bohr, Dirac, von Neumann, Planck) and has been intensely scrutinized ever since. Thus, the application of QP theory in cognitive modeling has exactly the same formal advantages as that of CP theory. Second, quantum theory allows us to consider the possible relevance in cognitive modeling of several novel concepts. For example, in quantum theory, a cognitive system can be in a superposition state. This means that relative to a question or measurement, the system is in an indefinite state, with all definite states having potential to be expressed. This provides an intrinsic formal representation of the conflict, ambiguity, or uncertainty that people experience in cognitive processes. For another example: states can be entangled, which means a change in one part of the system inexorably and instantaneously affects another part. Entanglement is a form of extreme association, which can be helpful for formalizing important cognitive processes, such as holism, cognitive dissonance, and social projection. Fundamental quantum conceptions, such as superposition, entanglement, interference, and complementarity, have no formal counterparts in cognitive theory. We are part of a growing group of researchers who have been intensely exploring their applicability in understanding human cognition. Quantum theory reveals alternative intuitions in probabilistic models of cognition. The quantum cognition research program aims to explore whether these alternative intuitions can explain paradoxical findings in decision, memory, and other areas of cognitive processing. The tutorial introduce the basic principles of quantum theory, in the context of well-known empirical findings in psychological literature. The basic elements of QP theory will require only some knowledge of linear algebra. No background in physics or quantum theory is assumed. The tutorial will be self-contained. It will show how probability