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Behavioral and Brain Sciences

Quantum probability and cognitive modeling: Some cautions and a promising direction in modeling physics learning

Donald R. Franceschetti, Elizabeth Gire

Published May 14, 2013• 1 citation
Publisher

Abstract

Quantum probability theory offers a viable alternative to classical probability, although there are some ambiguities inherent in transferring the quantum formalism to a less determined realm. A number of physicists are now looking at the applicability of quantum ideas to the assessment of physics learning, an area particularly suited to quantum probability ideas.

DOI
10.1017/s0140525x12002932

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Quantum probability theory offers a viable alternative to classical probability, although there are some ambiguities inherent in transferring the quantum formalism to a less determined realm. A number of physicists are now looking at the applicability of quantum ideas to the assessment of physics learning, an area particularly suited to quantum probability ideas.
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.
The Potential of Quantum Probability for Modeling Cognitive Processes Emmanuel M. Pothos (e.m.pothos@swansea.ac.uk) Department of Psychology, Swansea University, SA2 8PP, UK Jerome R. Busemeyer (jbusemey@indiana.edu), Richard M. Shiffrin (shiffrin@indiana.edu), Jennifer S. Trueblood (jstruebl@indiana.edu) Department of Psychological and Brain Sciences, Indiana University, Bloomington 47468, USA. Zheng Wang (wang.1243@osu.edu) Ohio State University, School of Communication, Columbus 43210, USA. Reinhard K. Blutner (reinhard@blutner.de) Institute of Logic, Language, and Computation, University of Amsterdam, 1090 GE Amsterdam, The Netherlands. Harald Atmanspacher (atmanspacher@collegium.ethz.ch) Department of Theory and Data Analysis, IGPP, D-79098 Freiburg, Germany. Keywords: Quantum probability, formal approaches, decision making, conceptual combination General Background and Speakers Quantum probability (QP) theory is a theory for how to assign probabilities to observables. In the context of physics, it has been successfully employed by researchers for over 100 years and has been the basis for some of the most impressive discoveries of the human mind (e.g., the transistor, and so the microchip, and the laser). But the applicability of QP theory is not limited to physical phenomena and, indeed, there has been growing interest in exploring the potential of QP theory in areas as diverse as economics (Baaquie, 2004), information theory (e.g., Grover, 1997), and psychology. We are interested in the latter objective. Probabilistic approaches to cognition have been recently enjoying considerable success (e.g., Griffiths et al., 2010). This is perhaps unsurprising. Several (if not most) aspects of cognitive processing involve inference about quantities which cannot be determined with certainty. Thus, probability theory seems an ideal tool for formalizing uncertainty in cognitive processes and describing the mechanisms which allow humans to be successful in an uncertain world. The question then becomes to identify the probabilistic framework which is most suitable for modeling particular aspects of cognition. Cognitive scientists have widely employed classical probability theory and there is no doubt that such approaches can be incredibly successful for particular problems (e.g., Oaksford & Chater, 2007). But is Bayesian probability always the most suitable probabilistic framework for describing cognitive processes? Human inference often appears to violate fundamental laws of classical probability. For example, in the famous Linda problem of Tversky and Kahneman (1983) participants consider as more likely a conjunctive statement than a corresponding single premise one (i.e., Probability (AB this is the conjunction fallacy). In one-shot prisoner’s dilemma games, naive participants choose to defect knowing their opponent defects, they choose to also defect knowing their opponent cooperates, but they reverse their judgment and choose to cooperate when their opponent’s action is unknown (Shafir & Tversky, 1992). This result is also hard to reconcile with classical probability theory, it violates the sure thing principle and the law of total probability. Findings such as the conjunction fallacy and the violation of the sure thing principle provide the motivation for exploring probabilistic frameworks alternative to classic probability theory. QP theory is mostly consistent with classical probability theory, but for a crucial difference. In classical probability theory Probability (AB Busemeyer, Wang, & Townsend, 2006; Pothos & Busemeyer, 2009), these properties of QP theory can lead to successful and simple QP models for empirical findings, such as the conjunction fallacy and the violation of the sure thing principle. Finally, QP theory remains suitable for describing cognition without involving any claim that the brain is a quantum computer. Rather, we adopt what is a standard approach in cognitive science and ask: 'does quantum probability theory produce results which predict human behavior well?’ The application of QP theory in cognition holds a lot of promise. The main objective of this symposium is to present the key ideas to the cognitive science community and summarize progress with QP theory cognitive models. What
Since the 70’s, researchers noticed that people do not follow the rules of probability theory while making decisions under risk.Just like quantum physics was created in order to accommodate paradoxical findings from classical physics, quantum cognition arose as a disciple with the promise of creating models that would accommodate and explain the violations found in human decision-making.In this work, we explore an alternative quantum structure to perform quantum probabilistic inferences. We propose a Quantum Probabilistic Graphical Model in order to predict human decisions under situations with high levels of uncertainty.Under the proposed network, if a node (event) is unobserved, then a particle can enter in a superposition state and produce interference effects. These effects provide some explanation in terms of cognition, since they can be seen as the feeling of confusion or ambiguity.This work also discusses the problem of creating a generalized quantum probabilistic model: the number of quantum parameters grows exponentially. We will see that for a given event, several outcomes are possible through quantum probability. A final question is posed and discussed: is it possible to find a method to assign quantum parameters in order to provide accurate predictions?
Recently the mathematical formalism of quantum mechanics, especially methods of quantum probability theory, started to be widely used in a variety of applications outside of physics, e.g., cognition and psychology as well as economy and finances. To distinguish such models from genuine quantum physical models, they often called quantum-like (although often people simply speak about, e.g., "quantum cognition"). These novel applications generate a number of foundational questions. Nowadays we can speak about a new science - foundations of quantum-like modeling. At the first stage this science was mainly about comparison of classical and quantum models, mainly in the probabilistic setting. It was found that statistical data from cognitive psychology violate some basic constraints posed on data by classical probability theory (Kolmogorov, 1933); in particular, the constraints given by the formula of total probability and Bell's type inequalities. Recently another question attracted some attention. In spite of real success in applications, there are no reason to believe that the quantum probability would cover completely all problems of, e.g., cognition. May be more general probability models have to be explored. A similar problem attracted a lot of attention in foundations of quantum physics culminating in a series of experiments to check Sorkin's equality for the triple-slit experiment by Weihs' group. In this note we present a similar test in the cognitive experimental setting. Performance of this test would either give further confirmation of the adequacy of the quantum probability model to cognitive applications or rejection of the conventional quantum model. Thus this note opens the door for a series of exciting experimental tests for the quantum-like model of cognition.
Quantum probability (QP) theory is a theory for how to assign probabilities to observables. In the context of physics, it has been successfully employed by researchers for over 100 years and has been the basis for some of the most impressive discoveries of the human mind (e.g., the transistor, and so the microchip, and the laser). But the applicability of QP theory is not limited to physical phenomena and, indeed, there has been growing interest in exploring the potential of QP theory in areas as diverse as economics (Baaquie, 2004), information theory (e.g., Grover, 1997), and psychology.