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Behavioral and Brain Sciences

If quantum probability = classical probability + bounded cognition; is this good, bad, or unnecessary?

Tim Rakow

Published May 14, 2013• 2 citations
Publisher

Abstract

Quantum probability models may supersede existing probabilistic models because they account for behaviour inconsistent with classical probability theory that are attributable to normal limitations of cognition. This intriguing position, however, may overstate weaknesses in classical probability theory by underestimating the role of current knowledge states and may under-employ available knowledge about the limitations of cognitive processes. In addition, flexibility in model specification has risks for the use of quantum probability.

DOI
10.1017/s0140525x12003172

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Quantum probability models may supersede existing probabilistic models because they account for behaviour inconsistent with classical probability theory that are attributable to normal limitations of cognition. This intriguing position, however, may overstate weaknesses in classical probability theory by underestimating the role of current knowledge states and may under-employ available knowledge about the limitations of cognitive processes. In addition, flexibility in model specification has risks for the use of quantum probability.
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.
Quantum probability theory (QPT) has provided a novel, rich mathematical framework for cognitive modelling, especially for situations which appear paradoxical from classical perspectives. This work concerns the dynamical aspects of QPT, as relevant to cognitive modelling. We aspire to shed light on how the mind's driving potentials (encoded in Hamiltonian and Lindbladian operators) impact the evolution of a mental state. Some existing QPT cognitive models do employ dynamical aspects when considering how a mental state changes with time, but it is often the case that several simplifying assumptions are introduced. What kind of modelling flexibility does QPT dynamics offer without any simplifying assumptions and is it likely that such flexibility will be relevant in cognitive modelling? We consider a series of nested QPT dynamical models, constructed with a view to accommodate results from a simple, hypothetical experimental paradigm on decision-making. We consider Hamiltonians more complex than the ones which have traditionally been employed with a view to explore the putative explanatory value of this additional complexity. We then proceed to compare simple models with extensions regarding both the initial state (e.g. a mixed state with a specific orthogonal decomposition; a general mixed state) and the dynamics (by introducing Hamiltonians which destroy the separability of the initial structure and by considering an open-system extension). We illustrate the relations between these models mathematically and numerically.This article is part of the themed issue 'Second quantum revolution: foundational questions'.
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
Purpose: Decision-making under uncertainty remains a foundational challenge in cognitive science and artificial intelligence. Classical Bayesian Probability Models (CBM) often fail to explain paradoxical cognitive behaviors such as order effects, ambiguity aversion, and context-dependent reasoning. This study seeks to compare Quantum Probability Theory (QPT) and Classical Bayesian Models in their ability to capture the dynamics of human decision-making. It aims to determine which framework more accurately reflects the cognitive mechanisms underlying reasoning under uncertainty. Methodology: A qualitative, exploratory research design was adopted, involving in-depth semi-structured interviews with 16 experts across psychology, philosophy, artificial intelligence, and cognitive neuroscience. Participants were purposively selected for their theoretical and empirical expertise in probabilistic reasoning. Data were analyzed using reflexive thematic analysis, guided by the Dual-Process Theory and Busemeyer’s Quantum Cognition framework. The analysis emphasized participants’ perspectives on theoretical assumptions, cognitive plausibility, and predictive utility between QPT and CBM paradigms. Findings: Thematic findings reveal that Quantum Probability Theory offers superior explanatory power in contexts involving cognitive ambiguity, contextual dependence, and non-commutativity of mental operations. Participants consistently reported that QPT better models real-world reasoning tasks where classical logic collapses, capturing the fluid and context-sensitive nature of human judgment. Conversely, while CBM remains effective in structured, low-uncertainty scenarios, it fails to accommodate superposition and interference effects inherent in human cognition. Unique Contribution to Theory, Practice, and Policy (Recommendations): The study contributes theoretically by demonstrating how quantum probabilistic models expand existing theories of bounded rationality and probabilistic reasoning in cognitive science. Practically, it encourages interdisciplinary collaboration between cognitive scientists, AI researchers, and philosophers to refine decision models that mirror human intuition more closely. Policy-wise, the findings support the integration of quantum-inspired approaches in the design of intelligent decision-support systems and cognitive architectures. The study recommends continued empirical validation of QPT within applied domains—such as behavioral economics, machine learning, and cognitive modeling—to strengthen its predictive and explanatory robustness.
Classical models of decision-making under uncertainty, grounded in expected utility theory and Bayesian probability, often fail to account for systematic cognitive anomalies such as preference reversals, order effects, ambiguity aversion, and context-dependent choices. Quantum cognition models offer a novel theoretical framework that applies the mathematical principles of quantum probability—such as superposition, interference, and non-commutativity—to cognitive processes without assuming physical quantum mechanisms in the brain. By representing cognitive states as probabilistic superpositions that collapse through decision “measurements,” these models provide parsimonious explanations for violations of classical rationality. This paper examines how quantum cognition frameworks capture contextual influence, belief updating, and interference effects in uncertain decision environments. Drawing on findings from cognitive psychology and behavioral economics, the study highlights the relevance of quantum cognition for applications in economic choice modeling, legal decision analysis, and artificial intelligence. The analysis suggests that quantum probability offers a robust alternative to classical approaches when modeling human decision-making in complex, ambiguous, and context-sensitive situations.