We present a general classification of the conditions under which cognitive science, concerned, e.g. with decision making, requires the use of quantum theoretical notions. The analysis is done in the frame of the mathematical approach based on the theory of quantum measurements. We stress that quantum effects in cognition can arise only when decisions are made under uncertainty. Conditions for the appearance of quantum interference in cognitive sciences and the conditions when interference cannot arise are formulated.
We present a general classification of the conditions under which cognitive science, concerned, e.g. with decision making, requires the use of quantum theoretical notions. The analysis is done in the frame of the mathematical approach based on the theory of quantum measurements. We stress that quantum effects in cognition can arise only when decisions are made under uncertainty. Conditions for the appearance of quantum interference in cognitive sciences and the conditions when interference cannot arise are formulated.
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.
Theory of quantum measurements is often classified as decision theory. An event in decision theory corresponds to the measurement of an observable. This analogy looks clear for operationally testable simple events. However, the situation is essentially more complicated in the case of composite events. The most difficult point is the relation between decisions under uncertainty and measurements under uncertainty. We suggest a unified language for describing the processes of quantum decision making and quantum measurements. The notion of quantum measurements under uncertainty is introduced. We show that the correct mathematical foundation for the theory of measurements under uncertainty, as well as for quantum decision theory dealing with uncertain events, requires the use of positive operator-valued measure that is a generalization of projection-valued measure. The latter is appropriate for operationally testable events, while the former is necessary for characterizing operationally uncertain events. In both decision making and quantum measurements, one has to distinguish composite nonentangled events from composite entangled events. Quantum probability can be essentially different from classical probability only for entangled events. The necessary condition for the appearance of an interference term in the quantum probability is the occurrence of entangled prospects and the existence of an entangled strategic state of a decision maker or of an entangled statistical state of a measuring device.
Growing empirical evidence reveals that traditional set-theoretic structures cannot in general be applied to cognitive phenomena. This has raised several problems, as illustrated, for example, by probability judgement errors and decision-making (DM) errors. We propose here a unified theoretical perspective which applies the mathematical formalism of quantum theory in Hilbert space to cognitive domains. In this perspective, judgements and decisions are described as intrinsically non-deterministic processes which involve a contextual interaction between a conceptual entity and the cognitive context surrounding it. When a given phenomenon is considered, the quantum-theoretic framework identifies entities, states, contexts, properties and outcome statistics, and applies the mathematical formalism of quantum theory to model the considered phenomenon. We explain how the quantum-theoretic framework works in a variety of judgement and decision situations where systematic and significant deviations from classicality occur.
Uncertainty is an intrinsic part of life; most events, affairs, and questions are uncertain. A key problem in behavioral sciences is how the mind copes with uncertain information. Quantum probability theory offers a set of principles for inference, which align well with intuition about psychological processes in certain cases: cases when it appears that inference is contextual, the mental state changes as a result of previous judgments, or there is interference between different possibilities. We motivate the use of quantum theory in cognition and its key characteristics. For each of these characteristics, we review relevant quantum cognitive models and empirical support. The scope of quantum cognitive models encompasses fallacies in decision-making (such as the conjunction fallacy or the disjunction effect), question order effects, conceptual combination, evidence accumulation, perception, over-/underdistribution effects in memory, and more. Quantum models often formalize psychological ideas previously expressed in heuristic terms, allow unified explanations of previously disparate findings, and have led to several surprising, novel predictions. We also cast a critical eye on quantum models and consider some of their shortcomings and issues regarding their further development.
Quantum Models of Cognition and Decision, Second Edition presents a fully updated and expanded version of this innovative and path-breaking text. It offers an accessible introduction to the intersection of quantum theory and cognitive science, covering new insights, modelling techniques, and applications for understanding human cognition and decision making. In it, Busemeyer and Bruza delve into such topics as the non-commutative nature of judgments, quantum interference as a general principle governing human decision making, contextuality in modelling human cognition, and thought-provoking speculation about what a quantum approach to cognition might reveal about the ultimate nature of the human mind. Additions include new material on measurement, open systems, and applications to computer science. Requiring no prior background in quantum physics, this book comes complete with a tutorial and fully worked-out applications in important areas of cognition and decision.
This article examines the empirical evidence for interference effects in psychological experiments. It also reviews the competing interpretation of these effects with respect to traditional cognitive models and new quantum cognition models. The conclusion is that quantum theory provides unifying principles for explaining interference effects found in a wide variety of different experimental paradigms, and it provides a viable new theoretical approach for understanding cognition and decision making.