Difficulties in prognosis of human behavior are due to the complexity of our cognition, routinely breaking the boundaries of classical rationality. The paper solves this problem for the simplest kind of such “irrational” behavior in which a single binary decision is made in three related contexts. Subjective meanings of these contexts relative to the basis decision alternative are represented by three qubit states, borrowed from quantum theory. These states are bound together by linear superpositions, which encode semantic composition of the contexts in the subject’s mind. The resulting theory supplements classical probabilistic model with nonlinear interference factor, accounting for the “irrational”, emotionally-semantic side of intelligence. This model is built for different realizations of two classic experiments used to study behavioral irrationality: the prisoner’s dilemma and the two-stage gambling task. In 24 such realizations, the interference phase is shown to fall in a narrow range of values, encoding regularities of semantic composition of contexts. Extrapolation of this regularity to novel experiments allows using the model in prognostic mode. This possibility is tested on the task of probabilistic prediction of target decision based on the same probability in two other contexts. For the prisoner’s dilemma and the two-stage gambling task the such prognosis has relative errors of 9 and 11% respectively. The proposed approach allows for putting other quantum models of cognition and decision to predictive and interpretable use, whereas its principles also apply to modeling of decisions with larger sets of contexts and behavioral options. By formalizing a novel type of semantic regularities behind “irrational” thinking, models of the present type open prospects for empowering the existing means for socio-economical analytics and prediction.
Difficulties in prognosis of human behavior are due to the complexity of our cognition, routinely breaking the boundaries of classical rationality. The paper solves this problem for the simplest kind of such “irrational” behavior in which a single binary decision is made in three related contexts. Subjective meanings of these contexts relative to the basis decision alternative are represented by three qubit states, borrowed from quantum theory. These states are bound together by linear superpositions, which encode semantic composition of the contexts in the subject’s mind. The resulting theory supplements classical probabilistic model with nonlinear interference factor, accounting for the “irrational”, emotionally-semantic side of intelligence. This model is built for different realizations of two classic experiments used to study behavioral irrationality: the prisoner’s dilemma and the two-stage gambling task. In 24 such realizations, the interference phase is shown to fall in a narrow range of values, encoding regularities of semantic composition of contexts. Extrapolation of this regularity to novel experiments allows using the model in prognostic mode. This possibility is tested on the task of probabilistic prediction of target decision based on the same probability in two other contexts. For the prisoner’s dilemma and the two-stage gambling task the such prognosis has relative errors of 9 and 11% respectively. The proposed approach allows for putting other quantum models of cognition and decision to predictive and interpretable use, whereas its principles also apply to modeling of decisions with larger sets of contexts and behavioral options. By formalizing a novel type of semantic regularities behind “irrational” thinking, models of the present type open prospects for empowering the existing means for socio-economical analytics and prediction.
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.
The paper presents a method for semantic data analysis by means of complex-valued matrix decomposition. The method is based on the quantum model of contextual decision-making, according to which observable probabilities are generated by qubit states, representing subjective meaning of the contexts relative to the basis decision. In the simplest three-context case, one of these qubits is decomposed to superposition of the remaining two, mathematically encoding semantic relations between the three contexts. For use in data analysis this model is translated to the matrix form, in which rows and columns correspond to the contexts and instances of experiment. The observable real-valued data then emerge from a complex-valued amplitude matrix, decomposed to a product of a real basis matrix and complex-valued matrix of superposition coefficients. This decomposition reveals stable process-semantic relations between the considered contexts, not captured by other methods of analysis. As a result, the data are approximated with higher precision and fewer parameters than singular and non-negative matrix decompositions, truncated to the same dimension. The model is experimentally approved in descriptive and prognostic regimes. The result opens prospects for development of nature-like computational architectures on novel logical grounds.
Abstract This paper presents a method for semantic data analysis by complex-valued matrix decomposition. The method is based on the quantum model of contextual decision-making, according to which observable probabilities are generated by the qubit states, representing the subjective meaning of the contexts relative to the basis decision. In the simplest three-context case, one of these qubits is decomposed into a superposition of the remaining two, mathematically encoding semantic relations between the three contexts. For use in data analysis, this model is translated to the matrix form, in which the rows and columns correspond to the contexts and samples of the experiment. The observable real-valued data then emerge from a complex-valued amplitude matrix, decomposed to a product of a real basis matrix and complex-valued matrix of superposition coefficients. This decomposition reveals stable process-semantic relations between the considered contexts, not captured by other methods of analysis. As a result, the data are approximated with higher precision and fewer parameters than singular and nonnegative matrix decompositions, truncated to the same dimension. The model is experimentally tested in the descriptive and prognostic regimes. The result opens prospects for development of nature-like computational architectures on novel logical grounds.
In cognitive psychology, some experiments of games were reported [1, 2, 3, 4], and these demonstrated that real players did not use the "rational strategy" provided by classical game theory. To discuss probabilities of such "irrational choice", recently, we proposed a decision-making model which is based on the formalism of quantum mechanics [5, 6, 7, 8]. In this paper, we briefly explain the above model and calculate the probability of irrational choice in several prisoner's dilemma (PD) games.
Empirical findings from cognitive psychology indicate that, in scenarios under high levels of uncertainty, many people tend to make irrational decisions. To address this problem, models based on quantum probability theory, such as the quantum-like Bayesian networks, have been proposed. However, this model makes use of a Bayes normalisation factor during probabilistic inference to convert the likelihoods that result from quantum interference effects into probability values. The interpretation of this operation is not clear and leads to extremely skewed intensity waves that make the task of prediction of these irrational decisions challenging. This article proposes the law of balance, a novel mathematical formalism for probabilistic inferences in quantum-like Bayesian networks, based on the notion of balanced intensity waves. The general idea is to balance the intensity waves resulting from quantum interference in such a way that, during Bayes normalisation, they cancel each other. With this representation, we also propose the law of maximum uncertainty, which is a method to predict these paradoxes by selecting the amplitudes of the wave with the highest entropy. Empirical results show that the law of balance together with the law of maximum uncertainty were able to accurately predict different experiments from cognitive psychology showing paradoxical or irrational decisions, namely in the Prisoner's Dilemma game and the Two-Stage Gambling Game.
Organizational decision making is often explored with theories from the heuristics and biases research program, which have demonstrated great value as descriptions of how people in organizations make decisions. Nevertheless, rational analysis and classical probability theory are still seen by many as the best accounts of how decisions should be made and classical probability theory is the preferred framework for cognitive modelling for many researchers. The focus of this work is quantum probability theory, an alternative probabilistic framework. Results in decision making, which appear paradoxical from a perspective of classical probability theory, may make perfect sense if one adopts quantum probability theory. We review some cognitive models of decision making based on quantum probability theory. Each of these models is based on a challenge to prescription from classical probability theory. The transition from labeling a particular behavior as irrational, by classical probability standards, to (potentially) rational (or, at any rate, not fallacious), raises interesting possibilities, including that of characterizing certain heuristics in formal, probabilistic terms.