Many paradoxical findings in decision-making that have resisted explanations by standard decision theories have accumulated over the past 50 years. Recent advances based on quantum probability theory have successfully accounted for many of these puzzling findings. Critics, however, claim that quantum probability theory is less constrained than standard probability theory, and hence quantum models only fit better because they are more complex than standard decision models. In this article, for the first time, a Bayesian method was used to quantitatively compare the 2 types of decision models, which is a method that evaluates models with respect to accuracy, parsimony, and robustness. A large experiment was used to compare the best-known models of each type, matching in their numbers of parameters, but possibly differing in the complexity of their functional forms. Surprisingly, the Bayesian model comparison overwhelmingly favored the quantum model, indicating that its success is due to its robust ability to make accurate predictions rather than accidental fits afforded by increased complexity.
Many paradoxical findings in decision-making that have resisted explanations by standard decision theories have accumulated over the past 50 years. Recent advances based on quantum probability theory have successfully accounted for many of these puzzling findings. Critics, however, claim that quantum probability theory is less constrained than standard probability theory, and hence quantum models only fit better because they are more complex than standard decision models. In this article, for the first time, a Bayesian method was used to quantitatively compare the 2 types of decision models, which is a method that evaluates models with respect to accuracy, parsimony, and robustness. A large experiment was used to compare the best-known models of each type, matching in their numbers of parameters, but possibly differing in the complexity of their functional forms. Surprisingly, the Bayesian model comparison overwhelmingly favored the quantum model, indicating that its success is due to its robust ability to make accurate predictions rather than accidental fits afforded by increased complexity.
Recent work in cognitive psychology has revealed that quantum probability theory provides another method of computing probabilities without falling into the restrictions that classical probability has in regard to modeling cognitive systems and decision-making. This enables the explanation of paradoxical scenarios that are difficult, or even impossible, to explain through classical probability theory. In this work, we perform an overview of the most important quantum models in the literature that are used to make predictions under scenarios where the Sure Thing Principle is being violated (the Quantum-Like Approach, the Quantum Dynamical Model, the Quantum Prospect Theory and Quantum-Like Bayesian Networks). We evaluated these models in terms of three metrics: interference effects, parameter tuning and scalability. The first examines if the analyzed model makes use of any type of quantum interference to explain human decision-making. The second is concerned with the assignment of values to a large number of quantum parameters. The last one consists of analyzing the ability of the models to be extended and generalized to more complex scenarios. We also studied the growth of the quantum parameters when the complexity and the levels of uncertainty of the decision scenario increase. Finally, we compared these quantum models with traditional classical models from the literature. We conclude with a discussion of the manner in which the models addressed in this paper can only deal with very small decision problems and why they do not scale well to larger, more complex decision scenarios.
How can we use quantum theory to model other phenomena of interest to researchers in cognition and decision making? Quantum theory is not easy for researchers in cognition and decision making to accept. In fact, quantum mechanics was not easy for physicists to accept either, but it was forced on them by several paradoxical findings that could not be explained using classical physics. We have a similar problem in cognition and decision making – there are numerous paradoxical findings that just seem irrational according to classic probability theory. For example, under some conditions, people judge the probability of event A and B to be greater than the probability of event B , which is called the conjunction fallacy (Tversky & Kahneman, 1983). Also, under the same conditions, they judge the probability of A or B to be less than the probability of event A (Carlson & Yates, 1989), which is called the disjunction fallacy. In this chapter we examine how quantum probability theory explains these and other puzzling results from human probability judgment research. This chapter has two main parts. In the first part, we use a quantum model to derive qualitative predictions for conjunction errors, disjunction errors, and other closely related findings. The first section provides a general set of predictions that do not depend on specific assumptions about the features used to represent events, and the predictions are parameter free. In the second part, we examine the quantitative predictions of the quantum model for a Bayesian inference task, which we use to explain order effects on inference.
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.
FINDING: Human decision-making under uncertainty and conflict is best modeled by quantum probability theory, not classical Bayesian logic. | MATH: Quantum probability amplitudes replace classical probabilities; decision basis states are vectors in Hilbert space; interference terms (e.g., ⟨ψ∣A∣ψ⟩2=∑i∣⟨i∣ψ⟩∣2∣⟨A∣i⟩∣2) account for context-dependent violations of the law of total probability. | CONNECTION: No explicit geometric ratios (0.382, 0.618, 0.786, 1.618, 2.618) or base-60 or crystallographic symmetries reported. The Hilbert space structure is linear, not inherently harmonic. | DEPTH: 6 — Foundational shift in probability theory for cognition, but no direct link to geometric harmony or universal constants. The mathematical essence is the replacement of Kolmogorov axioms with quantum probability, which introduces complex phases and interference. No specific equations or constants beyond the standard quant Author: Andrew Stewart Caldin, Independent Researcher, UK. Part of the E8 Intelligence Research series. Platform: e8intelligence.com
We test a simple quantum decision model of the Ellsberg paradox. We find that the theoretical predictions of the model are in conformity with our experimental results. The predictions of our quantum model are not statistically significantly different from those of the source dependent model. The source dependent model requires the specification of probability weighting functions in order to fit the evidence. On the other hand, our quantum model makes no recourse to probability weighting functions. This suggests that much of what is normally attributed to probability weighting may actually be due to quantum probability. When we replace quantum probability by Kolmogorov probability in our model, then the Ellsberg paradox reemerges. Hence, we make essential use of quantum probability theory. All our development uses no more than standard linear algebra and real numbers, which are very familiar to economists. This makes our paper accessible to a wider audience than the quantum community. JEL Classification: D01, D81, D91
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.