The present thesis (mostly) concerns the application of alternative mathematical methods to understand patterns in human cognition and to model them. The different chapters presented in this thesis show research that concerns the application of quantum probability (QP) theory in the modeling of human decision-making. Quantum probability (QP) theory is a theory for how to assign probabilities to events. QP theory can be thought of as the probability rules from quantum mechanics, without any of the physics. This work is not about the application of quantum physics to brain physiology. Rather, we are interested in QP theory as a mathematical framework for cognitive modelling. This theory is potentially relevant in any behavioural situation that involves uncertainty. QP theory is analogous to classical probability theory, though QP theory and classical probability (CP) theory are founded from different sets of axioms (the Kolmogorov and Dirac/von Neumann axioms respectively) and so are subject to alternative constraints. In this thesis we show that especially over the last decade, there has been a growing interest in decision-making and cognitive models using a quantum probabilistic (QP) framework. We see how this development encompasses publications in major journals (see Pothos and Busemeyer, 2013; Wang et al., 2014; and Yearsley and Pothos, 2014; among others), special issues, and dedicated workshops, as well as several comprehensive books (Busemeyer and Bruza, 2012; Khrennikov, 2010; and Haven and Khrennikov, 2010). However, uncertainty itself is neither ethical nor unethical – yet it is inherent to most situations in which, for instance, moral judgments and decisions have to be made. For a descriptive understanding of judgment and decisions in moral situations, it is an important lesson to acknowledge both the cognitive side (bounded rationality) and the environment (ecological rationality) – and thus the uncertainty of the world and how the mind deals with it. This thesis also shows significant interest in moral and social psychology. Specifically, we consider present technologies that suggest a need for evaluating alternative contexts for ethical decision-making. How the research on human-machine interaction feeds back into humans’ understanding of themselves as moral agents? This key question ultimately relates to the nature of ethical theory itself. Overall, this dissertation presents and addresses not only standard aspects of decision- making processes, such as similarity judgments (Chapters 1 to 4) or the constructive role of articulating impressions (Chapter 5), but also standard aspects of social psychology, such as moral judgments (Chapters 6 and 7) and game theory (Chapter 8). As stated in the Declarations section, the present thesis is a combination of a standard and a publication- based dissertation.
The present thesis (mostly) concerns the application of alternative mathematical methods to understand patterns in human cognition and to model them. The different chapters presented in this thesis show research that concerns the application of quantum probability (QP) theory in the modeling of human decision-making. Quantum probability (QP) theory is a theory for how to assign probabilities to events. QP theory can be thought of as the probability rules from quantum mechanics, without any of the physics. This work is not about the application of quantum physics to brain physiology. Rather, we are interested in QP theory as a mathematical framework for cognitive modelling. This theory is potentially relevant in any behavioural situation that involves uncertainty. QP theory is analogous to classical probability theory, though QP theory and classical probability (CP) theory are founded from different sets of axioms (the Kolmogorov and Dirac/von Neumann axioms respectively) and so are subject to alternative constraints. In this thesis we show that especially over the last decade, there has been a growing interest in decision-making and cognitive models using a quantum probabilistic (QP) framework. We see how this development encompasses publications in major journals (see Pothos and Busemeyer, 2013; Wang et al., 2014; and Yearsley and Pothos, 2014; among others), special issues, and dedicated workshops, as well as several comprehensive books (Busemeyer and Bruza, 2012; Khrennikov, 2010; and Haven and Khrennikov, 2010). However, uncertainty itself is neither ethical nor unethical – yet it is inherent to most situations in which, for instance, moral judgments and decisions have to be made. For a descriptive understanding of judgment and decisions in moral situations, it is an important lesson to acknowledge both the cognitive side (bounded rationality) and the environment (ecological rationality) – and thus the uncertainty of the world and how the mind deals with it. This thesis also shows significant interest in moral and social psychology. Specifically, we consider present technologies that suggest a need for evaluating alternative contexts for ethical decision-making. How the research on human-machine interaction feeds back into humans’ understanding of themselves as moral agents? This key question ultimately relates to the nature of ethical theory itself. Overall, this dissertation presents and addresses not only standard aspects of decision- making processes, such as similarity judgments (Chapters 1 to 4) or the constructive role of articulating impressions (Chapter 5), but also standard aspects of social psychology, such as moral judgments (Chapters 6 and 7) and game theory (Chapter 8). As stated in the Declarations section, the present thesis is a combination of a standard and a publication- based dissertation.
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
The core assumptions of modern economic utility theories such as rationality have been placed under scrutiny by recent studies in decision theory and behavioural economics and fi?nance. The main questions that were explored in these studies could be expressed as follows: do people always make rational choices? Do they make use of the normative rules of traditional logic and probability when dealing with risk and uncertainty? Are there any alternative methods to capture choices and reasoning when individuals are faced with uncertainty and risk? In this thesis I will elaborate on an interdisciplinary application of so-called QL (quantum-like) models to decision-making problems in ?finance and other socio-economic contexts. The core inquiry of this work is related to experimental tests of decision making with the help of investment related questions. Calculus and logic borrowed from quantum physics will be used to develop probabilistic models for the formation and evolution of decisions in ?finance context with the potential to generalize to other social decision- making settings. The main fi?ndings of this thesis can be summarized as follows: individuals exhibit preference reversals and context-dependent behaviour in different informational contexts. In particular, in condition of risk individuals exhibit uncertainty aversion and thus aversion to participating in other investment task, violating the postulates of classical probability theory. The core principle of rational (consequential) behaviour conceived by Savage (1954) [207], that is the "Savage Sure Thing" principle, was shown to be violated. In mathematical language, this violation is equivalent to the violation of the "Law of total probability". Implying contextuality of human judgement, different events cannot be jointly evaluated in a single probability space. Moreover, additional experimental fi?ndings showed that participants exhibited reference dependence in their risk attitudes depending on the preceding gain respective loss. These fi?ndings were statistically signi?cant and a quantum model for accommodating the above effects of contextual behaviour is introduced. A geometric depiction of the experimental fi?ndings was proposed. A so-called `state reconstruction' procedure from statistical data was performed via the inverse Born's rule (1926) [47], allowing the construction of a complete representation of agents' resolution from indeterminacy.
The article presents a review of foreign scientific literature on the quantum-like approach to understanding the modeling of cognition and decision-making processes. It is shown that the current application of quantum physics approaches to consciousness, psychological approaches such as perception, cognition, emotions, consciousness and learning, involves the search for a single objective mathematical model of what underlies the experience of the brain. The use of quantum physics algorithms can help in understanding the mechanisms of brain malfunctions and memory impairments that are found in pathologies such as dementia caused by Alzheimer's disease, schizophrenia, etc. Quantum physics approaches are applicable to issues of modeling cognition and decision-making processes, as well as in cognitive research, information processing by the human brain, artificial intelligence development, psychology, social and political sciences. Application of the abstract mathematical principles of quantum theory can help in understanding human consciousness and behavior. Quantum probability theory is applied to modeling human behavior due to the prevalence of uncertainty in human interaction with the world. Quantum cognitive models are especially useful in research in such areas as errors in decision making, order effects of questions, conceptual combinations, accumulation of evidence, perception, etc. Of particular interest to researchers are issues of quantum-like modeling of cognition and decision-making processes, the apparatus of quantum information and probability theory, useful for such modeling, as well as the use of such apparatus in cognitive research, the development of artificial intelligence, psychology, social and political sciences.
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.
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.