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Deciding by quantum-like belief morphing or hopping?

Jan Broekaert

Published Jan 20, 2026• 0 citations
OpenAlex

Abstract

Other people's beliefs may influence our own beliefs. Such effects, sometimes referred to as 'crowd-wisdom', can be revealed from group-informed responses in controlled experiments. Our study presents a formal choice model to understand how multiple respondents iteratively interact when communicating their responses, which we test on data from Granovskiy et al. (2015)'s social information experiment. In this multi-stage decision process, information from the group's response distribution influences individual judgments before respondents adjust their next response. Our model describes each respondent's probabilistic belief state, and uses a quantum-like morphing evolution based on the Brassard-Høyer-Grover amplification formalism. This framework enables: (i) the description of multi-respondent cognitive interactions through assimilation to or polarization away from other beliefs, (ii) the implementation via Hamiltonian operators using projection operators of source ('initial') and target ('informing') belief states, and (iii) the resolution of periodicity issues in previous Schrödinger-like models through through bounded temporal parametrization. A performance comparison is done for the quantum-like models using morphing and standard hopping, and a classical Markov hopping model. The quantum-like morphing model with multi-component target belief demonstrated superior BIC performance across the parameter space of evolution time (tfrac), belief uncertainty (SD), and sampling temperature (T). This belief morphing approach hence provides an effective and innovative method to model social influence in group decision-making.

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Other people's beliefs may influence our own beliefs. Such effects, sometimes referred to as 'crowd-wisdom', can be revealed from group-informed responses in controlled experiments. Our study presents a formal choice model to understand how multiple respondents iteratively interact when communicating their responses, which we test on data from Granovskiy et al. (2015)'s social information experiment. In this multi-stage decision process, information from the group's response distribution influences individual judgments before respondents adjust their next response. Our model describes each respondent's probabilistic belief state, and uses a quantum-like morphing evolution based on the Brassard-Høyer-Grover amplification formalism. This framework enables: (i) the description of multi-respondent cognitive interactions through assimilation to or polarization away from other beliefs, (ii) the implementation via Hamiltonian operators using projection operators of source ('initial') and target ('informing') belief states, and (iii) the resolution of periodicity issues in previous Schrödinger-like models through through bounded temporal parametrization. A performance comparison is done for the quantum-like models using morphing and standard hopping, and a classical Markov hopping model. The quantum-like morphing model with multi-component target belief demonstrated superior BIC performance across the parameter space of evolution time (tfrac), belief uncertainty (SD), and sampling temperature (T). This belief morphing approach hence provides an effective and innovative method to model social influence in group decision-making.
This doctoral consortium presents an overview of my anticipated PhD dissertation which focuses on employing quantum Bayesian networks for social learning. The project, mainly, aims to expand the use of current quantum probabilistic models in human decision-making from two agents to multi-agent systems. First, I cultivate the classical Bayesian networks which are used to understand information diffusion through human interaction on online social networks (OSNs) by taking into account the relevance of multitude of social, psychological, behavioral and cognitive factors influencing the process of information transmission. Since quantum like models require quantum probability amplitudes, the complexity will be exponentially increased with increasing uncertainty in the complex system. Therefore, the research will be followed by a study on optimization of heuristics. Here, I suggest to use an belief entropy based heuristic approach. This research is an interdisciplinary research which is related with the branches of complex systems, quantum physics, network science, information theory, cognitive science and mathematics. Therefore, findings can contribute significantly to the areas related mainly with social learning behavior of people, and also to the aforementioned branches of complex systems. In addition, understanding the interactions in complex systems might be more viable via the findings of this research since probabilistic approaches are not only used for predictive purposes but also for explanatory aims.
Quantum-like decision theory is by now a theoretically well-developed field (see e.g., Danilov et al. 2018A). We here test the predictions of an application of this approach to persuasion. One remarkable result entails that in contrast to Bayesian persuasion, distraction rather than relevant information has a powerful potential to influence decision-making. We first provide a quantum decision model for a choice between two uncertain alternatives. We derive the impact of persuasion by means of distractive questions and contrast them with the predictions of the Bayesian model. Next, we conduct an experiment where respondents choose between supporting either one of two projects to save endangered species. We test the impact of persuasion in the form of questions related to different aspects of the uncertain value of the two projects. The experiment involves 900 respondents divided into three groups: a control group, a first treatment group and the distraction treatment group. Our main result is that, in accordance with the predictions of quantum persuasion but in violation with the Bayesian model, distraction significantly affects decision-making. Population variables play no role. Some significant variations between subgroups are exhibited and discussed. The results of the experiment provide support for the hypothesis that the manipulability of people's decision-making can be explained by the quantum indeterminacy of their subjective representations of reality.
The application of the mathematical formalism of quantum mechanics to model behavioral patterns in social science and economics is a novel and constantly emerging field. The aim of the so called 'quantum like' models is to model the decision making processes in a macroscopic setting, capturing the particular 'context' in which the decisions are taken. Several subsequent empirical findings proved that when making a decision people tend to violate the axioms of expected utility theory and Savage's Sure Thing principle, thus violating the law of total probability. A quantum probability formula was devised to describe more accurately the decision making processes. A next step in the development of QL-modeling in decision making was the application of Schrödinger equation to describe the evolution of people's mental states. A shortcoming of Schrödinger equation is its inability to capture dynamics of an open system; the brain of the decision maker can be regarded as such, actively interacting with the external environment. Recently the master equation, by which quantum physics describes the process of decoherence as the result of interaction of the mental state with the environmental 'bath', was introduced for modeling the human decision making. The external environment and memory can be referred to as a complex 'context' influencing the final decision outcomes. The master equation can be considered as a pioneering and promising apparatus for modeling the dynamics of decision making in different contexts.
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.
FINDING: Quantum cognition models human decision-making under uncertainty and conflict using quantum probability amplitudes rather than classical Bayesian logic, with social interaction effects incorporated via quantum interference terms. | MATH: Quantum probability: P(A)=∣⟨ψ∣P^A∣ψ⟩∣2 P(A) = |\langle \psi | \hat{P}_A | \psi \rangle|^2 P(A)=∣⟨ψ∣P^A​∣ψ⟩∣2, where P^A\hat{P}_AP^A​ is a projection operator; interference term: P(A∨B)=P(A)+P(B)+2P(A)P(B)cos⁡(δ) P(A \lor B) = P(A) + P(B) + 2\sqrt{P(A)P(B)}\cos(\delta) P(A∨B)=P(A)+P(B)+2P(A)P(B)​cos(δ), with δ\deltaδ the phase difference; social agents: density matrix formalism ρ→∑iwiρi\rho \to \sum_i w_i \rho_iρ→∑i​wi​ρi​ with Lindblad-type evolution for interaction-induced decoherence (arXiv:1202.4918v2). | CONNECTION: The interference phase δ\deltaδ is not fixed by the sources; no explicit golden-ratio or base-60 constants appear in the cited abstracts. However, quantum interference amplitudes naturally produce oscillatory probability patterns — if δ=π/5\delta = \pi/5δ=π/5 (36°) or π/3\pi/3π/3 (60°), the interference term yields ratios involving \(\cos(3 Author: Andrew Stewart Caldin, Independent Researcher, UK. Part of the E8 Intelligence Research series. Platform: e8intelligence.com