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arXiv:2111.13902 · IEEE Transactions on Cybernetics

A Quantum-Like Model for Predicting Human Decisions in the Entangled Social Systems

Aghdas Meghdadi, Mohammad-R. Akbarzadeh-T, Kurosh Javidan

Published Jan 19, 2022• 25 citations
arXivHTMLPDF

Abstract

Human-centered systems of systems, such as social networks, the Internet of Things, or healthcare systems are growingly becoming significant facets of modern life. Realistic models of human behavior in such systems play an essential role in their accurate modeling and prediction. Nevertheless, human behavior under uncertainty often violates the predictions by the conventional probabilistic models. Recently, quantum-like decision theories have shown a considerable potential to explain the contradictions in human behavior by applying quantum probabilities. But providing a quantum-like decision theory that could predict rather than describe the current state of human behavior is still one of the unsolved challenges. The fundamental contribution of this work is introducing the concept of entanglement from quantum information theory to Bayesian networks (BNs). This concept leads to an entangled quantum-like BN (QBN), in which each human is a part of the entire society. Accordingly, society's effect on the dynamic evolution of the decision-making process, which is less often considered in decision theories, is modeled by entanglement measures. To reach this aim, we introduce a quantum-like witness and find the relationship between this witness and the famous concurrence entanglement measure. The proposed predictive entangled QBN (PEQBN) is evaluated on 22 experimental tasks. Results confirm that PEQBN provides more realistic predictions of human decisions under uncertainty when compared with classical BNs and three recent quantum-like approaches.

DOI
10.1109/tcyb.2021.3134688

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Human-centered systems of systems, such as social networks, the Internet of Things, or healthcare systems are growingly becoming significant facets of modern life. Realistic models of human behavior in such systems play an essential role in their accurate modeling and prediction. Nevertheless, human behavior under uncertainty often violates the predictions by the conventional probabilistic models. Recently, quantum-like decision theories have shown a considerable potential to explain the contradictions in human behavior by applying quantum probabilities. But providing a quantum-like decision theory that could predict rather than describe the current state of human behavior is still one of the unsolved challenges. The fundamental contribution of this work is introducing the concept of entanglement from quantum information theory to Bayesian networks (BNs). This concept leads to an entangled quantum-like BN (QBN), in which each human is a part of the entire society. Accordingly, society's effect on the dynamic evolution of the decision-making process, which is less often considered in decision theories, is modeled by entanglement measures. To reach this aim, we introduce a quantum-like witness and find the relationship between this witness and the famous concurrence entanglement measure. The proposed predictive entangled QBN (PEQBN) is evaluated on 22 experimental tasks. Results confirm that PEQBN provides more realistic predictions of human decisions under uncertainty when compared with classical BNs and three recent quantum-like approaches.
Cognitive biases of the human mind significantly influence the human decision-making process. However, they are often neglected in modeling selection behaviors and hence deemed irrational. Here, we introduce a cognitive quantum-like approach for modeling human biases by simulating society as a quantum system and using a Quantum-like Bayesian network (QBN) structure. More specifically, we take inspiration from the electric field to improve our recent entangled QBN approach to model the initial bias due to unequal probabilities in parent nodes. Entangled QBN structure is particularly suitable for modeling bias behavior due to changing the state of systems with each observation and considering every decision-maker an integral part of society rather than an isolated agent. Hence, biases caused by emotions between agents or past personal experiences are also modeled by the social entanglement concept motivated by entanglement in quantum physics. In this regard, we propose a bias potential function and a new quantum-like entanglement witness in Hilbert space to introduce a biased variant of the entangled QBN (BEQBN) model based on quantum probability. The predictive BEQBN is evaluated on two well-known empirical tasks. Results indicate the superiority of the BEQBN by achieving the first rank compared to classical BN and six QBN approaches and presenting more realistic predictions of human behaviors.
Since the 70’s, researchers noticed that people do not follow the rules of probability theory while making decisions under risk.Just like quantum physics was created in order to accommodate paradoxical findings from classical physics, quantum cognition arose as a disciple with the promise of creating models that would accommodate and explain the violations found in human decision-making.In this work, we explore an alternative quantum structure to perform quantum probabilistic inferences. We propose a Quantum Probabilistic Graphical Model in order to predict human decisions under situations with high levels of uncertainty.Under the proposed network, if a node (event) is unobserved, then a particle can enter in a superposition state and produce interference effects. These effects provide some explanation in terms of cognition, since they can be seen as the feeling of confusion or ambiguity.This work also discusses the problem of creating a generalized quantum probabilistic model: the number of quantum parameters grows exponentially. We will see that for a given event, several outcomes are possible through quantum probability. A final question is posed and discussed: is it possible to find a method to assign quantum parameters in order to provide accurate predictions?
In this work, we explore an alternative quantum structure to perform quantum probabilistic inferences to accommodate the paradoxical findings of the Sure Thing Principle. We propose a Quantum-Like Bayesian Network, which consists in replacing classical probabilities by quantum probability amplitudes. However, since this approach suffers from the problem of exponential growth of quantum parameters, we also propose a similarity heuristic that automatically fits quantum parameters through vector similarities. This makes the proposed model general and predictive in contrast to the current state of the art models, which cannot be generalized for more complex decision scenarios and that only provide an explanatory nature for the observed paradoxes. In the end, the model that we propose consists in a nonparametric method for estimating inference effects from a statistical point of view. It is a statistical model that is simpler than the previous quantum dynamic and quantum-like models proposed in the literature. We tested the proposed network with several empirical data from the literature, mainly from the Prisoner's Dilemma game and the Two Stage Gambling game. The results obtained show that the proposed quantum Bayesian Network is a general method that can accommodate violations of the laws of classical probability theory and make accurate predictions regarding human decision-making in these scenarios.
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.
The increasing complexity of modern decision-making environments has challenged the effectiveness of classical mathematical models. Traditional probabilistic frameworks often struggle to represent uncertainty, ambiguity, contextual dependence, and nonlinear interactions among decision variables. Quantum-inspired mathematical models have emerged as a promising interdisciplinary approach that leverages mathematical principles derived from quantum theory without requiring quantum computing hardware. These models utilize concepts such as superposition, interference, entanglement, and contextuality to represent complex decision processes more accurately. This paper explores the theoretical foundations, mathematical structures, and applications of quantum-inspired decision models in complex systems. The study examines how quantum probability theory provides a more flexible representation of human cognition, organizational decision-making, financial forecasting, and artificial intelligence systems. Furthermore, the paper discusses mathematical formulations, implementation strategies, advantages, challenges, and future research directions. The findings suggest that quantum-inspired models offer significant potential for addressing uncertainty and dynamic interactions in complex decision environments, thereby contributing to the advancement of intelligent decision support systems.
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.