Agent Mental Models and Bayesian Rules as a Tool to Create Opinion Dynamics Models

In recent years opinion dynamics has been widely used in political and economy. In this article we present a opinion dynamics model where agents show discrete actions and continuous opinions in a social network. Our model combines bounded confidence and real society network which differs from previous regular networks. In real life, the structure of social networks are often unknown, so uncovering the interacting structure of the underlying network is the key to get final opinions. Based on the sparse of social networks and observed time series, we use compressive sensing, an efficient way to reconstructing the social network where the opinion updates take place. We find that with a smaller threshold a better success rate of recovering is obtained. Also with the threshold increasing more final opinions survive at last. And the density of network also affects the final opinions.

Interest in how democracies form consensus has increased recently, with statistical physics and economics approaches both suggesting that there is convergence to a fixed point in belief networks, but with fluctuations in opinions when there are “stubborn” voters. We modify a model of opinion dynamics in which agents are fully Bayesian to account for two cognitive biases: confirmation bias and in-group bias. Confirmation bias occurs when the received information is considered to be more likely to align with the receiver's beliefs. In-group bias occurs when the receiver further considers the information to be more likely when the receiver's beliefs and the sender's beliefs are aligned. We find that when there are no cognitive biases, a network of agents always converges to complete consensus. With confirmation bias alone, polarization can occur. With both biases present, consensus and polarization are possible, but when agents attempt to counteract confirmation bias, there can be signatures of transient chaos and ongoing opinion fluctuations. Based on this simple model, we conjecture that complex opinion fluctuations might be a generic feature of opinion dynamics when agents are Bayesian with biases.

In this paper, we propose a new model for continuous time opinion dynamics on an evolving network. As opposed to existing models, in which the network typically evolves by discretely adding or removing edges, we instead propose a model for opinion formation which is coupled to a network evolving through a system of ordinary differential equations for the edge weights. We interpret each edge weight as the strength of the relationship between a pair of individuals, with edges increasing in weight if pairs continually listen to each other’s opinions and decreasing if not. We investigate the impact of various edge dynamics at different timescales on the opinion dynamics itself. This is done partly through analytic results and partly through extensive numerical simulations of two case studies: one using bounded confidence interaction dynamics in the opinion formation process (as in the classical Hegselmann–Krause model) and one using an exponentially decaying interaction function. We find that the dynamic edge weights can have a significant impact on the opinion formation process, since they may result in consensus formation but can also reinforce polarisation. Overall, the proposed modelling approach allows us to quantify and investigate how the network and opinion dynamics influence each other.

We explore the possibilities of enforcing and preventing consensus in continuous opinion dynamics that result from modifications in the communication rules. We refer to the model of Weisbuch and Deffuant, where n agents adjust their continuous opinions as a result of random pairwise encounters whenever their opinions differ not more than a given bound of confidence ε. A high ε leads to consensus, while a lower ε leads to a fragmentation into several opinion clusters. We drop the random encounter assumption and ask: How small may ε be such that consensus is still possible with a certain communication plan for the entire group? Mathematical analysis shows that ε may be significantly smaller than in the random pairwise case. On the other hand, we ask: How large may ε be such that preventing consensus is still possible? In answering this question, we prove Fortunato's simulation result that consensus cannot be prevented for ε > 0.5 for large groups. Next, we consider opinion dynamics under different individual strategies and examine their power to increase the chances of consensus. One result is that balancing agents increase chances of consensus, especially if the agents are cautious in adapting their opinions. However, curious agents increase chances of consensus only if those agents are not cautious in adapting their opinions.

Impact of informal networks on opinion dynamics in hierarchically formal organization

Models of continuous opinion dynamics under bounded confidence show a sharp transition between a consensus and a polarization phase at a critical global bound of confidence. In this paper, heterogeneous bounds of confidence are studied. The surprising result is that a society of agents with two different bounds of confidence (open‐ and closed‐minded agents) can find consensus even when both bounds of confidence are significantly below the critical bound of confidence of a homogeneous society. The phenomenon is shown by examples of agent‐based simulation and by numerical computation of the time evolution of the agents density. The result holds for the bounded confidence model of Deffuant, Weisbuch, and others (Weisbuch et al., Complexity 2002, 7, 55–63), as well as for the model of Hegselmann and Krause (Hegselmann and Krause, Journal of Artificial Societies and Social Simulation 2002, 5, 2). Thus, given an average level of confidence, diversity of bounds of confidence enhances the chances for consensus. The drawback of this enhancement is that opinion dynamics becomes suspect to severe drifts of clusters, where open‐minded agents can pull closed‐minded agents towards another cluster of closed‐minded agents. A final consensus might thus not lie in the center of the opinion interval as it happens for uniform initial opinion distributions under homogeneous bounds of confidence. It can be located at extremal locations. This is demonstrated by example, which also show that the extension to heterogeneous bounds of confidence enriches the complexity of the dynamics tremendously. © 2009 Wiley Periodicals, Inc. Complexity, 2010

Opinion dynamics with decentralized proportional–integral control strategy

In this era of fast and large-scale opinion formation, a mathematical understanding of opinion evolution, a.k.a. opinion dynamics, is especially important. Linear graph-based dynamics and bounded confidence dynamics are the two most popular models for opinion dynamics in social networks. Recently, stochastic bounded confidence opinion dynamics were proposed as a general framework that incorporates both these dynamics as special cases and also captures the inherent stochasticity and noise (errors) in real-life social exchanges. Although these dynamics are quite general and realistic, their analysis is particularly challenging compared to other opinion dynamics models. This is because these dynamics are nonlinear and stochastic, and belong to the class of Markov processes that have asymptotically zero drift and unbounded jumps. The asymptotic behavior of these dynamics was characterized in prior works. However, they do not shed light on their finite-time behavior, which is often of interest in practice. We take a stride in this direction by analyzing the finite time behavior of a two-agent system, which is fundamental to the understanding of multi-agent dynamics. In particular, we show that the opinion difference between the two agents is well concentrated around zero under the conditions that lead to asymptotic stability of the dynamics.

Purpose. Digital transformation of education determines the need to rethink the goals and meanings of the educational process and, at present, is associated with the problems of our time, the expansion of the role of artificial intelligence. The paper is devoted to the presentation of the taxonomy of educational goals from the standpoint of a mental model of thinking, which allows designing new educational results in the digital transformation of education. Methodology and methods. Unlike Bloom’s taxonomy, the main goal of modern education is the formation and development of computational thinking. The basis for constructing the taxonomy of educational goals is a mental approach, which is a set of principles and strategies for organizing the educational process aimed at forming and developing the cognitive abilities of the student. To identify the essence of computational thinking, a mental model of thinking is used, in which cognitive functions are determined by the mechanisms of perception, memorization, structuring and retrieval of information. In this model, knowledge is a structural set of mental images; mental schemes and mental models based on the first, second, and third signal systems. Results. Consideration of the mental characteristics of a modern person in a digital society, definition of the 3rd signal system in the “person + ICT + artificial intelligence” link, in which mental schemes and mental models play the main role, made it possible to formulate the stages of the educational process target settings in the form of the taxonomy of educational goals. The taxonomy of educational goals begins with the assignment of mental entropy - as a subject field of the future professional activity of a specialist, containing questions, tasks and problems. They can be formulated by traditional educational goals in the form of: know, be able to, master. The specification of these goals leads to target guidelines for the composition, volume and content of subject mental images, mental schemes and mental models. The set of mental images, schemes and models represent a knowledge block. In parallel, an ascending target block of universal cognitive operations is set, that a modern specialist must master. The pinnacle of the taxonomy is computational thinking. Based on the mental model of thinking, the essence of computational thinking is revealed and a set of universal cognitive operations is compiled. The basic composition of mental models that determine human cognitive behavior in a digital society is formed. Computational thinking is a type of thinking with the activation of conceptual-abstract and conceptual-machine superstructures of mental images, mental schemes and models in the circuit of the third signal system. Conclusion. The proposed mental taxonomy of educational goals determines the vector of the direction of digital transformation of education to achieve the main result - computational thinking. The stages of formation and the quality of computational thinking are determined by the formation of a set of universal cognitive operations, the volume and content of mental images, mental schemes and mental models of the subject area.

We propose two different schemes of realizing a virtual walk corresponding to a kinetic exchange model of opinion dynamics. The walks are either Markovian or non-Markovian in nature. The opinion dynamics model is characterized by a parameter [Formula: see text] which drives an order disorder transition at a critical value [Formula: see text]. The distribution [Formula: see text] of the displacements [Formula: see text] from the origin of the walkers is computed at different times. Below [Formula: see text], two time scales associated with a crossover behaviour in time are detected, which diverge in a power law manner at criticality with different exponent values. [Formula: see text] also carries the signature of the phase transition as it changes its form at [Formula: see text]. The walks show the features of a biased random walk below [Formula: see text], and above [Formula: see text], the walks are like unbiased random walks. The bias vanishes in a power law manner at [Formula: see text] and the width of the resulting Gaussian function shows a discontinuity. Some of the features of the walks are argued to be comparable to the critical quantities associated with the mean-field Ising model, to which class the opinion dynamics model belongs. The results for the Markovian and non-Markovian walks are almost identical which is justified by considering the different fluxes. We compare the present results with some earlier similar studies. This article is part of the theme issue 'Kinetic exchange models of societies and economies'.

<p id="p00005">Computerized classification testing (CCT) can adaptively classify test-takers into two or more different categories, and it has been widely used in qualifying tests and clinical psychology or medical diagnosis. As an essential part of CCT, the termination rule determines when the test is to be stopped and to which category the test-taker is ultimately classified into, directly affecting the test efficiency and classification accuracy. According to the theoretical basis of the termination rules, existing rules can be roughly divided into the likelihood ratio, Bayesian decision theory, and confidence interval rules. And their core ideas are constructing hypothesis tests, designing loss functions, and comparing the relative positions of confidence intervals, respectively. At the same time, when constructing specific termination rules, the requirement of different test scenarios (e.g., the number of categories and the number of tests’ dimensions) should also be considered. <br/>There are advantages and disadvantages to each of the three types of termination rules. Specifically, the likelihood ratio rule is based on the likelihood ratio test, with better theoretical properties. However, the method requires prior determination of the indifference interval and the type I and II error rates, introducing the impact of subjective factors. Also, it is more challenging to extend the method in complex test situations, such as multidimensional and multicategory CCT. Bayesian decision theory rules make classification decisions based on the loss function. It can dynamically optimize the decision from a more global perspective since it works backward from the final stage of the test. In addition, the variety of loss functions makes the method very flexible in form and makes it easy to be applied to different test situations. However, in practice, the flexibility will inevitably result in the uncertainty of the choice of loss function, and the inappropriate loss function may be biased. The confidence interval method is the most straightforward because of its relatively simple principle and low computational effort. However, this method is less robust and has a relatively low test efficiency. <br/>Currently, CCT is mainly applied in eligibility tests and clinical medicine questionnaires. In eligibility tests, all three types of termination rules have the potential to be widely applied. However, in practice, the principles of the likelihood ratio rule and the Bayesian decision theory rule are not easily understood by the general public, and these methods are also accompanied by the problem of over-exposure of items for their preference of cut-point based item selection methods. Therefore, the confidence interval rule, which is relatively simple in principle and has alleviated item exposure, has been widely used in existing qualifying tests. Bayesian decision theory rules are more applicable in clinical questionnaires because of their finer control over various classification losses. <br/>The following can be considered for future research on CCT termination rules. First, Bayesian decision theory rules can be improved by considering non-statistical constraints with the help of the flexibility of its loss function. Second, termination rules can be developed for multidimensional and multicategory CCT to meet more practical needs. Third, termination rules that integrate response time can be developed to improve test efficiency and classification accuracy. Fourth, it is possible to construct termination rules under the framework of machine learning.

Analysis of opinion dynamics in social networks plays an important role in today's life. For applications such as predicting users' political preference, it is particularly important to be able to analyze the dynamics of competing opinions. While observing the evolution of polar opinions of a social network's users over time, can we tell when the network "behaved" abnormally? Furthermore, can we predict how the opinions of the users will change in the future? Do opinions evolve according to existing network opinion dynamics models? To answer such questions, it is not sufficient to study individual user behavior, since opinions can spread far beyond users' egonets. We need a method to analyze opinion dynamics of all network users simultaneously and capture the effect of individuals' behavior on the global evolution pattern of the social network. In this work, we introduce Social Network Distance (SND) - a distance measure that quantifies the "cost" of evolution of one snapshot of a social network into another snapshot under various models of polar opinion propagation. SND has a rich semantics of a transportation problem, yet, is computable in time linear in the number of users, which makes SND applicable to the analysis of large-scale online social networks. In our experiments with synthetic and real-world Twitter data, we demonstrate the utility of our distance measure for anomalous event detection. It achieves a true positive rate of 0.83, twice as high as that of alternatives. When employed for opinion prediction in Twitter, our method's accuracy is 75.63%, which is 7.5% higher than that of the next best method. Source Code: https://cs.ucsb.edu/~victor/pub/ucsb/dbl/snd/

Bounded confidence opinion dynamics with opinion leaders and environmental noises

The Continued Influence Effect (CIE) refers to the persistent impact of misinformation on beliefs or reasoning, even after its retraction. Traditional accounts attribute CIE to memory failures – either in updating mental models or retrieving corrections. In contrast, newer theories propose that CIE persists despite successful encoding and retrieval of retractions, due to motivational and reasoning-based processes. Across six experiments (N = 1,446), we tested these competing explanations. Participants frequently relied on misinformation even when recognizing it as misleading, and those who knowingly used it showed greater overall reliance. However, after debriefing, CIE declined most among participants who identified it as misleading. Furthermore, participants cited perceived relevance and explanatory value as reasons for misinformation use, highlighting goal-directed reasoning. These patterns were robust across various conditions, including prebunking interventions and source credibility manipulations.To integrate these findings, we propose the Dynamic Inference Optimization (DIO) model, framing CIE as a trade-off between conserving cognitive resources and minimizing uncertainty (i.e., model entropy). DIO suggests that CIE occurs because misinformation is weighted over retraction due to its explanatory power, forming a low-entropy model that requires minimal cognitive effort. However, maladaptive mismatches between cognition and environment may strategically increase model entropy, enabling belief revision by reweighting information probabilities, at the cost of increased cognitive effort. This model offers a unified, process-level account of CIE grounded in principles of adaptive reasoning and cognitive effort. Importantly, DIO fits into dynamic models of cognition, offering a more nuanced and ecologically valid explanation of how misinformation continues to influence reasoning.

In this paper we introduce a novel model that can account for the spread of extreme opinions in a human population as a purely local, selforganising process. Our starting point is the well-known and influential Relative Agreement (RA) model of opinion dynamics introduced by Deffuant et al. (2002). The RA model explores the dynamics of opinions in populations that are initially seeded with some number of individuals, who hold opinions at the far ends of a continuous spectrum of opinions represented in the abstract RA model as a real value in the range [-1.0, +1.0]; but the majority of the individuals in the population are, at the outset, holding opinions closer to the central mid-range value of 0.0. Various researchers have demonstrated that the RA model generates opinion dynamics in which the influence of the extremists on the moderates leads, over time, to the distribution of opinion values in the population converging to attractor states that can be qualitatively characterised as one of either uni-polar and bi-polar extremes, or reversion to the centre (central convergence). However, a major weakness of the RA model is that it pre-supposes the existence of extremist individuals, and hence says nothing to answer the question of where do extremists come from? In this paper, we introduce the Relative Disagreement (RD) model, in which extremist individual arise spontaneously and can then exert influence over moderates, forming large groups of polar extremists, via an entirely internal, self-organisation process. We demonstrate that the RD model can readily exhibit the uni-polar, bi-polar, and central-convergence attractors that characterise the dynamics of the RA model, and hence this is the first paper to describe an opinion dynamic model in which extremist positions can spontaneously arise and spread in a population via a self-organising process opinion-influencing interactions between any two individuals are characterised not only by the extent to which they agree, but also by the extent to which they disagree.