Opinion Dynamics Model Research Articles

Phase transition and universality of the majority-rule model on complex networks

In this paper, we investigate the phenomena of order-disorder phase transition and the universality of the majority-rule model defined on three complex networks, namely the Barabási–Albert, Watts–Strogatz and Erdős–Rényi networks. Assume each agent holds two possible opinions randomly distributed across the networks’ nodes. Agents adopt anticonformity and independence behaviors, represented by the probability p, where with a probability p, agents adopt anticonformity or independence behavior. Based on our numerical simulation results and finite-size scaling analysis, it is found that the model undergoes a continuous phase transition for all networks, with critical points for the independence model greater than those for the anticonformity model in all three networks. We obtain critical exponents identical to the opinion dynamics model defined on a complete graph, indicating that the model exhibits the same universality class as the mean-field Ising model.

A data-driven kinetic model for opinion dynamics with social network contacts – ADDENDUM

A data-driven kinetic model for opinion dynamics with social network contacts – ADDENDUM

Noise and opinion dynamics: how ambiguity promotes pro-majority consensus in the presence of confirmation bias.

Opinion dynamics are affected by cognitive biases and noise. While mathematical models have focused extensively on biases, we still know surprisingly little about how noise shapes opinion patterns. Here, we use an agent-based opinion dynamics model to investigate the interplay between confirmation bias-represented as bounded confidence-and different types of noise. After analysing where noise can enter social interaction, we propose a type of noise that has not been discussed so far, ambiguity noise. While previously considered types of noise acted on agents either before, after or independent of social interaction, ambiguity noise acts on communicated messages, assuming that socially transmitted opinions are inherently noisy. We find that noise can induce agreement when confirmation bias is moderate, but different types of noise require quite different conditions for this effect to occur. An application of our model to the climate change debate shows that at just the right mix of confirmation bias and ambiguity noise, opinions tend to converge to high levels of climate change concern. This result is not observed with the other types. Our findings highlight the importance of considering and distinguishing between the various types of noise and the unique role of ambiguity in opinion formation.

Conformity and Mass Media Influence in the Sznajd Model on Regular Lattices.

The polarization of opinions and difficulties in reaching a consensus are central problems of many modern societies. Understanding the dynamics governing those processes is, therefore, one of the main aims of sociophysics. In this work, the Sznajd model of opinion dynamics is investigated with Monte Carlo simulations performed on four different regular lattices: triangular, honeycomb, and square with von Neumann or Moore neighborhood. The main objective is to discuss the interplay of the probability of convincing (conformity) and mass media (external) influence and to provide the details of the possible phase transitions. The results indicate that, while stronger bonds and openness to discussion and argumentation may help in reaching a consensus, external influence becomes destructive at different levels depending on the lattice.

Modeling the opinion dynamics of superstars in the film industry

One of the most challenging questions in the film industry is to rank superstars, which ultimately affects some performance indicators like movie success. In this work, we address this question by means of opinion dynamics models, where the evolution of opinions in a population is analyzed. We apply a model of this kind to study the evolution of opinions about a set of well-known movie superstars in a real-world population. Also, we use real-world data from a specialized cinema website to model mass communication processes (representing film releases and their related news and marketing campaigns), and to measure the performance of our model. Our results show that the proposed model is able to accurately represent this complex system, where the opinion dynamics of superstars are mostly driven by emotional mechanisms, and reveal that film releases and their corresponding marketing campaigns only have a short term effect on those opinions. To the best of our knowledge, this is the first work that applies opinion dynamics models to the study of opinions about superstars in the film industry.

A Novel Influence Analysis-Based University Major Similarity Study

In the field of education, investigating the relationships between different majors in universities is an important topic in current educational research. The application of social networks from informatics provides new opportunities and potentials for the field of education. Due to the complexity of social interactions, the social network connections surrounding individuals exert a significant influence on their daily decision-making processes. This paper aims to introduce the social network and influence analysis theories from informatics into the field of education, regarding major as a variable, and comparing and analyzing the influence relationships between majors. An empirical study was conducted, involving the collection of questionnaire data on graduates’ evaluations of various aspects of their university experiences across different majors. The evolution of this model follows the DeGroot opinion dynamics with the inclusion of stubborn nodes. By defining leader majors and general majors based on the data and modeling the questionnaire data as the outcome of a discrete random process, an influence matrix is ultimately generated through the opinion dynamic model. Through this modeling approach, we revealed the underlying influence relationships between different disciplines (majors). These findings provide schools with insights to adjust the directions of discipline cultivation, and offer new perspectives and methods for the study of majors in higher education.

Trust exploration- and leadership incubation- based opinion dynamics model for social network group decision-making: A quantum theory perspective

Social network (SN) holds significant sway over the consciousness and behavior of involved individuals, serving as an evolutionary medium for opinion dynamics models. Consensus is a fundamental concept in group decision-making (GDM). How to effectively explore the opinion evolution during the consensus-reaching process through SN is of paramount significance for decision-making science. Therefore, a dual-mechanism containing trust exploration and leadership incubation is developed for modeling opinion dynamics, creating a favorable condition for achieving consensus. First, a novel mechanism for analyzing the completeness of SN is proposed, encompassing a trust propagation process that considers trust discount and stability, as well as a trust aggregation method grounded by quantum theory. Second, a trust screening rule is discussed to retain the valid indirect trust relationships (TRs), and then a leadership incubation mechanism is developed to promote the effective achievement of consensus opinions in group decision-making. Finally, a numerical study is presented to elucidate the superiority and rationality of the proposed methods, and some simulation experiments and comparative analyses demonstrating the effectiveness and advantages of which are covered.

Optimal control in opinion dynamics models: diversity of influence mechanisms and complex influence hierarchies

Understanding how individuals change their opinions is essential to mitigating the harmful effect of fake news and stopping opinion polarization. The current situation in the field of opinion dynamics models is that we still do not know exactly how social influence changes individuals’ opinions and behavior. The question of which model best describes real social processes remains debatable. The current paper attempts to reconcile this problem. Building upon a relatively simple opinion dynamics model that can capture the key microscopic mechanisms of social influence and affords a tractable description of various complex influence hierarchies of social systems whereby agents may differ in how they are open to influence and how influential they are, we elaborate a framework to find optimal control, which, thus, can be applied to a broad set of opinion dynamics settings. Using a combination of theoretical and computational approaches, we characterize the properties of the optimal control and systematically demonstrate how these algorithms capture stylized examples, in which the key microscopic mechanisms of social influence as well as various influence hierarchies are covered.

Large-scale group decision-making involving community representatives: A perspective of combining strong and weak ties

In the era of social media, the issue of large-scale group decision-making (LSGDM) is becoming increasingly prominent. The complexity of large group interactions increases rapidly with the expansion of the group size. Current research has often used cluster analysis to reduce the dimensionality of LSGDM, but the decision agents following dimensionality reduction are not clearly defined, which hinders the practical application of LSGDM methods. This paper studies the LSGDM through the context of community representatives which are determined by combining strong and weak ties. The participation of such representatives in subsequent decision-making can reduce negotiation costs and efficiently form a consensus from both global and local perspectives. To identify these community representatives, this study improves the traditional Laplacian centrality, calculates the local and global centrality of individuals, and defines metrics for measuring representatives. The opinion dynamics model is used to verify the effectiveness of the LSGDM model with community representatives. The karate club network is used to illustrate the application of the proposed LSGDM model. Simulation and comparative analysis results show that the proposed model takes less time to reach consensus than traditional ones. Furthermore, there is no complete linear relationship between the representative size and the time taken to reach group consensus.

Collective group drift in a partial-differential-equation-based opinion dynamics model with biased perception kernels.

In the age of technology, individuals accelerate their biased gathering of information, which in turn leads to a population becoming extreme and more polarized. Here we study a partial-differential-equationmodel for opinion dynamics that exhibits collective behavior subject to nonlocal interactions. We developed an interaction kernel function to represent biased information gathering. Through a linear stability analysis, we show that biased populations can still form opinionated groups. However, a population that is too heavily biased can no longer come to a consensus, that is, the initial homogeneous mixed state becomes stable. Numerical simulations with biased information gathering show the ability for groups to collectively drift towards one end of the opinion space. This means that a small bias in each individual will collectively lead to groups of individuals becoming extreme together. The characteristic time scale for a group's existence is captured from numerical experiments using the temporal correlation function. Supplementing this, we included a measure of how different each population is after regular time intervals using a form of the Manhattan and Euclidean distance metrics. We conclude by exploring how wall boundary conditions induce pattern formation initially on the most extreme sides of the domain.

Quasistationary Distribution for The Invasion Model on a Complete Bipartite Graph

The Invasion Model on the complete bipartite graph was introduced and studied by physicists as a rudimentary model for opinion dynamics on complex networks. Our main result provides the limit of the Quasistationary Distribution (QSD) for the model as one partition size tends to infinity. This limit is a highly dispersed measure. The results are in stark contrast to the Voter Model whose QSD is essentially a perturbation to absorbing states. A distinct feature not present in the Voter Model and demanding a new approach developed here is the appearance of two time scales with a non-trivial interaction. Our analysis is based on decoupling of the scales and using a Stein-type operator to identify a limit distribution. It also involves an application of a known duality with coalescing Markov chains through which asymptotic survival rates associated with the QSD are obtained.

A data-driven kinetic model for opinion dynamics with social network contacts

Abstract Opinion dynamics is an important and very active area of research that delves into the complex processes through which individuals form and modify their opinions within a social context. The ability to comprehend and unravel the mechanisms that drive opinion formation is of great significance for predicting a wide range of social phenomena such as political polarisation, the diffusion of misinformation, the formation of public consensus and the emergence of collective behaviours. In this paper, we aim to contribute to that field by introducing a novel mathematical model that specifically accounts for the influence of social media networks on opinion dynamics. With the rise of platforms such as Twitter, Facebook, and Instagram and many others, social networks have become significant arenas where opinions are shared, discussed and potentially altered. To this aim after an analytical construction of our new model and through incorporation of real-life data from Twitter, we calibrate the model parameters to accurately reflect the dynamics that unfold in social media, showing in particular the role played by the so-called influencers in driving individual opinions towards predetermined directions.

A neural probabilistic bounded confidence model for opinion dynamics on social networks

Opinion dynamics (OD) models simulate the evolution of personal opinions using computer science, social dynamics, physics, and complexity science tools on social networks. However, current opinion dynamics models mainly utilize agent-based models to simulate user interactions but still need to leverage large-scale data fully. Social networks typically involve a vast number of users and information, making it difficult for models to capture the complex interactions in real social networks. Additionally, many models overlook the specific mechanisms of user interactions, such as how network individuals influence and interact with one another, resulting in inaccuracies in modeling individual opinion evolution. This paper proposes a novel approach that integrates the probabilistic bounded confidence model (PBC) with deep learning, i.e., Neural Probabilistic Bounded Confidence (NPBC), to tackle these challenges. The NPBC model adopts an attention network, a long short-term memory (LSTM) network, and a feedforward neural network to approximate the evolution of individual opinions within networks. It satisfies the data approximation and the users’ opinion update rule that conforms to the PBC model. This model enhances the understanding of opinion dynamics, helping to develop effective strategies for opinion guidance in social networks. Finally, the proposed NPBC model is evaluated on three synthetic and Twitter datasets. The results demonstrate that the proposed NPBC model performs better than the six baseline methods in predicting user opinions. Compared to baseline models, the model’s accuracy (ACC) and comprehensive evaluation (F1) scores improve by up to 18% and 7%, respectively.

Model of opinion dynamics caused by information pressure in multi-agent system with stochastic activation of links

The dynamic properties of a modified nonlinear noisy voter model on a square lattice are studied in the paper. The introduced modifications are as follows. First, the changes of the binary variable (opinion) at the voters (agents) are caused by avalanche-like perturbations of the system. Secondly, the structure of inter-agent links is not static. Its temporal evolution is due to a new characteristic of the agent called ‘activity’. It determines the probability for the agent to be linked with its nearest neighbors at a given time moment. In addition we introduce a binary variable that changes randomly in time (an ‘external opinion’). According to the proposed rules for opinion changes, an agent that unlinked to neighbors changes its opinion to a current value of the external opinion, regardless of the opinions of other agents. A linked agent can copy the opinion of its neighbor during an avalanche process. Analytically and numerically, we show that the agents’ ‘activity’ distribution and the time-averaged value of the external opinion completely determines the mode of opinion dynamics. The phase diagram for the model under consideration is obtained. In the case of large values of averaged agents’ ‘activity’ the system switches between two consensus states spending the most of time in the consensus with shared opinion corresponding to the prevailing value of the external opinion. For small value of averaged ‘activity’ the system tends to the state where the opposite opinions coexist, but agents predominate with opinion corresponding to sign of the time-averaged value of the external opinion. We demonstrate that the resulting model reflects the main features of the behavior of real multi-agent systems where the external information inflows into the system and, spreading among agents, drives opinion dynamics.

Phase coexistence in the fully heterogeneous Hegselmann-Krause opinion dynamics model.

We present an extensive study of the joint effects of heterogeneous social agents and their heterogeneous social links in a bounded confidence opinion dynamics model. The full phase diagram of the model is explored for two different network's topologies and compared to two opposed extreme cases: on one hand, the heterogeneous agents constitute a mixed population and on the other, their interactions are modeled by a lattice. The results show that when agents prone to compromise coexist with close-minded ones, the steady state of the dynamics shows coexistent phases. In particular, unlike the case of homogeneous agents in networks, or heterogeneous agents in a fully mixed population, it is possible that the society ends up in consensus around one extreme opinion. Moreover, during the dynamics, the consensus may be overturned from one extreme to the other of the opinion space. We also show that the standard order parameter, the normalized average size of the largest opinion cluster, may be misleading in this case, as it hides the existence of these phases. The phase where the opinion of the society is overturned does not require the presence of agents with special characteristics, (stubborn, extremists, etc.); it results from the interplay of agents which have agreed on an extreme opinion with the remaining group that holds the opposite one. Among the former, some may be prone to compromise with other agents which are out of the majority group, these agents, according to their location in the network, may act like bridges between the two groups and slowly attract the whole society to the other extreme.

Friedkin-Johnsen Model for Opinion Dynamics on Signed Graphs

Friedkin-Johnsen Model for Opinion Dynamics on Signed Graphs

Linear Opinion Dynamics Model With Higher Order Interactions

Linear Opinion Dynamics Model With Higher Order Interactions

Raising the Spectrum of Polarization: Generating Issue Alignment with a Weighted Balance Opinion Dynamics Model

Raising the Spectrum of Polarization: Generating Issue Alignment with a Weighted Balance Opinion Dynamics Model

Effect of three-stage cascade of opinion dynamics models in coupled networks

Information technology has contributed to the spread of public opinion across multiple coupled networks, and the scope of information spread has expanded. Owing to the impact of personal subjective cognition, information attenuation occurs during the process of opinion transmission in social networks, particularly in multi-layer social networks. In this paper, we construct a three-stage cascade opinion dynamics model, based on the Hegselmann–Krause (HK) model, to analyze the effect of information dissemination attenuation on group decision behavior in coupled social networks. This model considers three-stage cascade information transmission and two competitive opinion leader subgroups in two different social network environments, and can describe a public opinion dissemination environment more closely. The results show that the combination of the network structure and the level of trust of the public can effectively guide the spread of public opinion, which provides valuable insights into the role of social media in shaping public opinion and its impact on various fields. These findings can be useful for advertisers and policymakers to control public opinion and reach a consensus in group decision-making.

Convergence analysis of expressed and private opinion dynamics model on signed network

Due to the discrepancy between an individual's expressed opinion and private opinion in many social situations, this paper aims to study the convergence and bipartite consensus of expressed and private opinion (EPO) model on signed directed network G ( W ) without satisfying common strong connectivity. First, by constructing an enlarged network G ( P ) of G ( W ) and studying the properties of CSCCs in G ( P ) , we establish some general convergence criteria for the EPO model. Second, we explore the relationship between the final private opinion, final expressed opinion and initial opinion of an individual and prove that the self-confidence of an individual can influence the gap between his final expressed opinion and group pressure. Third, by structural balance theory, we establish the bipartite consensus criterion of the EPO model. Finally, numerical simulations are presented to illustrate the effectiveness of our results.