Opinion Dynamics In Social Networks Research Articles

Asynchronous opinion dynamics in social networks

AbstractOpinion spreading in a society decides the fate of elections, the success of products, and the impact of political or social movements. A prominent model to study opinion formation processes is due to Hegselmann and Krause. It has the distinguishing feature that stable states do not necessarily show consensus, i.e., the population of agents might not agree on the same opinion. We focus on the social variant of the Hegselmann–Krause model. There are n agents, which are connected by a social network. Their opinions evolve in an iterative, asynchronous process, in which agents are activated one after another at random. When activated, an agent adopts the average of the opinions of its neighbors having a similar opinion (where similarity of opinions is defined using a parameter $$\varepsilon $$ ε ). Thus, the set of influencing neighbors of an agent may change over time. We show that such opinion dynamics are guaranteed to converge for any social network. We provide an upper bound of $${\text {O}}(n|E|^2 (\varepsilon /\delta )^2)$$ O ( n | E | 2 ( ε / δ ) 2 ) on the expected number of opinion updates until convergence to a stable state, where $$|E|$$ | E | is the number of edges of the social network, and $$\delta $$ δ is a parameter of the stability concept. For the complete social network we show a bound of $${\text {O}}(n^3(n^2 + (\varepsilon /\delta )^2))$$ O ( n 3 ( n 2 + ( ε / δ ) 2 ) ) that represents a major improvement over the previously best upper bound of $${\text {O}}(n^9 (\varepsilon /\delta )^2)$$ O ( n 9 ( ε / δ ) 2 ) .

A game approach to multi-dimensional opinion dynamics in social networks with stubborn strategist agents

In a social network, individuals express their opinions on several interdependent topics, and therefore the evolution of their opinions on these topics is also mutually dependent. In this work, we propose a differential game model for the multi-dimensional opinion formation of a social network whose population of agents interacts according to a communication graph. Each individual’s opinion evolves according to an aggregation of disagreements between the agent’s opinions and its graph neighbors on multiple interdependent topics exposed to an unknown extraneous disturbance. For a social network with strategist agents, the opinions evolve over time with respect to the minimization of a quadratic cost function that solely represents each individual’s motives against the disturbance. We find the unique Nash/worst-case equilibrium solution for the proposed differential game model of coupled multi-dimensional opinions under an open-loop information structure. Moreover, we propose a distributed implementation of the Nash/worst-case equilibrium solution. We examine the non-distributed and proposed distributed open-loop Nash/worst-case strategies on a small social network with strategist agents in a two-dimensional opinion space. Then we compare the evolved opinions based on the Nash/worst-case strategy with the opinions corresponding to social optimality actions for non-strategist agents.

The Memory Influence on Opinion Dynamics in Coopetitive Social Networks: Analysis, Application, and Simulation

In social psychology, it is well known that the evolution of opinion dynamics in a society depends not only on the current opinions of individuals, but also on the past opinions stored in memory. However, it is still difficult to clearly characterize and analyze the memory influence on opinion dynamics in social networks, especially in coopetitive (cooperative and competitive) networks. In this paper, we propose a novel model of opinion dynamics to describe the memory influence in coopetitive networks. In this model, memory and memoryless communication rules are simultaneously proposed for the opinion update mechanism. In terms of the network topological structure and the graph spectrum, sufficient and/or necessary conditions are respectively established to ensure that the opinion is nonstationary polarization, nonstationary consensus and neutral. We employ the Kahneman's seminal experiment on choices in risky and riskless contexts to interpret the results obtained in the present paper. Simulation analysis shows that the memory capacity of the individual is inversely proportional to the speeds of the ultimate opinions formational, and the opinions reach a persistent disagreement when the individuals are very confident.

Human Crowds as Social Networks: Collective Dynamics of Consensus and Polarization

A ubiquitous type of collective behavior and decision-making is the coordinated motion of bird flocks, fish schools, and human crowds. Collective decisions to move in the same direction, turn right or left, or split into subgroups arise in a self-organized fashion from local interactions between individuals without central plans or designated leaders. Strikingly similar phenomena of consensus (collective motion), clustering (subgroup formation), and bipolarization (splitting into extreme groups) are also observed in opinion formation. As we developed models of crowd dynamics and analyzed crowd networks, we found ourselves going down the same path as models of opinion dynamics in social networks. In this article, we draw out the parallels between human crowds and social networks. We show that models of crowd dynamics and opinion dynamics have a similar mathematical form and generate analogous phenomena in multiagent simulations. We suggest that they can be unified by a common collective dynamics, which may be extended to other psychological collectives. Models of collective dynamics thus offer a means to account for collective behavior and collective decisions without appealing to a priori mental structures.

Managing consensus based on community classification in opinion dynamics

<abstract><p>Opinion dynamics in social networks are fast becoming an essential instrument for concentrating on the effect of individual choices on external public information. One of the main challenges in seeing the dynamics is reaching an opinion consensus acceptable to managers in a social network. This issue is referred to as a consensus-reaching process (CRP). Most studies of CRP focus only on network structure and ignore the effect of agent opinions. In addition, existing methods ignore the diversities between divided communities. How to synthesize individual opinions with community diversities to solve CRP issues has remained unclear. Using the DeGroot model for opinion control, this paper considers the effects of network structures and agent opinions when dividing communities, incorporating community classification and targeted opinion control strategies. First, a community classification enhancement approach is utilized, introducing the concept of ambiguous nodes and their division methods. Second, we separate all communities into three levels, $ Center $, $ Base $, and $ Fringe $, according to the logical regions for opinion control. Third, an edge expansion algorithm and three opinion control strategies are proposed based on the community levels, which can significantly reduce the time it takes for the network to reach a consensus. Finally, numerical analysis and comparison are given to verify the feasibility of the proposed opinion control strategy.</p></abstract>

Influence in social networks with stubborn agents: From competition to bargaining

The literature on game-theoretic models of opinion dynamics in social networks mainly focuses on the Nash equilibrium, which reflects a competitive situation between influencing agents called players. In some real-world situations, however, players negotiate over a game; thus, a different type of solution needs to be considered to account for possible outcomes. In this paper, we examine an opinion dynamics game based on the Friedkin–Johnsen model for which we characterize the Pareto frontier, including the Nash bargaining solution. Next, we analyze this solution when there are changes in the susceptibility of noninfluencing agents with respect to their initial opinions. We also quantify how the Nash equilibrium outcome differs from the outcome prescribed by the Nash bargaining solution.

Resilient Consensus for Multi-Agent Systems Under Adversarial Spreading Processes

This paper addresses novel consensus problems for multi-agent systems operating in an unreliable environment where adversaries are spreading. The dynamics of the adversarial spreading processes follows the susceptible-infected-recovered (SIR) model, where the infection induces faulty behaviors in the agents and affects their state values. Such a problem setting serves as a model of opinion dynamics in social networks where consensus is to be formed at the time of pandemic and infected individuals may deviate from their true opinions. To ensure resilient consensus among the noninfectious agents, the difficulty is that the number of infectious agents changes over time. We assume that a local policy maker announces the local level of infection in real-time, which can be adopted by the agent for its preventative measures. It is demonstrated that this problem can be formulated as resilient consensus in the presence of the socalled mobile malicious models, where the mean subsequence reduced (MSR) algorithms are known to be effective. We characterize sufficient conditions on the network structures for different policies regarding the announced infection levels and the strength of the epidemic. Numerical simulations are carried out for random graphs to verify the effectiveness of our approach.

Opinion dynamics in social networks under competition: the role of influencing factors in consensus-reaching.

The rapid development of information technology and social media has provided easy access to the vast data on individual preferences and social interactions. Despite a series of problems, such as privacy disclosure and data sensitivity, it cannot be denied that this access also provides beneficial opportunities and convenience for campaigns involving opinion control (e.g. marketing campaigns and political election). The profitability of opinion and the finiteness of individual attention have already spawned extensive competition for individual preferences on social networks. It is necessary to investigate opinion dynamics over social networks in a competitive environment. To this end, this paper develops a novel social network DeGroot model based on competition game (DGCG) to characterize opinion evolution in a competitive opinion dynamics. Social interactions based on trust relationships are captured in the DGCG model. From the model, we then obtain equilibrium results in a stable state of opinion evolution. We also analyse what role relevant factors play in the final consensus and competitive outcomes, including the resource ratio of both contestants, initial opinions, self-confidence and network structure. Theoretical analyses and numerical simulations show that these factors can significantly sway the consensus and even reverse competition outcomes.

Robust Opinion Control Under Network Perturbation

Online social networks connect people together and facilitate them to share their experiences and thoughts, while they also enable users with extreme opinions to further publicize their opinions and influence others. Thus, it is critical to study users' opinion formation process and to design effective mechanisms to control the opinion dynamics in social networks. In this work, we consider the scenario where users with extreme opinions may change the network structure, e.g., by adding new links or tuning the edge weights, to further spread their opinions to the public, and theoretically analyze its impact on the network opinions at equilibrium. We also propose a robust opinion control scheme that can reduce the influence of such network structure perturbation on network opinions. Simulations verify the correctness of our analysis and the effectiveness of our proposed opinion control algorithm.

Modeling and Analysis of Opinion Dynamics in Social Networks Using Multiple-Population Mean Field Games

The dominanceof social networks has advanced immensely as many users become more dependent on these networks to be able to engage on social discussions and activities. The behavior of these users about a specific topic or issue can be extracted from their own belief or opinion as well as that of their connections. In order to derive meaningful and important behavioral information, these users can be modeled and analyzed together according to similarities in attributes such as political orientation, race, gender, and age. In this research work, the opinion dynamics of a multiple-population social network is investigated through the application of multiple-population mean field game (MPMFG) for behavior modeling and analysis. As a consequence of the proposed MPMFG model, information can be gained on the behavior of social network users belonging to different populations or groups. Specifically, the proposed MPFMG model can be utilized to estimate and predict the behavior of a social network group as well as their effect on the belief and opinion of other groups. Simulations are provided to demonstrate the belief and opinion dynamics of social network users in multiple-population settings. Moreover, theoretical and experimental results as well as comprehensive performance analysis are presented to demonstrate the effectiveness and validity of the proposed MPMFG approach in modeling and analyzing the evolution of opinions in multiple-population social networks.

Graphical Evolutionary Game Theoretic Modeling of Strategy Evolution Over Heterogeneous Networks

The rapid development of the Internet and networking technologies greatly facilitates the interactions among heterogeneous agents, while it also causes problems such as the breakout of rumors and online bullying. Thus, it is critical to study the <i>strategy evolution</i> process in complex networks, that is, how heterogeneous agents interact with each other, update their opinions, and make decisions. In the literature, there have been numerous works on the modeling and analysis of decision making and opinion dynamics in social networks. However, most works assume that agents are homogeneous or only consider one single attribute in agent heterogeneity. In complex social networks, agents differ in many attributes and they constantly influence each other&#x0027;s decisions. How strategy evolves in complex networks with heterogeneous agents remains unknown. In this work, we consider three different attributes of agents: influence, susceptibility, and interest. We use graphical evolutionary game theory to theoretically analyze the impact of different attributes on the strategy evolution process and the evolutionary stable states (ESS). Both theoretical analysis and simulation results show that the influence attribute alone cannot change the ESS of the strategy evolution, while super agents who are both influential and stubborn have the largest impact on the ESS. Furthermore, real data validation shows that our proposed model can effectively model the information diffusion process in online social networks. This study is critical to the better understanding of agents&#x0027; decision making process, and provides important guidelines on the management of social networks.

Multidimensional Model of Opinion Dynamics in Social Networks: Polarization Indices

Multidimensional Model of Opinion Dynamics in Social Networks: Polarization Indices

Robust mean field social control problems with applications in analysis of opinion dynamics

This paper investigates the social optimality of linear quadratic mean field control systems with unmodelled dynamics. The objective of agents is to optimise the social cost, which is the sum of costs of all agents. By variational analysis and direct decoupling methods, the social optimal control problem is analysed, and two equivalent auxiliary robust optimal control problems are obtained for a representative agent. By solving the auxiliary problem with consistent mean field approximations, a set of decentralised strategies is designed, and its asymptotic social optimality is further proved. Next, the results are applied into the study of opinion dynamics in social networks. The evolution of opinions is analysed over finite and infinite horizons, respectively. All opinions are shown to reach agreement with the average opinion in a probabilistic sense. Finally, local interactions among multiple sub-populations are examined via graphon theory.

The influence of communication structure on opinion dynamics in social networks with multiple true states

In order to study the influence of communication structure on opinion dynamics in social networks with multiple true states, a social learning model is proposed in which the social network is composed of strongly connected communities and some uninformed individuals outside the communities. Multiple communities correspond to multiple underlying true states. At each time step, the individual in a community receives his private signal and updates his opinion to be a weighted linear combination of his own Bayesian posterior opinion and the opinions of his neighbors, while the uninformed individual outside the communities has no private signal and only takes the neighbors’ weighted average opinion as his own opinion. Simulation results show that in the social network environment with multiple true states, for the uninformed individual, the opinion will depend on the weighted average opinion of his neighbors, and for the individual in the strongly connected community, the opinion dynamics will depend on the communication types between communities. If communities are not connected, he will achieve asymptotic learning. If communities are unidirectionally connected, he will learn the true state of the root community. If communities are bidirectionally connected, his opinion will appear chaos phenomenon and oscillate within a certain range. So, in a society with multiple true states, the absence of communication between communities is conducive to asymptotic learning and bidirectional communications between communities will hinder asymptotic learning.

The impact of noise and topology on opinion dynamics in social networks.

We investigate the impact of noise and topology on opinion diversity in social networks. We do so by extending well-established models of opinion dynamics to a stochastic setting where agents are subject both to assimilative forces by their local social interactions, as well as to idiosyncratic factors preventing their population from reaching consensus. We model the latter to account for both scenarios where noise is entirely exogenous to peer influence and cases where it is instead endogenous, arising from the agents’ desire to maintain some uniqueness in their opinions. We derive a general analytical expression for opinion diversity, which holds for any network and depends on the network’s topology through its spectral properties alone. Using this expression, we find that opinion diversity decreases as communities and clusters are broken down. We test our predictions against data describing empirical influence networks between major news outlets and find that incorporating our measure in linear models for the sentiment expressed by such sources on a variety of topics yields a notable improvement in terms of explanatory power.

A study of a complex model of opinion dynamics in social networks

Many micro-level models of information processes in social networks consider either a change in the information-psychological state of agents (opinions, beliefs, attitudes) or a change in their observable behavior (actions). The goal in this paper is to develop and analyze a complex agent-based model of opinion dynamics that describes the dynamics of agents’ beliefs and the process of performing actions by agents. The issues of reaching consensus and polarizing opinions of agents are investigated.

Reaching Consensus Based on the Opinion Dynamics in Social Networks

This paper studies the minimum consensus cost strategy in the whole group decision-making (GDM) process under the condition of experts’ opinion and weight evolving over time. Based on the traditional minimum cost consensus model (MCCM), the updated algorithm of opinion dynamics is introduced to obtain the expert’s opinion value and weight, which is used for the optimal strategy of group consensus decision making. In the existing MCCM, the consensus mechanism is established through a simple optimization model, in which each expert’s opinion value and weight coefficient are in a static state and do not change dynamically with time. However, in actual GDM, the expert’s opinion and their own importance (weight coefficient) are random and easily affected by the decision-making environment. Therefore, this paper proposes three novel kinds of MCCMs based on opinion dynamics in social networks. Numerical results show that this method can reach a higher degree of consensus in a reasonable time compared with traditional consensus model. In addition, some comparative experimental data also show that compared with some static consensus, the optimal decision strategy proposed can greatly reduce the cost. In particular, the MCCM model with confidence parameter reduces the consensus cost to the lowest and obtains the highest degree of consensus.

Opinion Dynamics in Social Networks: The Effect of Centralized Interaction Tuning on Emerging Behaviors

The algorithmic filtering of contents exchanged on digital social networks entails a centralized control of the intensity of users’ interaction. The aim of this article is to investigate how this centralized action can affect the time evolution of users’ opinions on a specific issue. To this purpose, this article proposes a stochastic multiagent model that incorporates a simplified description of the modulation of the interaction intensity exerted by the platform manager. Various transient and steady-state properties of the model are established. In particular, it is studied how emerging collective behaviors, e.g., consensus, polarization, and community cleavage, depend on the interaction intensity parameter. Notably, the nonmonotonic effects of such a parameter are observed for suitable distributions of influenceability across the community. By means of a newly introduced concept of individual stochastic social power, some insights are given on the role of the interaction intensity parameter in the conflict between opposite factions in simple scenarios. A major finding of this article is that an apparently neutral intervention, i.e., unbiased with respect to the conflicting opinions, can favor one faction just by tuning the interaction intensity.

Characterization of vulnerability of road networks to fluvial flooding using SIS network diffusion model

This study aims to characterize the vulnerability of road networks to fluvial flooding using a network diffusion-based method. Various network diffusion models have been applied widely for modeling the spreading of contagious diseases or capturing opinion dynamics in social networks. By comparison, their application in the context of physical infrastructure networks has just started to gain some momentum, although physical infrastructure networks also exhibit diffusion-like phenomena under certain stressors. This study applies a susceptible-impacted-susceptible (SIS) diffusion model to capture the impact of flooding on the road network connectivity. To that end, this paper undertook the following four steps. First, the road network was modeled as primal graphs and nodes that were flood-prone (or the origins of the fluvial flood) were identified. Second, temporal changes in the flood depth within the road network during a flooding event were obtained using a data-driven geospatial model. Third, based on the relationship between vehicle speed and flood depth on road networks, at each time step, the nodes in the road network were divided into two discrete categories, namely functional and closed, standing for Susceptible and Impacted in the SIS diffusion model, respectively. Then, two parameters of the SIS model, average transition probabilities between states, were estimated using the results of the hydraulic simulation. Fourth, the robustness of the road network under various SIS diffusion scenarios was estimated, which was used to test the statistical significance of the difference between the robustness of the road network against diffusions started from the randomly chosen nodes and nodes with different high centrality measures. The methodology was demonstrated using the road network in the Memorial super neighborhood in Houston. The results show that diffusive disruptions that start from nodes with high centrality values do not necessarily cause a more significant loss to the connectivity of the road network. The proposed method has important implications for applying link predictions on road networks, and it casts significant insights into the mechanism by which cascading disruptions spread from flood control infrastructure to road networks, as well as the diffusion process in the road networks.

Targeted Bipartite Consensus of Opinion Dynamics in Social Networks With Credibility Intervals.

This article investigates the targeted bipartite consensus problem of opinion dynamics in cooperative-antagonistic networks. Each agent in the network is assigned with a convergence set to represent a credibility interval, in which its opinion is trustworthy. The network topology is characterized by a signed switching digraph. The objective is to achieve the bipartite consensus targeted within these credibility intervals. A gradient term is introduced in the opinion dynamics besides the consensus term. Under the assumption that the underlying graph is uniformly jointly strongly connected and structurally balanced, it is first shown that the considered opinion dynamics reaches the targeted bipartite consensus within the intersections of the convergence sets associated with two antagonistic groups. Next, by relaxing the connectivity condition to uniform joint quasistrong connectivity, the targeted bipartite consensus result is also proven with an additional convergence set assumption. Numerical examples are provided to validate the proposed theoretical results.