Opinion Dynamics Model Research Articles

The power of social networks and social media’s filter bubble in shaping polarisation: an agent-based model

AbstractTthe role social media platforms play on the emergence of polarisation is an ongoing debate in the political communication literature. Social media’s filter bubbles and online echo chambers shape people’s opinions by curating the information they have available. However, the extent to which this is the case remains unclear. Social simulation scholars have provided valuable insights into the subject through opinion dynamics models and agent-based modelling approaches. This article proposes a social simulation approach to the topic of opinion dynamics from a political communication perspective to understand how social network configurations and the media environment contribute to the emergence of national identity polarisation. We built an agent-based simulation model of national identity dynamics with a multilayer multiplex network of interacting agents in a hybrid media environment of both, traditional media and social media platforms. We use the Catalan secessionist movement to ground, contextualise and empirically inform parts of our model. We found that the initial social network setup conditions had a large impact on the emergence of polarisation amongst agents. In particular, homophily-based social networks composed of a majority of like-minded individuals produced greater polarisation compared to random networks. This was aggravated in the presence of social media filtering algorithms, selectively exposing agents to supportive information. These results emphasise the importance of both the selective exposure by social media filtering algorithms and one’s social networks (echo chambers) for polarisation to emerge. This interaction reinforces the influence of social media platforms and social networks have on the emergence of polarisation.

Leveraging uncertainty in collective opinion dynamics with heterogeneity

Natural and artificial collectives exhibit heterogeneities across different dimensions, contributing to the complexity of their behavior. We investigate the effect of two such heterogeneities on collective opinion dynamics: heterogeneity of the quality of agents’ prior information and of degree centrality in the network. To study these heterogeneities, we introduce uncertainty as an additional dimension to the consensus opinion dynamics model, and consider a spectrum of heterogeneous networks with varying centrality. By quantifying and updating the uncertainty using Bayesian inference, we provide a mechanism for each agent to adaptively weigh their individual against social information. We observe that uncertainties develop throughout the interaction between agents, and capture information on heterogeneities. Therefore, we use uncertainty as an additional observable and show the bidirectional relation between centrality and information quality. In extensive simulations on heterogeneous opinion dynamics with Gaussian uncertainties, we demonstrate that uncertainty-driven adaptive weighting leads to increased accuracy and speed of consensus, especially with increasing heterogeneity. We also show the detrimental effect of overconfident central agents on consensus accuracy which can pose challenges in designing such systems. The opportunities for improved performance and observablility suggest the importance of considering uncertainty both for the study of natural and the design of artificial heterogeneous systems.

Opinion response functions are key to understanding the tipping of social conventions

Abstract The extent to which committed minorities can overturn social conventions is an active area of research in the mathematical modeling of opinion dynamics. Researchers generally use simulations of agent-based models (ABMs) to compute approximate values for the minimum committed minority size needed to overturn a social convention. In this manuscript, we expand on previous work by studying an ABM’s mean-field behavior using ordinary differential equation models and a new tool, namely opinion response functions (ORFs). Using this method allows for formal analysis of the deterministic model, which can provide a theoretical explanation for observed behaviors, e.g. coexistence or overturning of opinions. In particular, ORFs are a method for characterizing equilibria in our social model. Our analysis confirms earlier numerical results and supplements them with a precise formula for computing the minimum committed minority size required to overturn a social convention.

On Some Dynamics in Conceptual Spaces

AbstractIn this text, we consider Gärdenfors’ conceptual spaces that are separable Hilbert spaces. In particular, the results we obtained apply to finite-dimensional Euclidean spaces. Our main contribution can be formulated as a combination of the theory of opinion dynamics with the theory of conceptual spaces. This combination, in turn, leads us to propose a new model for the time evolution of conceptual spaces. To achieve this goal, we propose some extension of the multidimensional opinion dynamics model of Parsegov, Proskurnikov, Tempo and Friedkin to opinions with values in Hilbert spaces.

Opinion dynamics beyond social influence

Abstract We present an opinion dynamics model framework discarding two common assumptions in the literature: (a) that there is direct influence between beliefs of neighboring agents, and (b) that agent belief is static in the absence of social influence. Agents in our framework learn from random experiences which possibly reinforce their belief. Agents determine whether they switch opinions by comparing their belief to a threshold. Subsequently, influence of an alter on an ego is not direct incorporation of the alter’s belief into the ego’s but by adjusting the ego’s decision-making criteria. We provide an instance from the framework in which social influence between agents generalizes majority rules updating. We conduct a sensitivity analysis as well as a pair of experiments concerning heterogeneous population parameters. We conclude that the framework is capable of producing consensus, polarization and fragmentation with only assimilative forces between agents which typically, in other models, lead exclusively to consensus.

Three-Stage Cascade Information Attenuation for Opinion Dynamics in Social Networks.

In social network analysis, entropy quantifies the uncertainty or diversity of opinions, reflecting the complexity of opinion dynamics. To enhance the understanding of how opinions evolve, this study introduces a novel approach to modeling opinion dynamics in social networks by incorporating three-stage cascade information attenuation. Traditional models have often neglected the influence of second- and third-order neighbors and the attenuation of information as it propagates through a network. To correct this oversight, we redefine the interaction weights between individuals, taking into account the distance of opining, bounded confidence, and information attenuation. We propose two models of opinion dynamics using a three-stage cascade mechanism for information transmission, designed for environments with either a single or two subgroups of opinion leaders. These models capture the shifts in opinion distribution and entropy as information propagates and attenuates through the network. Through simulation experiments, we examine the ingredients influencing opinion dynamics. The results demonstrate that an increased presence of opinion leaders, coupled with a higher level of trust from their followers, significantly amplifies their influence. Furthermore, comparative experiments highlight the advantages of our proposed models, including rapid convergence, effective leadership influence, and robustness across different network structures.

Multi-population opinion dynamics model

Multi-population opinion dynamics model

Competitive resource allocation on a network considering opinion dynamics with self-confidence evolution

The formation of public opinion is typically influenced by different stakeholders, such as governments and firms. Recently, various real-world problems related to the management of public opinion have emerged, necessitating stakeholders to strategically allocate resources on networks to achieve their objectives. To address this, it is imperative to consider the dynamics of opinion formation. Notably, in existing opinion dynamics models, individuals possess self-confidence parameters reflecting their adherence to historical opinions. However, most extant studies assume the individuals’ self-confidence levels remain constant over time, which cannot accurately capture the intricacies of human behavior. In response to this gap, we first introduce a self-confidence evolution model, which encompasses two influencing factors: the self-confidence levels of one's group mates and the passage of time. Furthermore, we present the social network DeGroot model with self-confidence evolution, and conduct some theoretical analyses. Moreover, we propose a game model to identify the optimal resource allocation strategies of players on a network. Finally, we provide sensitivity analyses, comparative studies, and a case study. This paper highlights the significance of incorporating self-confidence evolution into the process of opinion dynamics, and the results can provide valuable practical insights for players seeking to improve their optimal resource allocation on a network to more effectively manage public opinions.

Large-scale multiple criteria group decision-making with information emendation based on unsupervised opinion evolutions

Large-scale multiple criteria group decision-making (MCGDM) is prevalent in diverse decision-making scenarios, involving numerous decision makers (DMs), the set of alternatives and criteria, and continuous temporal cycles. Opinions from DMs dynamically evolve through iterative interaction, leading to dynamic opinion evolutions. However, traditional MCGDM methodology usually establish the opinion formation on a static time point throughout information aggregation, which will lead to information distortion. This study develops a novel large-scale MCGDM method with information emendation based on an unsupervised opinion dynamics (UOD) model, combining with the intuitionistic fuzzy set (IFS) and the technique for order preference by similarity to an ideal solution (TOPSIS). The IFS is utilized to quantify opinions since it can effectively achieve a tradeoff between information retention and convenience of evaluation. Simultaneously, in the proposed UOD model, the weight updating mechanism is further considered to improve the interaction adequacy, and the unsupervised mechanism for interaction threshold helps to decrease the influences of subjectivity from DMs. Moreover, numerical simulations validate the UOD model’s feasibility. Finally, a school site selection problem is carried out to elaborate the effectiveness of the proposed method. This study will provide a methodological reference for solving large-scale MCGDM problems, facilitating rapid convergence of opinions within large-scale groups, and enrich the research on opinion dynamics in the field of decision-making.

Independence role in the generalized Sznajd model

The Sznajd model is one of sociophysics’s well-known opinion dynamics models. Based on social validation, it has found application in diverse social systems and remains an intriguing subject of study, particularly in scenarios where interacting agents deviate from prevailing norms. This paper investigates the generalized Sznajd model, featuring independent agents on a complete graph and a two-dimensional square lattice. Agents in the network act independently with a probability p, signifying a change in their opinion or state without external influence. This model defines a paired agent size r, influencing a neighboring agent size n to adopt their opinion. This study incorporates analytical and numerical approaches, especially on the complete graph. Our results show that the macroscopic state of the system remains unaffected by the neighbor size n but is contingent solely on the number of paired agents r. Additionally, the time required to reach a stationary state is inversely proportional to the number of neighboring agents n. For the two-dimensional square lattice, two critical points p=pc emerge based on the configuration of agents. The results indicate that the universality class of the model on the complete graph aligns with the mean-field Ising universality class. Furthermore, the universality class of the model on the two-dimensional square lattice, featuring two distinct configurations, is identical and falls within the two-dimensional Ising universality class.

Opinion dynamics models describing the emergence of polarization phenomena

Some novel models of opinion dynamics are here formulated in terms of ordinary and of stochastic differential equations. The focus is on the possible emergence of polarization phenomena. Alongside attitudes and mechanisms related to individual-individual interactions, issues such as the influence of persuaders, acting perhaps on different time-scales, and uncertainty are taken into account. The existence of stationary solutions corresponding to polarized opinion distributions, together with their stability or instability properties, is established in correspondence to different parameter values.

Biswas-Chatterjee-Sen Model on Solomon Networks with Two Three-Dimensional Lattices.

The Biswas-Chatterjee-Sen (BChS) model of opinion dynamics has been studied on three-dimensional Solomon networks by means of extensive Monte Carlo simulations. Finite-size scaling relations for different lattice sizes have been used in order to obtain the relevant quantities of the system in the thermodynamic limit. From the simulation data it is clear that the BChS model undergoes a second-order phase transition. At the transition point, the critical exponents describing the behavior of the order parameter, the corresponding order parameter susceptibility, and the correlation length, have been evaluated. From the values obtained for these critical exponents one can confidently conclude that the BChS model in three dimensions is in a different universality class to the respective model defined on one- and two-dimensional Solomon networks, as well as in a different universality class as the usual Ising model on the same networks.

Erratum: Bounded-confidence model of opinion dynamics with heterogeneous node-activity levels [Phys. Rev. Research 5 , 023179 (2023)

Erratum: Bounded-confidence model of opinion dynamics with heterogeneous node-activity levels [Phys. Rev. Research <b>5</b> , 023179 (2023)

Emergence of Polarization in a Sigmoidal Bounded-Confidence Model of Opinion Dynamics

Emergence of Polarization in a Sigmoidal Bounded-Confidence Model of Opinion Dynamics

Bridging the gap between agent based models and continuous opinion dynamics

There is a rich literature on microscopic models for opinion dynamics; most of them fall into one of two categories – agent-based models or differential equation models – with a general understanding that the two are connected in certain scaling limits. In this paper we show rigorously this is indeed the case. In particular we show that both ordinary and stochastic differential equations can be obtained as a limit of agent-based models by simultaneously rescaling time and the extent to which an agent updates their opinion after an interaction. This approach provides a pathway to analyse much more diverse modelling paradigms, for example: the motivation behind several possible multiplicative noise terms in stochastic differential equation models; the connection between selection noise and the mollification of the discontinuous bounded confidence interaction function; and how the method for selecting interacting pairs can determine the normalisation in the corresponding differential equation. Our computational experiments confirm our findings, showing excellent agreement of solutions to the two classes of models in a variety of settings.

Fake News: “No Ban, No Spread—With Sequestration”

To curb the spread of fake news, I propose an alternative to the current trend of implementing coercive measures. This approach would preserve freedom of speech while neutralizing the social impact of fake news. The proposal relies on creating an environment to naturally sequestrate fake news within quite small networks of people. I illustrate the process using a stylized model of opinion dynamics. In particular, I explore the effect of a simultaneous activation of prejudice tie breaking and contrarian behavior, on the spread of fake news. The results show that indeed most pieces of fake news do not propagate beyond quite small groups of people and thus pose no global threat. However, some peculiar sets of parameters are found to boost fake news so that it “naturally” invades an entire community with no resistance, even if initially shared by only a handful of agents. These findings identify the modifications of the parameters required to reverse the boosting effect into a sequestration effect by an appropriate reshaping of the social geometry of the opinion dynamics landscape. Then, all fake news items become “naturally” trapped inside limited networks of people. No prohibition is required. The next significant challenge is implementing this groundbreaking scheme within social media.

Universality of opinions disappearing in sociophysical models of opinion dynamics: From initial multitude of opinions to ultimate consensus.

Possibility of reaching a consensus in social systems with strong initial fragmentation is one of the most interesting issues in sociophysics. It is also intriguing what the dynamics of such processes is. To address those problems, we performed computer simulations using well-established models of social opinion formation, namely, the voter, Sznajd, and Latané models. We investigated opinion dynamics in cases where the initial number of opinions is very large, equal to the number of actors (the voter and Latané models) or when every second actor has their own opinion (Sznajd model), with some variations on the update schemes, lattice topologies, effective ranges of interaction, and information noise levels. For all considered models, the number of opinions assumed by the actors is finally almost always reduced to only one. However, while the voter and Latané models exhibit a power-law time decrease in the number of opinions, the Sznajd model follows a complex three-stage behavior. We also demonstrated the mean/median time of reaching the consensus scales with system size according to a power law for voter and Sznajd models, while for the Latané model, this increase is even faster. Our results show that in the studied models, the consensus is possible, provided that a long enough and model-dependent time to reach this state is available.

A method of predicting and managing public opinion on social media: An agent-based simulation

In current opinion dynamics models for predicting public opinion, the spread of events within social media has been inadequately considered, resulting in suboptimal prediction performance and inefficient strategies for public opinion management. This deficiency is particularly consequential for governments and enterprises, as adverse public opinions associated with them can inflict significant harm. This study develops a link prediction-based opinion dynamics (LPOD) model to address this gap in predicting and managing public opinion. The proposed model integrates insights from epidemiology, specifically the susceptible-infected-recovered model, to characterize the spread of events. The LPOD model enhances the updating process of relationships and opinions by redesigning the link and opinion prediction methods. Subsequently, a link-recommendation-based management approach is formulated to manage public opinion effectively. Experimental results reveal that, compared to existing models, the proposed model elevates opinion prediction accuracy from 0.81 to 0.92 and link prediction accuracy from 0.60 to 0.70. In terms of public opinion management efficacy, when compared to conventional methods such as managing opinion leaders and introducing particular nodes in social networks, the developed approach demonstrates a 20% and 18% increase in success rates, respectively. Furthermore, validation through simulations and real-world scenarios robustly confirms the model's versatile applicability and effectiveness.

Social network group decision-making model considering interactions between trust relationships and opinion evolution

PurposeSocial network group decision-making (SNGDM) has rapidly developed because of the impact of social relationships on decision-making behavior. However, not only do social relationships affect decision-making behavior, but decision-making behavior also affects social relationships. Such complicated interactions are rarely considered in current research. To bridge this gap, this study proposes an SNGDM model that considers the interaction between social trust relationships and opinion evolution.Design/methodology/approachFirst, the trust propagation and aggregation operators are improved to obtain a complete social trust relationship among decision-makers (DMs). Second, the evolution of preference information under the influence of trust relationships is measured, and the development of trust relationships during consensus interactions is predicted. Finally, the iteration of consensus interactions is simulated using an opinion dynamics model. A case study is used to verify the feasibility of the proposed model.FindingsThe proposed model can predict consensus achievement based on a group’s initial trust relationship and preference information and effectively captures the dynamic characteristics of opinion evolution in social networks.Originality/valueThis study proposes an SNGDM model that considers the interaction of trust and opinion. The proposed model improves trust propagation and aggregation operators, determines improved preference information based on the existing trust relationships and predicts the evolution of trust relationships in the consensus process. The dynamic interaction between the two accelerates DMs to reach a consensus.

A Proportional-Integral-Derivative Inspired Model for Opinion Dynamics in a Trust Relationship Network

A Proportional-Integral-Derivative Inspired Model for Opinion Dynamics in a Trust Relationship Network