Dynamics of an agent-based opinion model with complete social connectivity network

The 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.

We study a tractable opinion dynamics model that generates long-run disagreements and persistent opinion fluctuations. Our model involves an inhomogeneous stochastic gossip process of continuous opinion dynamics in a society consisting of two types of agents: (1) regular agents who update their beliefs according to information that they receive from their social neighbors and (2) stubborn agents who never update their opinions and might represent leaders, political parties, or media sources attempting to influence the beliefs in the rest of the society. When the society contains stubborn agents with different opinions, the belief dynamics never lead to a consensus (among the regular agents). Instead, beliefs in the society fail to converge almost surely, the belief profile keeps on fluctuating in an ergodic fashion, and it converges in law to a nondegenerate random vector. The structure of the graph describing the social network and the location of the stubborn agents within it shape the opinion dynamics. The expected belief vector is proved to evolve according to an ordinary differential equation coinciding with the Kolmogorov backward equation of a continuous-time Markov chain on the graph with absorbing states corresponding to the stubborn agents, and hence to converge to a harmonic vector, with every regular agent's value being the weighted average of its neighbors' values, and boundary conditions corresponding to the stubborn agents' beliefs. Expected cross products of the agents' beliefs allow for a similar characterization in terms of coupled Markov chains on the graph describing the social network. We prove that, in large-scale societies, which are highly fluid, meaning that the product of the mixing time of the Markov chain on the graph describing the social network and the relative size of the linkages to stubborn agents vanishes as the population size grows large, a condition of homogeneous influence emerges, whereby the stationary beliefs' marginal distributions of most of the regular agents have approximately equal first and second moments.

This article investigates the Multiple Equilibria Regulation (MER) model, i.e., an agent-based simulation model, to represent opinion dynamics in social networks. It relies on a small set of micro-prerequisites (intra-individual balance and confidence bound), leading to emergence of (non)stationary macro-outcomes. These outcomes may refer to consensus, polarization or fragmentation of opinions about taxation (e.g., congestion pricing) or other policy measures, according to the way communication is structured. In contrast with other models of opinion dynamics, it allows for the impact of both the regulation of intra-personal discrepancy and the interpersonal variability of opinions on social learning and network dynamics. Several simulation experiments are presented to demonstrate, through the MER model, the role of different network structures (complete, star, cellular automata, small-world and random graphs) on opinion formation dynamics and the overall evolution of the system. The findings can help to identify specific topological characteristics, such as density, number of neighbourhoods and critical nodes-agents, that affect the stability and system dynamics. This knowledge can be used to better organize the information diffusion and learning in the community, enhance the predictability of outcomes and manage possible conflicts. It is shown that a small-world organization, which depicts more realistic aspects of real-life and virtual social systems, provides increased predictability and stability towards a less fragmented and more manageable grouping of opinions, compared to random networks. Such macro-level organizations may be enhanced with use of web-based technologies to increase the density of communication and public acceptability of policy measures.

Opinion dynamics in social networks with stubborn agents: Equilibrium and convergence rate

Effect of the media on the opinion dynamics in online social networks

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.

The opinion dynamics literature argues that the way people perceive social influence depends not only on the opinions of interacting individuals, but also on the individuals’ non-opinion characteristics, such as age, education, gender, or place of residence. The current paper advances this line of research by studying longitudinal data that describe the opinion dynamics of a large sample (~30,000) of online social network users, all citizens of one city. Using these data, we systematically investigate the effects of users’ demographic (age, gender) and structural (degree centrality, the number of common friends) properties on opinion formation processes. We revealed that females are less easily influenced than males. Next, we found that individuals that are characterized by similar ages have more chances to reach a consensus. Additionally, we report that individuals who have many common peers find an agreement more often. We also demonstrated that the impacts of these effects are virtually the same, and despite being statistically significant, are far less strong than that of opinion-related features: knowing the current opinion of an individual and, what is even more important, the distance in opinions between this individual and the person that attempts to influence the individual is much more valuable. Next, after conducting a series of simulations with an agent-based model, we revealed that accounting for non-opinion characteristics may lead to not very sound but statistically significant changes in the macroscopic predictions of the populations of opinion camps, primarily among the agents with radical opinions (≈3% of all votes). In turn, predictions for the populations of neutral individuals are virtually the same. In addition, we demonstrated that the accumulative effect of non-opinion features on opinion dynamics is seriously moderated by whether the underlying social network correlates with the agents’ characteristics. After applying the procedure of random shuffling (in which the agents and their characteristics were randomly scattered over the network), the macroscopic predictions have changed by ≈9% of all votes. What is interesting is that the population of neutral agents was again not affected by this intervention.

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/

Continuous Opinion Dynamics Under Bounded Confidence on a Complete Network

Opinion formation and propagation are crucial phenomena in social networks and have been extensively studied across several disciplines. Traditionally, theoretical models of opinion dynamics have been proposed to describe the interactions between individuals (i.e., social interaction) and their impact on the evolution of collective opinions. Although these models can incorporate sociological and psychological knowledge on the mechanisms of social interaction, they demand extensive calibration with real data to make reliable predictions, requiring much time and effort. Recently, the widespread use of social media platforms provides new paradigms to learn deep learning models from a large volume of social media data. However, these methods ignore any scientific knowledge about the mechanism of social interaction. In this work, we present the first hybrid method called Sociologically-Informed Neural Network (SINN), which integrates theoretical models and social media data by transporting the concepts of physics-informed neural networks (PINNs) from natural science (i.e., physics) into social science (i.e., sociology and social psychology). In particular, we recast theoretical models as ordinary differential equations (ODEs). Then we train a neural network that simultaneously approximates the data and conforms to the ODEs that represent the social scientific knowledge. In addition, we extend PINNs by integrating matrix factorization and a language model to incorporate rich side information (e.g., user profiles) and structural knowledge (e.g., cluster structure of the social interaction network). Moreover, we develop an end-to-end training procedure for SINN, which involves Gumbel-Softmax approximation to include stochastic mechanisms of social interaction. Extensive experiments on real-world and synthetic datasets show SINN outperforms six baseline methods in predicting opinion dynamics.

In this work, we mimic interactions among agents on social networks and examine their impact on the evolution of agents' opinions. Each agent is entitled to an opinion represented by unit vectors of varying orientation. Agents are also characterized based on their inclination to alter their opinion and their susceptibility to the influence of peers with contrasting opinions. The agents constitute the nodes of a directed and time-varying influence network whose edges form their respective familiarity neighborhoods and govern their interactions. We also devise an interpersonal influence score to quantify the strength of the influence and the probability of acquisition, retention, or loss of a tie. This characterization of agents' behavior and their interpersonal relationships differs from traditional bounded-confidence models based on the agreement in opinions alone. The agents with different traits form groups—liberal and conservative—distinguished by the distribution in opinions of their constituents. We analyze their interactions with different initial opinions, group compositions, network structures, and network evolution rates through simulations. The results reveal that flexible agents facilitate consensus among group members, while stubborn agents are instrumental in forming opinion clusters. This is substantiated by observing the average connectedness of the influence network and the average number of opinion clusters; groups with mostly flexible agents have better connectedness and fewer clusters than groups with stubborn agents in a majority. The simulations with stubborn agents reveal that new ties among agent pairs do not facilitate group consensus.

Beyond the intrinsic pleasure that people derive from spending time with others, social connections have positive spill-over effects for individual and societal well-being. People with extensive and supportive networks have better health, tend to live longer, and are more likely to be employed. At a society-wide level, social connections can generate shared values – such as trust in others and norms of reciprocity – which influence a range of outcomes, including economic growth, democratic participation and crime. The indicators used in this chapter to measure different aspects of social connections refer to social network support and to the frequency of social contact. Overall, personal social networks are relatively strong in OECD countries, with most people seeing friends and/or relatives on a regular basis and reporting that they have someone to count on in times of need. However, there are significant differences between different socio-economic and demographic groups, with the old, the poor and the less-educated having weaker social support networks. There are also wide crosscountry differences in levels of interpersonal trust – one key indicator of the outcomes of social connections. Measuring social connections remains challenging, however, and more work is needed to develop comparable measures in this field.

This chapter extends an established model of Brownian agent to investigate the role of social networks in migration and economic aggregation under a multiregion system. The regional conditions are represented by three variables: wage level, tax rate, and welfare. In the model, Brownian agents make their movements by exploiting their social networks to find regional locations with better incomes. We examined the model under four types of network structures: (1) complete network, (2) random network, (3) regular network, and (4) scale-free network. Via computer simulations, the results prove that social networks affect agent migration and economic aggregation and reduce the stability of the whole system. Some findings are summarized as follows: 1. Regardless of the network structure, agents always move to locations with a high welfare service. 2. Agents move frequently when the network has highly connected links (complete and random network) and no obvious economic center appears and remains, whereas in the case of a loosely connected network (regular and scale-free network), agents mainly migrate to regions with a high tax rate for better welfare; the multiregion system finally evolves toward a stable state.

Linking social, semantic and sentiment analyses to support modeling transit customers’ satisfaction: Towards formal study of opinion dynamics

Social networks can shape many aspects of social and economic activity: migration and trade, job-seeking, innovation, consumer preferences and sentiment, public health, social mobility, and more. In turn, social networks themselves are associated with geographic proximity, historical ties, political boundaries, and other factors. Traditionally, the unavailability of large-scale and representative data on social connectedness between individuals or geographic regions has posed a challenge for empirical research on social networks. More recently, a body of such research has begun to emerge using data on social connectedness from online social networking services such as Facebook, LinkedIn, and Twitter. To date, most of these research projects have been built on anonymized administrative microdata from Facebook, typically by working with coauthor teams that include Facebook employees. However, there is an inherent limit to the number of researchers that will be able to work with social network data through such collaborations. In this paper, we therefore introduce a new measure of social connectedness at the US county level. Our Social Connectedness Index is based on friendship links on Facebook, the global online social networking service. Specifically, the Social Connectedness Index corresponds to the relative frequency of Facebook friendship links between every county-pair in the United States, and between every US county and every foreign country. Given Facebook’s scale as well as the relative representativeness of Facebook’s user body, these data provide the first comprehensive measure of friendship networks at a national level.