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Evaluation and Control of Opinion Polarization and Disagreement: A Review

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 Added by Yuejiang Li
 Publication date 2021
and research's language is English




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With the recent advances of networking technology, connections among people are unprecedentedly enhanced. People with different ideologies and backgrounds interact with each other, and there may exist severe opinion polarization and disagreement in the social network. There have been a lot of reviews on modeling opinion formation. However, less attention has been paid to opinion polarization and disagreement. In this work, we review recent advances in opinion polarization and disagreement and pay attention to how they are evaluated and controlled. In literature, three metrics: polarization, disagreement, and polarization-disagreement index (PDI) are usually adopted, and there is a tradeoff between polarization and disagreement. Different strategies have been proposed in literature which can significantly control opinion polarization and disagreement based on these metrics. This review is of crucial importance to summarize works on opinion polarization and disagreement, and to the better understanding and control of them.



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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: regular agents, who update their beliefs according to information that they receive from their social neighbors; and stubborn agents, who never update their opinions. 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 non-degenerate random vector. The structure of the network and the location of the stubborn agents within it shape the opinion dynamics. The expected belief vector evolves according to an ordinary differential equation coinciding with the Kolmogorov backward equation of a continuous-time Markov chain with absorbing states corresponding to the stubborn agents and converges to a harmonic vector, with every regular agents value being the weighted average of its neighbors values, and boundary conditions corresponding to the stubborn agents. Expected cross-products of the agents beliefs allow for a similar characterization in terms of coupled Markov chains on the 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 emph{homogeneous influence} emerges, whereby the stationary beliefs marginal distributions of most of the regular agents have approximately equal first and second moments.
Opinion dynamics concerns social processes through which populations or groups of individuals agree or disagree on specific issues. As such, modelling opinion dynamics represents an important research area that has been progressively acquiring relevance in many different domains. Existing approaches have mostly represented opinions through discrete binary or continuous variables by exploring a whole panoply of cases: e.g. independence, noise, external effects, multiple issues. In most of these cases the crucial ingredient is an attractive dynamics through which similar or similar enough agents get closer. Only rarely the possibility of explicit disagreement has been taken into account (i.e., the possibility for a repulsive interaction among individuals opinions), and mostly for discrete or 1-dimensional opinions, through the introduction of additional model parameters. Here we introduce a new model of opinion formation, which focuses on the interplay between the possibility of explicit disagreement, modulated in a self-consistent way by the existing opinions overlaps between the interacting individuals, and the effect of external information on the system. Opinions are modelled as a vector of continuous variables related to multiple possible choices for an issue. Information can be modulated to account for promoting multiple possible choices. Numerical results show that extreme information results in segregation and has a limited effect on the population, while milder messages have better success and a cohesion effect. Additionally, the initial condition plays an important role, with the population forming one or multiple clusters based on the initial average similarity between individuals, with a transition point depending on the number of opinion choices.
One of the main subjects in the field of social networks is to quantify conflict, disagreement, controversy, and polarization, and some quantitative indicators have been developed to quantify these concepts. However, direct computation of these indicators involves the operations of matrix inversion and multiplication, which make it computationally infeasible for large-scale graphs with millions of nodes. In this paper, by reducing the problem of computing relevant quantities to evaluating $ell_2$ norms of some vectors, we present a nearly linear time algorithm to estimate all these quantities. Our algorithm is based on the Laplacian solvers, and has a proved theoretical guarantee of error for each quantity. We execute extensive numerical experiments on a variety of real networks, which demonstrate that our approximation algorithm is efficient and effective, scalable to large graphs having millions of nodes.
We explore a method to influence or even control the diversity of opinions within a polarised social group. We leverage the voter model in which users hold binary opinions and repeatedly update their beliefs based on others they connect with. Stubborn agents who never change their minds (zealots) are also disseminated through the network, which is modelled by a connected graph. Building on earlier results, we provide a closed-form expression for the average opinion of the group at equilibrium. This leads us to a strategy to inject zealots into a polarised network in order to shift the average opinion towards any target value. We account for the possible presence of a backfire effect, which may lead the group to react negatively and reinforce its level of polarisation in response. Our results are supported by numerical experiments on synthetic data.
In this paper, we study the implications of the commonplace assumption that most social media studies make with respect to the nature of message shares (such as retweets) as a predominantly positive interaction. By analyzing two large longitudinal Brazilian Twitter datasets containing 5 years of conversations on two polarizing topics - Politics and Sports - we empirically demonstrate that groups holding antagonistic views can actually retweet each other more often than they retweet other groups. We show that assuming retweets as endorsement interactions can lead to misleading conclusions with respect to the level of antagonism among social communities, and that this apparent paradox is explained in part by the use of retweets to quote the original content creator out of the messages original temporal context, for humor and criticism purposes. As a consequence, messages diffused on online media can have their polarity reversed over time, what poses challenges for social and computer scientists aiming to classify and track opinion groups on online media. On the other hand, we found that the time users take to retweet a message after it has been originally posted can be a useful signal to infer antagonism in social platforms, and that surges of out-of-context retweets correlate with sentiment drifts triggered by real-world events. We also discuss how such evidences can be embedded in sentiment analysis models.
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