An Adaptive Bounded-Confidence Model of Opinion Dynamics on Networks

Individuals who interact with each other in social networks often exchange ideas and influence each other's opinions. A popular approach to studying the dynamics of opinion spread on networks is by examining bounded-confidence (BC) models, in which the nodes of a network have continuous-valued states that encode their opinions and are receptive to other opinions if they lie within some confidence bound of their own opinion. We extend the Deffuant--Weisbuch (DW) model, which is a well-known BC model, by studying opinion dynamics that coevolve with network structure. We propose an adaptive variant of the DW model in which the nodes of a network can (1) alter their opinion when they interact with a neighboring node and (2) break a connection with a neighbor based on an opinion tolerance threshold and then form a new connection to a node following the principle of homophily. This opinion tolerance threshold acts as a threshold to determine if the opinions of adjacent nodes are sufficiently different to be viewed as discordant. We find that our adaptive BC model requires a larger confidence bound than the standard DW model for the nodes of a network to achieve a consensus. Interestingly, our model includes regions with `pseudo-consensus' steady states, in which there exist two subclusters within an opinion-consensus group that deviate from each other by a small amount. We conduct extensive numerical simulations of our adaptive BC model and examine the importance of early-time dynamics and nodes with initial moderate opinions for achieving consensus. We also examine the effects of coevolution on the convergence time of the dynamics.

Stochastic events can explain sustained clustering and polarisation of opinions in social networks

Understanding the processes underlying development and persistence of polarised opinions has been one of the key challenges in social networks for more than two decades. While plausible mechanisms have been suggested, they assume quite specialised interactions between individuals or groups that may only be relevant in particular contexts. We propose that a more broadly relevant explanation might be associated with the influence of external events. An agent-based bounded-confidence model has been used to demonstrate persistent polarisation of opinions within populations exposed to stochastic events (of positive and negative influence) even when all interactions between individuals are noisy and assimilative. Events can have a large impact on the distribution of opinions because their influence acts synchronistically across a large proportion of the population, whereas an individual can only interact with small numbers of other individuals at any particular time.

Modeling the Evolution of Ideological Landscapes through Opinion Dynamics

This paper explores the possibilities to explain the stylized facts of empirically observed ideological landscapes through the bounded confidence model of opinion dynamics. Empirically, left-right self-placements are often not normally distributed but have multiple peaks (e.g. extreme-left-center-right-extreme). Some stylized facts are extracted from histograms from the European Social Survey. In the bounded confidence model, agents repeatedly adjust their ideological position in their ideological neighborhood. As an extension of the classical model, agents sometimes completely reassesses their opinion depending on their ideological openness and their propensity for reassessment, respectively. Simulations show that this leads to the emergence of clustered ideological landscapes similar to the ones observed empirically. However, not all stylized facts of real world ideological landscapes can be reproduced with the model. Changes in the model parameters show that the ideological landscapes are susceptible to interesting slow and abrupt changes.A long term goal is to integrate models of opinion dynamics into the classical spatial model of electoral competition as a dynamic element taking into account that voters themselves shape the political landscape by adjusting their positions and preferences through interaction.

How Opinion Leaders Affect Others on Seeking Truth in a Bounded Confidence Model

Seeking truth is an important objective of agents in social groups. Opinion leaders in social groups may help or hinder the other agents on seeking the truth by symmetric nature. This paper studies the impact of opinion leaders by considering four characteristics of opinion leaders—reputation, stubbornness, appeal, and extremeness—on the truth-seeking behavior of agents based on a bounded confidence model. Simulations show that increasing the appeal of the leader whose opinion is opposite to the truth has a straightforward impact, i.e., it normally prevents the agents from finding the truth. On the other hand, it also makes the agents who start out close to the truth move away from the truth by increasing the group bound of confidence, if there is an opinion leader opposite to the truth. The results demonstrate that the opinion of the leader is important in affecting the normal agents to reach the truth. Furthermore, for some cases, small variations of the parameters defining the agents’ characteristics can lead to large scale changes in the social group.

Modeling and Simulation of Opinion Natural Reversal Dynamics with Opinion Leader Based on HK Bounded Confidence Model

Opinion natural reversals are important and common phenomena in network management. It is a naturally emerging process of opinions characterized by interactions between individuals and the evolution of attitudes themselves. To explore the underlying mechanism of this social phenomenon and to reveal its dynamic traits, we propose here a novel model which takes the effects of natural reversal parameter and opinion interaction on the individual’s view choice behavior into account based on the Hegselmann and Krause (HK) bounded confidence model. Experimental results show that the evolution of individual opinions is not only influenced by the interactions between neighboring individuals but also updated naturally due to individual factors themselves in the absence of interaction, which in turn proves that the proposed model can provide a reasonable description of the entire process of public opinion natural reversal under the Internet environment. Besides, the proportion of group opinion tendency, network topology, identification method, and the influence weight of opinion leader will play significant roles in this process, which further indicates our improved model is very robust and thus can provide some insightful evidence to understand the phenomena of opinion natural reversal.