Continuous Opinion Dynamics Under Bounded Confidence: A Survey

Abstract

Models of continuous opinion dynamics under bounded confidence have been presented independently by Krause and Hegselmann and by Deffuant et al in 2000. They have raised a fair amount of attention in the communities of social simulation, sociophysics and complexity science. The researchers working on it come from disciplines as physics, mathematics, computer science, social psychology and philosophy.In these models agents hold continuous opinions which they can gradually adjust if they hear the opinions of others. The idea of bounded confidence is that agents only interact if they are close in opinion to each other. Usually, the models are analyzed with agent-based simulations in a Monte-Carlo style, but they can also be reformulated on the agent's density in the opinion space in a master-equation style. The contribution of this survey is fourfold. First, it will present the agent-based and density-based modeling frameworks including the cases of multidimensional opinions and heterogeneous bounds of confidence. Second, it will give the bifurcation diagrams of cluster configuration in the homogeneous model with uniformly distributed initial opinions. Third, it will review the several extensions and the evolving phenomena which have been studied so far, and fourth it will state some open questions.

Heterogeneous bounds of confidence: Meet, discuss and find consensus!

“…So, [11]), but this result is achieved using the density based approach and it turns out by simulation that consensus in the region of 0.19 is only achieved for very large and very uniform distributed intital conditions. Thus, Figure 2 is another exam- ple where consensus is never achieved in the homogeneous models (with system sizes of n = 300), while mixing can lead to consensus.…”

“…For the HK model the same approach was first applied independently in [10] and [14], for an overview and discussion of different methods see [11].…”

“…This reformulation allows a better estimate of the critical values for the bound of confidence [9,10,11]. The approach also extends naturally to heterogeneous bounds of confidence.…”

Clustering and asymptotic behavior in opinion formation

“…Thanks to the development of social media, the dynamics of opinion formation has recently generated much interest [1,4,10,11,17,20,21]. Through a complex network of interactions between individuals emerge groups with different opinions raising several questions; for instance how groups are formed and how many of them will survive throughout time.…”

“…Different models have been introduced to study opinion dynamics [2,3,10,12,13,[15][16][17]21]. In this paper, we focus on a widely-used model referred to as the consensus model [7-9, 13, 14].…”