Bounded Confidence under Preferential Flip: A Coupled Dynamics of Structural Balance and Opinions

TL;DR

This paper models the coupled evolution of social balance and opinions, showing how agents form opinion-based social groups with internal consensus or multiple clusters, influenced by bounded confidence and social tie dynamics.

Contribution

It introduces a novel coupled model of opinion formation and social balance considering bounded confidence and evolving social ties, with analysis of one- and two-dimensional opinions.

Findings

Agents segregate into two cliques with distinct opinions.

Bounded confidence level determines whether opinions within a clique reach consensus or form multiple clusters.

In the two-dimensional case, cliques are separated by a hyperplane in opinion space.

Abstract

In this work we study the coupled dynamics of social balance and opinion formation. We propose a model where agents form opinions under bounded confidence, but only considering the opinions of their friends. The signs of social ties -friendships and enmities- evolve seeking for social balance, taking into account how similar agents' opinions are. We consider both the case where opinions have one and two dimensions. We find that our dynamics produces the segregation of agents into two cliques, with the opinions of agents in one clique differing from those in the other. Depending on the level of bounded confidence, the dynamics can produce either consensus of opinions within each clique or the coexistence of several opinion clusters in a clique. For the uni-dimensional case, the opinions in one clique are all below the opinions in the other clique, hence defining a "left clique" and a "right clique". In the two-dimensional case, our numerical results suggest that the two cliques are separated by a hyperplane in the opinion space. We also show that the phenomenon of unidimensional opinions identified by DeMarzo, Vayanos and Zwiebel (Q J Econ 2003) extends partially to our dynamics. Finally, in the context of politics, we comment about the possible relation of our results to the fragmentation of an ideology and the emergence of new political parties.