Multi-topic belief formation through bifurcations over signed social networks

TL;DR

This paper introduces a nonlinear dynamic model for multi-dimensional belief formation in signed social networks, revealing how bifurcations lead to opinionated states and oscillations influenced by network structure.

Contribution

It provides a novel theoretical framework analyzing bifurcations in belief dynamics over signed networks, incorporating social psychology factors and offering conditions for multi-stable equilibria.

Findings

Agents become opinionated due to bifurcations.

Network structure controls belief oscillations.

Conditions for multi-stable belief states are derived.

Abstract

We propose and analyze a nonlinear dynamic model of continuous-time multi-dimensional belief formation over signed social networks. Our model accounts for the effects of a structured belief system, self-appraisal, internal biases, and various sources of cognitive dissonance posited by recent theories in social psychology. We prove that agents become opinionated as a consequence of a bifurcation. We analyze how the balance of social network effects in the model controls the nature of the bifurcation and, therefore, the belief-forming limit-set solutions. Our analysis provides constructive conditions on how multi-stable network belief equilibria and belief oscillations emerging at a belief-forming bifurcation depend on the communication network graph and belief system network graph. Our model and analysis provide new theoretical insights on the dynamics of social systems and a new principled framework for designing decentralized decision-making on engineered networks in the presence of structured relationships among alternatives.