Multi-topic belief formation through bifurcations over signed social networks

• DOI: 10.48550/arxiv.2308.02755
• Publication Date: 2025-01-01
• Authors: Anastasia Bizyaeva; Alessio Franci; Naomi E. Leonard
• Keywords: Social and Information Networks (cs.SI); FOS: Computer and information sciences; Physics - Physics and Society; Optimization and Control (math.OC); FOS: Mathematics; FOS: Physical sciences; Computer Science - Multiagent Systems; Computer Science - Social and Information Networks; Physics and Society (physics.soc-ph); Dynamical Systems (math.DS); Mathematics - Dynamical Systems; Mathematics - Optimization and Control; Multiagent Systems (cs.MA)

16 pages, 7 figures<br/>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.<br/>