Nonlinear Dynamics of Beliefs Over Social Networks

Abstract: Motivated by the study of complex social behavior, we introduce a nonlinear dynamic model of belief formation dynamics. According to our model, belief updates of individuals are informed by the complex interplay of external factors, i.e. social network effects, and internal factors, i.e. internal biases, networked relationships between an individual's belief representations, and nonlinear processing of social information. We rigorously show how groups overcome deadlock to form strong beliefs when it is urgent to do so, how the structure of social relationships and of the underlying belief system shapes social decisions in the group, and how group-level beliefs can be highly sensitive to the personal biases of a small number of individuals. This work provides novel insights into the dynamics of complex social systems in nature and society and motivates a new approach for the design of distributed behavior in engineered networks of social agents.