Nonlinear dynamics of belief formation over social networks*

In the presented work, we investigate how social effects shape belief formation and social decisions using a new agent-based nonlinear model of belief formation dynamics. We motivate, analyze, and apply this model to gain new insights about the dynamics of social systems. 

Following the seminal work of DeGroot, mathematical models of belief dynamics have been a popular tool central to interdisciplinary investigations of collective behavior. These models assign real-valued opinions or beliefs to agents in a social network and describe how they are updated in time in response to interactions with neighboring agents. An individual's belief state may reflect, for example, the value assigned to an option under evaluation, strength of preference towards a candidate in an election, or alignment with a political topic.

Existing models often have strong limitations, mainly focusing on scalar beliefs and linear dynamics. Our model, however, integrates recent insights from social psychology to account for multiple interdependent belief states that evolve simultaneously, seeking to overcome various internal and external sources of cognitive dissonance. The model captures complex interactions of beliefs between individuals in a social network, as well as within individuals’ cognition.

We illustrate rigorously that our model captures key features of complex social systems, such as multistability of belief states and critical state transitions. Furthermore, we analyze how groups overcome deadlock to form strong beliefs, how the structure of social relationships and of the underlying belief system shape social decisions, and how the group’s decision can be strongly swayed by the biases of a small number of influential individuals.