Graph-Theoretic Analysis of Belief System Dynamics under Logic Constraints

TL;DR

This paper uses graph theory to analyze how belief systems evolve and converge under social interactions and logical constraints, revealing the influence of network structure and logic on opinion dynamics.

Contribution

It introduces a graph-theoretic framework to determine convergence, speed, and convergence points of belief systems with logic constraints in social networks.

Findings

Convergence depends on network structure and logic constraints.

Explicit conditions for convergence in large-scale networks.

Analysis of how belief systems stabilize over social interactions.

Abstract

Opinion formation cannot be modeled solely as an ideological deduction from a set of principles; rather, repeated social interactions and logic constraints among statements are consequential in the construct of belief systems. We address three basic questions in the analysis of social opinion dynamics: (i) Will a belief system converge? (ii) How long does it take to converge? (iii) Where does it converge? We provide graph-theoretic answers to these questions for a model of opinion dynamics of a belief system with logic constraints. Our results make plain the implicit dependence of the convergence properties of a belief system on the underlying social network and on the set of logic constraints that relate beliefs on different statements. Moreover, we provide an explicit analysis of a variety of commonly used large-scale network models.