Graph-Theoretic Analysis of Belief System Dynamics under Logic Constraints

Angelia Nedić,César A Uribe,Alex Olshevsky

doi:10.1038/s41598-019-45076-4

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.

Highlights

Proposed generalizations of opinion dynamics models integrate functional interdependencies among issues that coherently bound ideas and attitudes[13]
We study how the structural properties of the social network of agents and the set of logic constraints influence the dynamics of a belief system from a graph-theoretic point of view
The agents use shared opinions, as well as underlying logical dependencies among them, to update their beliefs. The agents exchange their opinions by interacting over a social network captured by a graph = (V, E), where V is the set of agents, and E is a set of edges

Summary

Introduction

Proposed generalizations of opinion dynamics models integrate functional interdependencies among issues that coherently bound ideas and attitudes[13]. The existence of logic constraints in a belief system provides a successful model for the evolution of opinions in both large-scale populations and small groups[12]. Logic constraints build upon the natural idea that believing a specific statement is true may depend on the belief that some other related statements are true as well. Even though sophisticated algebraic tools[13,21] exists for the analysis of opinion dynamics, they can be unpractical or intractable for large-scale complex networks. We study how the structural properties of the social network of agents and the set of logic constraints influence the dynamics of a belief system from a graph-theoretic point of view. We answer the following three questions with graph-theoretic conditions that are accessible for a number of commonly used topologies in large-scale complex networks: 1.

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Conclusion