Majority Rule for Belief Evolution in Social Networks

TL;DR

This paper investigates how beliefs evolve in social networks under majority rule, analyzing convergence properties and demonstrating that belief updates do not always stabilize, but do so in random asynchronous settings.

Contribution

It introduces a general belief evolution framework and specifically studies the majority rule, providing insights into convergence behavior in social networks.

Findings

Belief evolution under majority rule does not always converge.

Random asynchronous belief updates guarantee convergence.

The framework applies to various social network belief dynamics.

Abstract

In this paper, we study how an agent's belief is affected by her neighbors in a social network. We first introduce a general framework, where every agent has an initial belief on a statement, and updates her belief according to her and her neighbors' current beliefs under some belief evolution functions, which, arguably, should satisfy some basic properties. Then, we focus on the majority rule belief evolution function, that is, an agent will (dis)believe the statement iff more than half of her neighbors (dis)believe it. We consider some fundamental issues about majority rule belief evolution, for instance, whether the belief evolution process will eventually converge. The answer is no in general. However, for random asynchronous belief evolution, this is indeed the case.