Majority dynamics with one nonconformist

TL;DR

This paper studies how opinions evolve in a network where most agents follow majority rules, but one agent may act differently, revealing conditions that limit the complexity of possible opinion cycles.

Contribution

It introduces a model of majority dynamics with a single nonconformist agent and analyzes how restrictions affect the emergence of periodic opinion states.

Findings

Limited periods occur under certain structural restrictions.

Without restrictions, any periodic behavior is possible.

The model extends understanding of opinion dynamics with nonconformity.

Abstract

We consider a system in which a group of agents represented by the vertices of a graph synchronously update their opinion based on that of their neighbours. If each agent adopts a positive opinion if and only if that opinion is sufficiently popular among his neighbours, the system will eventually settle into a fixed state or alternate between two states. If one agent acts in a different way, other periods may arise. We show that only a small number of periods may arise if natural restrictions are placed either on the neighbourhood structure or on the way in which the nonconforming agent may act; without either of these restrictions any period is possible.