Majority dynamics with one nonconformist
Combinatorics
2020-08-12 v1
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.
Cite
@article{arxiv.1606.05496,
title = {Majority dynamics with one nonconformist},
author = {John Haslegrave and Chris Cannings},
journal= {arXiv preprint arXiv:1606.05496},
year = {2020}
}