English

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.

Keywords

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}
}
R2 v1 2026-06-22T14:27:52.141Z