The Zealot Voter Model

TL;DR

This paper introduces a voter model on infinite trees incorporating zealots and biased opinion dynamics, analyzing conditions for the persistence and local survival of zealots in social networks.

Contribution

It develops a new variant of the biased voter model on trees that accounts for zealots and analyzes their survival conditions.

Findings

Identifies parameters for zealot survival on trees.

Characterizes local versus global persistence of zealots.

Provides insights into opinion spread dynamics in social networks.

Abstract

Inspired by the spread of discontent as in the 2016 presidential election, we consider a voter model in which 0's are ordinary voters and 1's are zealots. Thinking of a social network, but desiring the simplicity of an infinite object that can have a nontrivial stationary distribution, space is represented by a tree. The dynamics are a variant of the biased voter: if $x$ has degree $d(x)$ then at rate $d(x)p_k$ the individual at $x$ consults $k\ge 1$ neighbors. If at least one neighbor is 1, they adopt state 1, otherwise they become 0. In addition at rate $p_0$ individuals with opinion 1 change to 0. As in the contact process on trees, we are interested in determining when the zealots survive and when they will survive locally.