Stochastic Dynamics of the Multi-State Voter Model over a Network based on Interacting Cliques and Zealot Candidates

TL;DR

This paper studies the stochastic multi-state voter model on complex networks of cliques with political candidates, revealing scaling behaviors and vote distributions similar to real elections through simulations and a tailored mean field theory.

Contribution

It introduces a mean field theory for the multi-state voter model on clique-based networks, capturing inter/intra-clique interactions and reproducing empirical election-like vote distributions.

Findings

Model displays empirical scaling similar to previous studies.

Vote distribution resembles that of Brazilian elections.

Proper thermodynamic limit maintains fixed average degree while increasing network size.

Abstract

The stochastic dynamics of the multi-state voter model is investigated on a class of complex networks made of non-overlapping cliques, each hosting a political candidate and interacting with the others via Erd\H{o}s-R\'enyi links. Numerical simulations of the model are interpreted in terms of an ad-hoc mean field theory, specifically tuned to resolve the inter/intra-clique interactions. Under a proper definition of the thermodynamic limit (with the average degree of the agents kept fixed while increasing the network size), the model is found to display the empirical scaling discovered by Fortunato and Castellano (Phys Rev Lett 99(13):138701, 2007), while the vote distribution resembles roughly that observed in Brazilian elections.