Polarization and Consensus by Opposing External Sources

TL;DR

This paper extends the voter model to include opposing news sources, demonstrating how they prevent consensus and promote polarization in social networks, with analytical results on the timescales involved.

Contribution

It introduces a socially motivated extension of the voter model with opposing news sources and analyzes polarization dynamics on different network structures.

Findings

Consensus time scales as N^α, with α depending on influence parameters.

Polarization occurs faster than consensus under certain conditions.

Reducing interclique links or increasing news influence promotes polarization.

Abstract

We introduce a socially motivated extension of the voter model in which individual voters are also influenced by two opposing, fixed-opinion news sources. These sources forestall consensus and instead drive the population to a politically polarized state, with roughly half the population in each opinion state. Two types social networks for the voters are studied: (a) the complete graph of $N$ voters and, more realistically, (b) the two-clique graph with $N$ voters in each clique. For the complete graph, many dynamical properties are soluble within an annealed-link approximation, in which a link between a news source and a voter is replaced by an average link density. In this approximation, we show that the average consensus time grows as $N^\alpha$, with $\alpha = p\ell/(1-p)$. Here $p$ is the probability that a voter consults a news source rather than a neighboring voter, and $\ell$ is the link density between a news source and voters, so that $\alpha$ can be greater than 1. The polarization time, namely, the time to reach a politically polarized state from an initial strong majority state, is typically much less than the consensus time. For voters on the two-clique graph, either reducing the density of interclique links or enhancing the influence of news sources again promotes polarization.