Emergence of polarization in a voter model with personalized information

TL;DR

This paper presents a simplified voter model with personalized information that reveals how filter bubbles can lead to polarization, showing that consensus is only possible under weak influence and small population sizes.

Contribution

It introduces an analytically solvable voter model incorporating personalized information, revealing conditions under which polarization emerges or consensus is achieved.

Findings

Polarization occurs when influence from personalized information exceeds a threshold.

Consensus is only possible for weak interaction with personalized content and small population sizes.

The critical population size for polarization depends non-linearly on interaction probability.

Abstract

The flourishing of fake news is favored by recommendation algorithms of online social networks which, based on previous users activity, provide content adapted to their preferences and so create filter bubbles. We introduce an analytically tractable voter model with personalized information, in which an external field tends to align the agent opinion with the one she held more frequently in the past. Our model shows a surprisingly rich dynamics despite its simplicity. An analytical mean-field approach, confirmed by numerical simulations, allows us to build a phase diagram and to predict if and how consensus is reached. Remarkably, polarization can be avoided only for weak interaction with the personalized information and if the number of agents is below a threshold. We analytically compute this critical size, which depends on the interaction probability in a strongly non linear way.