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How opinions crystallise: an analysis of polarisation in the voter model

Antoine Vendeville 1, 2 Benjamin Guedj 3, 1, 4, 5, 2 Shi Zhou 1
5 MODAL - MOdel for Data Analysis and Learning
LPP - Laboratoire Paul Painlevé - UMR 8524, Université de Lille, Sciences et Technologies, Inria Lille - Nord Europe, METRICS - Evaluation des technologies de santé et des pratiques médicales - ULR 2694, Polytech Lille - École polytechnique universitaire de Lille
Abstract : We address the phenomenon of sedimentation of opinions in networks. We investigate how agents who never change their minds ("stubborn") can influence the opinion of a social group and foster the formation of polarised communities. We study the voter model in which users are divided in two camps and repeatedly update their opinions based on others they connect with. Assuming a proportion of the agents are stubborn, the distribution of opinions reaches an equilibrium. We give novel formulas based on Markov Chain analysis to compute the distribution of opinions at any time and speed of convergence to stationary equilibrium. Theoretical results are supported by numerical experiments on synthetic data, and we discuss a strategy to mitigate the polarisation phenomenon.
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Contributor : Benjamin Guedj <>
Submitted on : Wednesday, June 17, 2020 - 3:56:30 PM
Last modification on : Friday, February 5, 2021 - 3:29:24 AM


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  • HAL Id : hal-02872161, version 1
  • ARXIV : 2006.07265



Antoine Vendeville, Benjamin Guedj, Shi Zhou. How opinions crystallise: an analysis of polarisation in the voter model. 2020. ⟨hal-02872161⟩



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