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arXiv · 2103.04248

Divergence and Consensus in Majority Rule

P. L. Krapivsky·S. Redner
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Abstract

We investigate majority rule dynamics in a population with two classes of people, each with two opinion states $\pm 1$, and with tunable interactions between people in different classes. In an update, a randomly selected group adopts the majority opinion if all group members belong to the same class; if not, majority rule is applied with probability $\epsilon$. Consensus is achieved in a time that scales logarithmically with population size if $\epsilon\geq \epsilon_c=\frac{1}{9}$. For $\epsilon <\epsilon_c$, the population can get trapped in a polarized state, with one class preferring the $+1$ state and the other preferring $-1$. The time to escape this polarized state and reach consensus scales exponentially with population size.

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BibTeXRIS

P. L. Krapivsky, S. Redner. 2021-03-07. Divergence and Consensus in Majority Rule. https://doi.org/10.1103/physreve.103.l060301

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