Divergence and consensus in majority rule

Abstract

We investigate majority rule dynamics in a population with two classes of people, each with two opinion states $\ifmmode\pm\else\textpm\fi{}1$, 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 rate $\ensuremath{\epsilon}$. Consensus is achieved in a time that scales logarithmically with population size if $\ensuremath{\epsilon}\ensuremath{\ge}{\ensuremath{\epsilon}}_{c}=\frac{1}{9}$. For $\ensuremath{\epsilon}<{\ensuremath{\epsilon}}_{c}$, the population can get trapped in a polarized state, with one class preferring the $+1$ state and the other preferring $\ensuremath{-}1$. The time to escape this polarized state and reach consensus scales exponentially with population size.

Locations

• Physical review. E - View
• arXiv (Cornell University) - View - PDF
• DataCite API - View