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Majority rule dynamics in two-class populations show consensus is reached quickly if interaction rates (ε) are high. Low interaction rates can trap populations in polarized states, delaying consensus exponentially with size.

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Area of Science:

  • Sociophysics
  • Statistical Mechanics
  • Opinion Dynamics

Background:

  • Understanding how collective opinions form and stabilize is crucial.
  • Social interactions and group structures significantly influence opinion dynamics.

Purpose of the Study:

  • To investigate majority rule dynamics in a two-class population with tunable inter-class interactions.
  • To determine the conditions leading to consensus or persistent polarization.

Main Methods:

  • Simulated a population with two classes and two opinion states (±1).
  • Applied majority rule updates with a class-dependent rate (ε).
  • Analyzed consensus times and polarized state escape dynamics.

Main Results:

  • Consensus time scales logarithmically with population size for ε ≥ εc = 1/9.
  • For ε < εc, populations can become trapped in polarized states.
  • Escape from polarized states to consensus scales exponentially with population size.

Conclusions:

  • Tunable inter-class interactions critically affect consensus achievement.
  • Low interaction rates (ε < 1/9) can lead to stable, long-lasting polarization.
  • The model provides insights into factors driving social consensus and division.