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This study introduces a kinetic exchange opinion model, showing it avoids frozen states and achieves consensus exponentially slowly. It reveals a "domain-wall state" delaying consensus, with findings compared to Brexit opinion dynamics.

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Area of Science:

  • Statistical Physics
  • Social Dynamics
  • Computational Social Science

Background:

  • Consensus formation in binary voting is complex, with polarization leading to "support-bubbles" and unattainable consensus.
  • Previous Z2-symmetric models often result in frozen, fragmented, and polarized states without external noise.
  • Understanding societal opinion dynamics is crucial for predicting collective behavior.

Purpose of the Study:

  • To investigate consensus formation dynamics in a kinetic exchange opinion model on L×L square lattices.
  • To determine if the model can avoid frozen states and how consensus is achieved.
  • To analyze the timescale of consensus and compare opinion dynamics with real-world data, such as Brexit.

Main Methods:

  • Simulation of a kinetic exchange opinion model on L×L square lattices.
  • Analysis of consensus formation time, persistence probability, and zero-crossing intervals of average opinion.
  • Comparison of model-generated scale-free distributions with historical opinion survey data (e.g., Brexit).

Main Results:

  • The model avoids frozen states, exhibiting an exponentially slow approach to consensus.
  • Two consensus timescales were identified: L^2 for direct consensus and L^3.6 for a metastable "domain-wall state".
  • The zero-crossing distribution of average opinion follows a scale-free pattern, consistent with Brexit opinion data.

Conclusions:

  • The kinetic exchange opinion model offers a more dynamic approach to consensus formation than previous static models.
  • The emergence of a "domain-wall state" highlights complex metastable dynamics influencing consensus.
  • The model's scale-free properties provide a potential framework for analyzing real-world opinion shifts and polarization.