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Local and global ordering dynamics in multistate voter models.

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This study analyzes opinion dynamics in voter models, finding that active links and entropy decay exponentially. Metastable states can be engineered by introducing zealots for specific opinions.

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Area of Science:

  • Statistical physics
  • Social dynamics
  • Network science

Background:

  • Voter models are used to study opinion formation and consensus in populations.
  • Understanding the dynamics of opinion evolution on networks is crucial for social science and information diffusion studies.

Purpose of the Study:

  • To investigate the time evolution of active links and entropy in multistate voter models.
  • To analytically calculate average link density and entropy in metastable states.
  • To explore methods for engineering metastable states.

Main Methods:

  • Analysis of multistate voter models with all-to-all interaction on uncorrelated networks.
  • Analytical calculation of average density of active links and entropy.
  • Mathematical modeling of opinion elimination and metastable state formation.

Main Results:

  • Density of active links and entropy vary between realizations but can be analytically averaged.
  • Averaged active link density decays exponentially, independent of initial opinion states.
  • Entropy decay is exponential only at long times with two or fewer opinions.
  • Metastable states can be engineered by introducing zealots.

Conclusions:

  • The study provides analytical insights into opinion dynamics and consensus reaching in complex systems.
  • Network structure and size influence the timescale of opinion convergence.
  • Zealot introduction offers a method to control opinion states in models.