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Summary

This study explores opinion dynamics using a modified threshold model. We found that social hysteresis, crucial for opinion shifts, depends on social influence thresholds and network structure.

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Area of Science:

  • Sociophysics
  • Computational Social Science
  • Statistical Mechanics

Background:

  • The Granovetter's threshold model explains social behavior based on neighborhood influence.
  • Understanding opinion dynamics is key to modeling social phenomena and manipulation.
  • Previous models often simplify the role of individual independence and network structure.

Purpose of the Study:

  • To investigate the homogeneous symmetrical threshold model with independence (noise).
  • To analyze the impact of the threshold parameter (r) and network properties on phase transitions and social hysteresis.
  • To compare findings with the majority-vote and q-voter models.

Main Methods:

  • Utilized pair approximation and Monte Carlo simulations.
  • Employed Erdős-Rényi and Watts-Strogatz random graph models.
  • Analyzed a modified Granovetter's threshold model incorporating independent voter behavior.

Main Results:

  • Phase transition character is dependent on the threshold (r) and graph parameters.
  • Continuous phase transitions occur for r=0.5, while discontinuous transitions are possible for r>0.5.
  • Social hysteresis increases with average degree and rewriting parameter, showing non-monotonic dependence on r.

Conclusions:

  • The threshold parameter (r) significantly influences the nature of phase transitions in opinion dynamics.
  • Social hysteresis, a key feature for opinion manipulation, is tunable via network structure and influence thresholds.
  • The findings offer insights into opinion formation and the stability of social norms.