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Homophily Based on Few Attributes Can Impede Structural Balance.

Piotr J Górski1, Klavdiya Bochenina2, Janusz A Hołyst1,2

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Achieving global cooperation requires a high number of agent attributes and a strong willingness for consensus. Many social systems lack sufficient attributes for this "paradise state" of structural balance.

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Area of Science:

  • Social Network Analysis
  • Computational Social Science
  • Agent-Based Modeling

Background:

  • Homophily and structural balance are key mechanisms shaping social group dynamics, influencing outcomes like consensus or polarization.
  • Existing models often study these mechanisms separately, limiting a unified understanding of social system evolution.

Purpose of the Study:

  • To propose a unified model integrating pair (homophily) and triadic (structural balance) interactions in social networks.
  • To investigate the conditions necessary for achieving a globally cooperative state characterized by positive link polarities.

Main Methods:

  • Developed a model of N fully connected agents with G underlying attributes, where agent similarity (homophily) defines link weights.
  • Employed a triad-updating rule for structural balance, allowing for intentional attribute changes and accidental link modifications.
  • Utilized Fokker-Planck equation for large G to analyze link weight dynamics and identify phase transition conditions.

Main Results:

  • Derived conditions for a phase transition to a 'paradise state' of global cooperation (all positive links).
  • This state requires a large number of attributes (G > O(N^2)) and a high willingness for consensus (p > 0.5).
  • Revealed that many real-world social systems possess a subcritical number of attributes, hindering structural balance.

Conclusions:

  • A unified model demonstrates that achieving global cooperation through structural balance is computationally demanding.
  • The number of agent attributes and the propensity for consensus critically influence the emergence of a balanced social system.
  • Findings suggest limitations in current social systems' ability to reach widespread cooperation due to insufficient attribute diversity.