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This study introduces a generalized q-voter model to explain collective decision-making, incorporating personal biases and external influences. It reveals that larger groups can lead to coexisting opinions, challenging simple majority adoption.

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Area of Science:

  • Social dynamics and collective behavior modeling.
  • Statistical physics of social phenomena.
  • Agent-based modeling of opinion formation.

Background:

  • Collective decision-making is crucial for societal dynamics, often modeled using binary dynamics.
  • The q-voter model, a popular framework, assumes opinion changes driven by unanimous peer pressure.
  • Real-world decisions are influenced by personal history and external biases, not captured by standard models.

Purpose of the Study:

  • To propose and analyze a generalized q-voter model that incorporates individual biases and external influences.
  • To extend existing models by allowing asymmetric opinion change probabilities.
  • To investigate the impact of group size and initial opinion distribution on collective outcomes.

Main Methods:

  • Development of a generalized q-voter model with state-dependent opinion change probabilities.
  • Analytical methods applied to a complete graph.
  • Monte Carlo simulations to validate analytical findings and explore system dynamics.

Main Results:

  • For larger influence groups (q>3), a novel phase emerges where both fully adopted and partially adopted states coexist.
  • In small systems, initial majority support does not guarantee widespread adoption, indicated by unique exit probability curves.
  • The model recovers established q-voter models and recent variations as limiting cases.

Conclusions:

  • The generalized q-voter model provides a more realistic framework for understanding collective decision-making under diverse influences.
  • Group size significantly impacts collective action, potentially leading to complex opinion states and non-intuitive adoption dynamics.
  • Findings underscore the importance of considering individual biases and external factors in social science models.