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Competition between group interactions and nonlinearity in voter dynamics on hypergraphs.

Jihye Kim1,2, Deok-Sun Lee2,3, Byungjoon Min4

  • 1Korea University, Department of Physics, Seoul 02841, Korea.

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|June 19, 2025
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Summary
This summary is machine-generated.

The group-driven voter model (GVM) uses nonlinear group interactions to reach social consensus faster than traditional models. This new model optimizes consensus speed by balancing nonlinearity and group size in complex social dynamics.

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Area of Science:

  • Complex Systems
  • Network Science
  • Social Dynamics

Background:

  • Social dynamics involve both pairwise (dyadic) and higher-order (polyadic) relationships.
  • Hypergraphs can model these complex group interactions.

Purpose of the Study:

  • To investigate the impact of polyadic relationships on dynamical processes in networks.
  • To introduce and analyze a new model, the group-driven voter model (GVM), for social dynamics.

Main Methods:

  • Formulation of the group-driven voter model (GVM) incorporating nonlinear interactions within group constraints (hyperedges).
  • Analysis using mean-field theory on annealed uniform hypergraphs.
  • Examination of the competition between nonlinearity and group sizes.

Main Results:

  • The GVM achieves consensus faster than standard voter models.
  • An optimal exit time is identified, minimizing consensus time.
  • Exit time scales as AlnN, with the prefactor A dependent on nonlinearity and group-constraint factors.

Conclusions:

  • The competition between group interactions and nonlinearity significantly shapes GVM dynamics.
  • Polyadic interactions and competing effects are crucial in complex systems.
  • The GVM provides a framework for understanding consensus formation in groups.