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Simple model for multiple-choice collective decision making.

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Summary
This summary is machine-generated.

This study introduces a model for interacting agents making choices, revealing how social interactions drive spontaneous symmetry breaking and hierarchy formation. The model offers insights into collective decision-making dynamics.

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Area of Science:

  • Complex Systems
  • Statistical Physics
  • Social Dynamics

Background:

  • Understanding collective decision-making in heterogeneous agent systems is crucial.
  • Existing models often simplify agent interactions and decision processes.
  • The role of social interactions in emergent order requires further investigation.

Purpose of the Study:

  • To develop a simple, solvable model for heterogeneous, interacting agents with discrete choices.
  • To investigate the mechanisms of spontaneous symmetry breaking (SSB) driven by cooperative social interactions.
  • To explore the emergence of hierarchies and phase transitions in agent-based decision-making.

Main Methods:

  • Formulating a model analogous to mean-field Potts-like models, solvable by optimizing average energy (E).
  • Analyzing decision change propagation through avalanches to capture macroscopic dynamics via gradient flow.
  • Examining the permutation-symmetric case to isolate the effects of cooperative interactions on SSB.
  • Extending the model to finite-degree graphs to study emergent equilibria.

Main Results:

  • Cooperative social interactions can lead to spontaneous symmetry breaking (SSB) and the formation of decision hierarchies.
  • SSB is shown to be a preferred instability over discontinuous phase transitions between symmetric states.
  • Beyond the mean-field approximation, a large number of stable equilibria emerge on finite-degree graphs.
  • The model's dynamics are effectively captured by a gradient flow along the average energy landscape.

Conclusions:

  • The developed model provides a framework for understanding emergent order and hierarchy in collective decision-making.
  • Spontaneous symmetry breaking is a key mechanism driven by social interactions, offering an alternative to abrupt phase transitions.
  • The model highlights the rich emergent behavior, including numerous stable states, possible in networked agent systems.