A Model of Symmetry Breaking in Collective Decisions

Heiko Hamann, Bernd Meyer, Thomas Schmickl, Karl Crailsheim
Simulation of Adaptive Behavior (SAB'10) (2010)

Abstract:

  Symmetry breaking is commonly found in self-organized collective
  decision making. It serves an important functional role,
  specifically in biological and bio-inspired systems. The analysis of
  symmetry breaking is thus an important key to understanding
  self-organized decision making. However, in many systems of
  practical importance available analytic methods cannot be applied
  due to the complexity of the scenario and consequentially the
  model. This applies specifically to self-organization in
  bio-inspired engineering. We propose a new modeling approach which
  allows us to formally analyze important properties of such
  processes. The core idea of our approach is to infer a compact model
  based on stochastic processes for a one-dimensional symmetry
  parameter. This enables us to analyze the fundamental properties of
  even complex collective decision making processes via Fokker--Planck
  theory. We are able to quantitatively address the effectiveness of
  symmetry breaking, the stability, the time taken to reach a
  consensus, and other parameters. This is demonstrated with two
  examples from swarm robotics.


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