Lack of consensus in social systemsI. J. Benczik, S. Z. Benczik, B. Schmittmann and R. K. P. Zia
Department of Physics, Virginia Tech - Blacksburg, VA 24061-0435, USA
received 23 October 2007; accepted in final form 4 April 2008; published May 2008
published online 14 May 2008
We propose an exactly solvable model for the dynamics of voters in a two-party system. The opinion formation process is modeled on a random network of agents. The dynamical nature of interpersonal relations is also reflected in the model, as the connections in the network evolve with the dynamics of the voters. In the infinite time limit, an exact solution predicts the emergence of consensus, for arbitrary initial conditions. However, before consensus is reached, two different metastable states can persist for exponentially long times. One state reflects a perfect balancing of opinions, the other reflects a completely static situation. An estimate of the associated lifetimes suggests that lack of consensus is typical for large systems.
89.75.Hc - Networks and genealogical trees.
02.50.Le - Decision theory and game theory.
05.70.Ln - Nonequilibrium and irreversible thermodynamics.
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