Finite Size Effects in the Dynamics of Opinion Formation
Raul Toral 1*, Claudio J. Tessone 11 Instituto Mediterraneo de Estudios Avanzados (IMEDEA), CSIC-UIB, Ed. Mateu Orfila, Campus UIB, E-07122 Palma de Mallorca, Spain.
Received 26 July 2006; Accepted (in revised version) 6 August 2006
Communicated by Dietrich Stauffer
Available online 30 September 2006
For some models of relevance in the social sciences we review some examples in which system size plays an important role in the final outcome of the dynamics. We discuss the conditions under which changes of behavior can appear only when the number of agents in the model takes a finite value. Those changes of behavior can be related to the apparent phase transitions that appear in some physical models. We show examples in the Galam's model of opinion transmission and the Axelrod's model of culture formation stressing the role that the network of interactions has on the main results of both models. Finally, we present the phenomenon of system-size stochastic resonance by which a forcing signal (identified as an advertising agent) is optimally amplified by a population of the right (intermediate) size. Our work stresses the role that the system size has in the dynamics of social systems and the inappropriateness of taking the thermodynamic limit for these systems.
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PACS: 05.45.-a, 05.40.Ca, 02.50.-r
Key words: Dynamics of social systems, finite size effects, scaling laws.
Email: firstname.lastname@example.org (R. Toral), email@example.com (C. J. Tessone)