Finite Size Effects in the Dynamics of Opinion Formation (Communications in Computational Physics, 2018)
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 thenumber of agents in the model takes a finite value. Those changes of behavior canbe related to the apparent phase transitions that appear in some physical models. Weshow examples in the Galam's model of opinion transmission and the Axelrod's modelof culture formation stressing the role that the network of interactions has on the mainresults of both models. Finally, we present the phenomenon of system-size stochasticresonance by which a forcing signal (identified as an advertising agent) is optimallyamplified by a population of the right (intermediate) size. Our work stresses the rolethat the system size has in the dynamics of social systems and the inappropriatenessof taking the thermodynamic limit for these systems.
Keywords: Dynamics of social systems; finite size effects; scaling laws.