Finite size effects in the dynamics of opinion formation

TL;DR

This paper reviews how finite system size influences opinion formation dynamics, revealing size-dependent phase transitions, the impact of interaction networks, and the phenomenon of stochastic resonance in social models.

Contribution

It highlights the importance of finite size effects in social opinion models, challenging the common assumption of infinite populations and exploring size-dependent phenomena.

Findings

Finite size can induce behavioral changes not seen in infinite models.

Network structure significantly affects opinion dynamics.

System-size stochastic resonance amplifies signals in social systems.

Abstract

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.