  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.
