On the structure of competitive societies
Theoretical Division and Center for Nonlinear Studies, Los Alamos National Laboratory, Los Alamos, New Mexico, 87545, USA
2 Department of Physics, Boston University, Boston, Massachusetts, 02215, USA
Published online: 31 March 2006
We model the dynamics of social structure by a simple interacting particle system. The social standing of an individual agent is represented by an integer-valued fitness that changes via two offsetting processes. When two agents interact one advances: the fitter with probability p and the less fit with probability 1-p. The fitness of an agent may also decline with rate r. From a scaling analysis of the underlying master equations for the fitness distribution of the population, we find four distinct social structures as a function of the governing parameters p and r. These include: (i) a static lower-class society where all agents have finite fitness; (ii) an upwardly-mobile middle-class society; (iii) a hierarchical society where a finite fraction of the population belongs to a middle class and a complementary fraction to the lower class; (iv) an egalitarian society where all agents are upwardly mobile and have nearly the same fitness. We determine the basic features of the fitness distributions in these four phases.
PACS: 87.23.Ge – Dynamics of social systems / 02.50.Ey – Stochastic processes / 05.40.-a – Fluctuation phenomena, random processes, noise, and Brownian motion / 89.65.Ef – Social organizations; anthropology
© EDP Sciences, Società Italiana di Fisica, Springer-Verlag, 2006