  We present a novel system of equations to describe the evolution of
self-organized structured societies (biological or human) composed of several
trait groups. The suggested approach is based on the combination of ideas
employed in the theory of biological populations, system theory, and utility
theory. The evolution equations are defined as utility rate equations, whose
parameters are characterized by the utility of each group with respect to the
society as a whole and by the mutual utilities of groups with respect to each
other. We analyze in detail the cases of two groups (cooperators and defectors)
and of three groups (cooperators, defectors, and regulators) and find that, in
a self-organized society, neither defectors nor regulators can overpass the
maximal fractions of about 10% each. This is in agreement with the data for bee
and ant colonies. The classification of societies by their distance from
equilibrium is proposed. We apply the formalism to rank the countries according
to the introduced metric quantifying their relative stability, which depends on
the cost of defectors and regulators as well as their respective population
fractions. We find a remarkable concordance with more standard economic ranking
based, for instance, on GDP per capita.
