  Since its early beginnings, mankind has put to test many different society
forms, and this fact raises a complex of interesting questions. The objective
of this paper is to present a general population model which takes essential
features of any society into account and which gives interesting answers on the
basis of only two natural hypotheses. One is that societies want to survive,
the second, that individuals in a society would, in general, like to increase
their standard of living. We start by presenting a mathematical model, which
may be seen as a particular type of a controlled branching process. All
conditions of the model are justified and interpreted. After several
preliminary results about societies in general we can show that two society
forms should attract particular attention, both from a qualitative and a
quantitative point of view. These are the so-called weakest-first society and
the strongest-first society. In particular we prove then that these two
societies stand out since they form an envelope of all possible societies in a
sense we will make precise. This result (the envelopment theorem) is seen as
significant because it is paralleled with precise survival criteria for the
enveloping societies. Moreover, given that one of the "limiting" societies can
be seen as an extreme form of communism, and the other one as being close to an
extreme version of capitalism, we conclude that, remarkably, humanity is close
to having already tested the limits.
