  In the simplest version of the model of group decision making in the
stochastic environment, the participants are segregated into egoists and a
group of collectivists. A "proposal of the environment" is a stochastically
generated vector of algebraic increments of participants' capitals. The social
dynamics is determined by the sequence of proposals accepted by a majority
voting (with a threshold) of the participants. In this paper, we obtain
analytical expressions for the expected values of capitals for all the
participants, including collectivists and egoists. In addition, distinctions
between some principles of group voting are discussed.
