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Analytical Expression of the Expected Values of Capital at Voting in the Stochastic Environment

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.