Analytical expression of the expected values of capital at voting in the stochastic environment

In the simplest variant of the model of collective decision making in the stochastic environment, the participants were segregated into egoists and a group of collectivists. ‘Proposal of the environment’ is the stochastically generated vector of algebraic increments of capitals. The social dynamics was defined by the sequence of proposals accepted by threshold-majority voting. Analytical expressions of the expected values of the capitals of participants, collectivists and egoists were obtained. Distinctions of some principles of group voting were discussed.