Voting in a stochastic environment: the case of two groups

For a society consisting of two solidary groups of similar size, the social dynamics determined by voting in a stochastic environment is studied. Within the model of random walks controlled by voting, closed-form expressions for the increments of groups' capital as functions of groups' claim thresholds and the parameters of the environment are obtained. The voting procedure of the unanimous approval of proposals and that of the unanimous rejection of proposals are considered. The group claim thresholds that maximize the group capital and the capital of the whole society are determined.