Social dynamics determined by voting in a stochastic environment is analyzed for a society composed of two cohesive groups of similar size. Within the model of random walks determined by voting, explicit formulas are derived for the capital increments of the groups against the parameters of the environment and "claim thresholds" of the groups. The "unanimous acceptance" and "unanimous rejection" group rules are considered as the voting procedures. Claim thresholds are evaluated that are most beneficial to the participants of the groups and to the society as a whole.