Models of collective decision making use apparatus of matrix theory and theory of stochastic processes, especially Markov chains, to simulate a result of collective decision making process. An equilibrium model of that process is developed in this paper. Two versions of the model are presented. Both of them are based on discrete time iterations of a row stochastic leverage matrix, which describe mutual influences by actors in the given policy network. A positive solution for the convergence problem of the model through the classification of states of the finite homogenous Markov chain is shown. The outcome of the empirical test is presented.