Approaches to modeling and simulating processes related to elections and changing voters’ opinions in bipartisan democracies on the basis of Markov chains are discussed. The basic approach suggested by the “state-probability of action” model (SPA model) is combined with ideas featured by pairwise comparisons and the Analytic Hierarchy Process. The one-level SPA model, focusing on election results, and the twolevel model regarding criteria which affect decisions are considered. Some modifications of traditional homogenous Markov chains, such as switching roles or random transition probabilities, are explored. Some approaches to using non-homogenous Markov chains are outlined.