The author makes an attempt to systematize the range of problems that rise when focal cognitive elements of democracy are reconsidered from the positions of analytical political theory. Thus, contradictions and impasses are shown up, which are faced by modern theories - theories of elections, of elites, of political market, of interest groups, of political participation, of organizational structures, of authoritarianism, of consensus, etc. In conclusion, the notion of "constructive folly" is discussed, the application of which, in the author's opinion, is to help surmount seemingly insurmountable political barriers.