Which kind of political process preferences citizens have? Some of the previous research points that these preferences goes beyond the classical debate between representation and participation, but which are the specific dimensions of this debate is quite less clear and the role of a potential stealth democracy model should be clarified. The paper will use two surveys developed in Spain (one national and one local) that include a rich set of questions allowing testing these ideas. First, we analyze the dimensionality of these preferences and the similarities and preferences that appear when comparing both surveys results. Second, we focus on the core supporters of each of the three main models (representation, participation, stealth) to clarify through this comparison which is the specific meaning of the ideals of the stealth democracy model.