The main purpose of this PhD dissertation is to compare the systems of direct and representative democracy from a theoretical point of view. Faced with the undeniable success and popular acceptance of instruments of direct democracy such as referendums and popular consultations when making decisions, a very natural first question is when voters prefer a system of direct democracy or a system of representative democracy. In Chapter 1, we propose a model to investigate under which conditions voters prefer either one or the other system. We show that direct democracy is the preferred instrument for collective choices in societies in which the populist rhetoric of people against the elite succeeds. We also find that the demand for direct democracy is increasing in the polarization of the electorate. The success of direct democracy is recently resulting in the emergence of social movements and political parties asking for the direct participation of citizens in the decision making process. These groups highlight the inability of representative democracy to implement what the majority of people desires for each issue that comes up for discussion. In Chapter 2, we study under which conditions direct democracy and representative democracy may be equivalent in terms of outcomes. We find that this equivalence becomes less likely to be held the more divided the electorate in evaluating which are the more relevant issues for the society and the less polarized are the politicians. Concerning how voters’ preferences are aggregated, in Chapter 3 we consider a class of preference aggregation mechanisms, known as scoring rules, and show that none of them is guaranteed to select the Condorcet winner from among the set of alternatives at every profile of preferences, except in very specific cases.
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