Participatory Democracy is a process of collective decision making that combines elements from both Direct and Representative Democracy: Citizens have the power to decide on policy and politicians assume the role of policy implementation. The aim of this paper is to understand how Participatory Democracy operates, and to study its implications over the behavior of citizens and politicians and over the final policy outcomes. To this end, we explore a formal model inspired by the experience of Participatory Budgeting implemented in the Brazilian city of Porto Alegre, that builds on the model of meetings with costly participation by Osborne, Rosenthal, and Turner (2000).