This essay proceeds in three steps. First, it will briefly outline the often invoked “crisis” of representative democracy and its major symptoms. Second, it will discuss a popular yet, as I shall argue, worryingly misguided response to that crisis: namely, the switch to plebiscitarian methods of “direct” democracy, as advocated, for example, by rightist populist forces in many European Union member states. The United Kingdom's Brexit referendum of June 2016 illuminates the weaknesses of this approach. Third, it will suggest a rough design for enriching representative electoral democracy with nonelectoral (but “aleatory,” or randomized) and nonmajoritarian (but deliberative and consultative) bodies and their peculiar methods of political will formation (as opposed to the expression of a popular will already formed).