In this paper we show how a realistic normative democratic theory can work within the constraints set by the most pessimistic empirical results about voting behaviour and elite capture of the policy process. After setting out the empirical evidence and discussing some extant responses by political theorists, we argue that the evidence produces a two-pronged challenge for democracy: an epistemic challenge concerning the quality and focus of decision-making and an oligarchic challenge concerning power concentration. To address the challenges we then put forward three main normative claims, each of which is compatible with the evidence. We start with a critique of the epistocratic position commonly thought to be supported by the evidence. We then introduce a qualified critique of referenda and other forms of plebiscite, and an outline of a tribune-based system of popular control over oligarchic influence on the policy process. Our discussion points towards a renewal of democracy in a plebeian but not plebiscitarian direction: Attention to the relative power of social classes matters more than formal dispersal of power through voting. We close with some methodological reflections about the compatibility between our normative claims and the realist program in political philosophy.