After the Brexit vote: what's left of 'split' popular sovereignty?

Political theory develops its normative positions on EU legitimacy with a view to what seems possible and acceptable under given political, social, and cultural conditions. Thus, the Brexit vote should give it a pause. In this article, I discuss if and to what extent we can hold on to the claim that the EU is based on a pouvoir constituant mixte. In particular, I examine three problems that the UK's decision to leave the EU gives rise to. First, I address the analytical challenge of whether 'split' popular sovereignty is refuted as a rational reconstruction of the EU. Second, I turn to the normative-theoretical challenge of whether it is a category mistake to refer to (dual) constituent power in the context of the EU. Third, I deal with the political challenge of whether pouvoir constituant mixte is prone to confuse citizens and to scare them off with excessive 'EUphoria'.