Nowadays, several social movements asking for direct participation of citizens in the decision-making process are emerging in western democracies. These groups argue that traditional representative systems fail to adequately represent the will of the majority (often defined as “people” by populist movements) and support direct democracy as the only political system to restore the will of the majority. In this paper we consider a setting where several decisions about independent issues have to be made, and analyze under what conditions the two systems coincide; that is, the policy implemented by the winner of an electoral competition coincides with the one that citizens would choose by means of direct democracy. We find necessary and sufficient conditions for this equivalence to hold, implying that, as long as at least one of them is not fulfilled, the equivalence between direct democracy and representative democracy ceases to exist and disaffection in representative democracy would arise. The theoretical predictions of the model state, that the more divided the electorate over the proposals to be carried out for the bundle of issues and the less polarized are the politicians, the more likely it is that the conditions fail to be satisfied. We illustrate how the failure of our conditions leads to reasons for the emergence of mistrust in systems of representative democracy. Deeply divided societies, the activity of lobbies and special-interest groups, and the failure of electoral competition stand as responsible.