The fact that most of us are ignorant on politically relevant matters presents a problem for democracy. In light of this, some have suggested that we should impose epistemic constraints on democratic participation, and specifically that the franchise be restricted along competency lines – a suggestion that in turn runs the risk of violating a long-standing condition on political legitimacy to the effect that legitimate political arrangements cannot be open to reasonable objections. The present paper therefore outlines a way to (...) solve the problem of public ignorance without restricting the franchise. The proposal involves filtering the electoral input of a universal franchise through a statistical model that simulates what the public's political preferences would have been, had they been informed on politically relevant matters. The result is modelled democracy. A case is made that such democracy both solves the problem of public ignorance and satisfies the aforementioned condition on legitimacy. (shrink)