There is now a growing consensus among democratic theorists that we should incorporate both “democratic deliberation” and “aggregative voting” into our democratic processes. But how should the two democratic mechanisms of deliberation and voting interact? In this article, we introduce a new axiom, which we call “Nonnegative Response toward Successful Deliberation” (NNRD). The basic idea is that if some individuals change their preferences toward other individuals’ preferences through democratic deliberation, then the social choice rule should not make everybody who has successfully persuaded others through reasoned deliberation worse off than what they would have achieved without deliberation. We prove an impossibility theorem that shows that there exists no aggregation rule that can simultaneously satisfy NNRD along with other mild axioms that reflect deliberative democracy's core commitment to unanimous consensus and political equality. We offer potential escape routes; however, each escape route can succeed only by compromising some core value of deliberative democracy.