The premises of Condorcet's Jury Theorem are not simultaneously justified

Condorcet's famous jury theorem reaches an optimistic conclusion on the correctness of majority decisions, based on two controversial premises about voters: they are competent and vote independently, in a technical sense. I carefully analyse these premises and show that: (i) whether a premise is justi…ed depends on the notion of probability considered; (ii) none of the notions renders both premises simultaneously justi…ed. Under the perhaps most interesting notions, the independence assumption should be weakened.