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 justified depends on the notion of probability considered and (ii) none of the notions renders both premises simultaneously justified. Under the perhaps most interesting notions, the independence assumption should be weakened.