Separate common causes and EPR correlations—a no-go result

One diagnosis of Bell’s theorem is that its premise of Outcome Independence is unreasonably strong, as it postulates one common screener system that purports to explain all the correlations involved. This poses a challenge of constructing a model for quantum correla-tions that is local, non-conspiratorial, and has many separate screener systems rather than one common screener system. In particular, the assumptions of such models should not entail Bell’s inequalities. We prove that the models described do not exist, and hence, the diagnosis above is incorrect.