Bell-type inequalities in the nonideal case: Proof of a conjecture of bell

Recently Bell has conjectured that, with "epsilonics," one should be able to argue, à la EPR, from "almost ideal correlations" (in parallel Bohm-Bell pair experiments) to "almost determinism," and that this should suffice to derive an approximate Bell-type inequality. Here we prove that this is indeed the case. Such an inequality-in principle testable-is derived employing only weak locality conditions, imperfect correlation, and a propensity interpretation of certain conditional probabilities. Outcome-independence (Jarrett's "completeness" condition), hence "factorability" of joint probabilities, is not assumed, but rather an approximate form of this is derived. An alternative proof to the original one of Bell [1971] constraining stochastic, contextual hidden-variables theories is thus provided.