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The experimental violation of Bell inequality establishes necessary but notsufficient conditions that any theory must obey. Namely, a theory compatiblewith the experimental observations can satisfy at most two of the threehypotheses at the basis of Bell's theorem: free will, no-signaling, andoutcome-Independence. Quantum mechanics satisfies the first two hypotheses butnot the latter. Experiments not only violate Bell inequality, but show anexcellent agreement with quantum mechanics. This fact restricts further theclass of admissible theories. In this work, the author determines the form ofthe hidden-variable models that reproduce the quantum mechanical predictionsfor a spin singlet while satisfying both the hypotheses of free will andno-signaling. Two classes of hidden-variable models are given as an example,and a general recipe to build infinitely many possible models is provided.

Determination of hidden variable models reproducing the spin-singlet