  In this paper, we study the Hardy nonlocal argument (HNA) and the Cabello
nonlocal argument (CNA) under the Information Causality, Macroscopic Locality
and Local Orthogonality principles in the context of Local Randomness. We see
that, in the context of all the possibilities of local randomness, the gap
between the quantum mechanics and the above principles, in the Cabello's
nonlocality argument is larger than the Hardy's case. Therefore the CNA is
stronger control than the HNA for detecting post-quantum nosignalling
correlations.
