  We show that no probability distribution of spin measurement outcomes on
pairs of spin 1/2 particles is unambiguously more nonlocal than the quantum
correlations. That is, any distribution that produces a CHSH violation larger
than the quantum violation for some axis choices also produces a smaller CHSH
violation for some other axis choices. In this sense, it is not possible for
nature to be strictly more nonlocal than quantum theory allows.
