  The anarchy principle leading to the see-saw ensemble is studied analytically
with the usual tools of random matrix theory. The probability density function
for the see-saw ensemble of $N\times N$ matrices is obtained in terms of a
multidimensional integral. This integral involves all light neutrino masses,
leading to a complicated probability density function. It is shown that the
probability density function for the neutrino mixing angles and phases is the
appropriate Haar measure. The decoupling of the light neutrino masses and
neutrino mixings implies no correlation between the neutrino mass eigenstates
and the neutrino mixing matrix and leads to a loss of predictive power when
comparing with observations. This decoupling is in agreement with some of the
claims found in the literature.
