  If the connection between the fundamental theory and neutrino mass matrices
M_\nu is sufficiently complicated all traces of underlying symmetries might be
erased and an 'anarchical' M_\nu, with random entries, can arise. It has been
claimed that such random matrices generically prefer large mixing making
unnecessary to invoke flavour symmetries to explain the observed pattern of
neutrino mixing angles. A critical analysis of this idea (paying particular
attention to the role of unphysical phases and coordinate dependence) shows
that basis-independent, random M_nu's are not biased towards large values of
the neutrino mixing angles, contrary to previous claims. As a result, the case
for anarchy in the neutrino sector is considerably weakened.
