  The implications of the anarchy principle on CP violation in the lepton
sector are investigated. A systematic method is introduced to compute the
probability density functions for the CP-violating rephasing invariants of the
PMNS matrix from the Haar measure relevant to the anarchy principle. Contrary
to the CKM matrix which is hierarchical, it is shown that the Haar measure, and
hence the anarchy principle, are very likely to lead to the observed PMNS
matrix. Predictions on the CP-violating Dirac rephasing invariant $|j_D|$ and
Majorana rephasing invariant $|j_1|$ are also obtained. They correspond to
$\langle|j_D|\rangle_\text{Haar}=\pi/105\approx0.030$ and
$\langle|j_1|\rangle_\text{Haar}=1/(6\pi)\approx0.053$ respectively, in
agreement with the experimental hint from T2K of
$|j_D^\text{exp}|\approx0.032\pm0.005$ (or $\approx0.033\pm0.003$) for the
normal (or inverted) hierarchy.
