  We introduce a new renormalization procedure on double rotations, which is
reminiscent of the classical Rauzy induction. Using this renormalization we
prove that the set of parameters which induce infinite type double rotations
has Hausdorff dimension strictly smaller than 3. Moreover, we construct a
natural invariant measure supported on these parameters and show that, with
respect to this measure, almost all double rotations are uniquely ergodic.
