Polarization of final electrons in the Compton effect

A final electron polarization is calculated for scattering of a polarized photon by a polarized electron. The electron polarization is obtained in terms of the electron helicity and the transverse polarization vector in an arbitrary frame of reference. As an example, we consider the Compton scattering of high energy electrons off a laser beam in the set-up which is important for future γγ and γe colliders. In this case we find that the polarization effects are significant and should be taken into account in calculating multiple electron scattering by a laser beam.