  The cross section for $e^-e^- \to e^-e^-$ with arbitrary electron
polarizations is calculated within the Electroweak Standard Model for energies
large compared to the electron mass, including the complete virtual and
soft-photonic $O(\alpha)$ radiative corrections. The relevant analytical
results are listed, and a numerical evaluation is presented for the unpolarized
and polarized cross sections as well as for polarization asymmetries. The
relative weak corrections are typically of the order of 10%. At low energies,
the bulk of the corrections is due to the running of the electromagnetic
coupling constant. For left-handed electrons, at high energies the vertex and
box corrections involving virtual W bosons become very important. The
polarization asymmetry is considerably reduced by the weak radiative
corrections.
