We have performed a novel comparison between electron-beam polarimeters based on M{o}ller and Compton scattering. A sequence of electron-beam polarization measurements were performed at low beam currents ($<$ 5 $mu$A) during the $Q_{rm weak}$ experiment in Hall C at Jefferson Lab. These low current measurements were bracketed by the regular high current (180 $mu$A) operation of the Compton polarimeter. All measurements were found to be consistent within experimental uncertainties of 1% or less, demonstrating that electron polarization does not depend significantly on the beam current. This result lends confidence to the common practice of applying M{o}ller measurements made at low beam currents to physics experiments performed at higher beam currents. The agreement between two polarimetry techniques based on independent physical processes sets an important benchmark for future precision asymmetry measurements that require sub-1% precision in polarimetry.
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