Precision measurements of the relative analyzing powers of five electron beam polarimeters, based on Compton, Moller, and Mott scattering, have been performed using the CEBAF accelerator at the Thomas Jefferson National Accelerator Facility ( Jefferson Laboratory). A Wien filter in the 100 keV beam line of the injector was used to vary the electron spin orientation exiting the injector. High statistical precision measurements of the scattering asymmetry as a function of the spin orientation were made with each polarimeter. Since each polarimeter receives beam with the same magnitude of polarization, these asymmetry measurements permit a high statistical precision comparison of the relative analyzing powers of the five polarimeters. This is the first time a precise comparison of the analyzing powers of Compton, Moller, and Mott scattering polarimeters has been made. Statistically significant disagreements among the values of the beam polarization calculated from the asymmetry measurements made with each polarimeter reveal either errors in the values of the analyzing power or failure to correctly include all systematic effects. The measurements reported here represent a first step toward understanding the systematic effects of these electron polarimeters. Such studies are necessary to realize high absolute accuracy (ca. 1%) electron polarization measurements, as required for some parity violation measurements planned at Jefferson Laboratory. Finally, a comparison of the value of the spin orientation exiting the injector that provides maximum longitudinal polarization in each experimental hall leads to an independent and very precise ( better than 10-4) absolute measurement of the final electron beam energy