  We constrain the most likely range of masses for the Milky Way and M31 using
an application of the Numerical Action Method (NAM) that optimizes the fit to
observed parameters over a large ensemble of NAM-generated solutions. Our 95%
confidence level mass ranges, 1.5-4.5 x 10^12 m_sun for MW and 1.5-5.5 x 10^12
m_sun for M31, are consistent with the upper range of estimates from other
methods and suggests that a larger proportion of the total mass becomes
detectable when the peculiar motions of many nearby satellites are taken into
account in the dynamical analysis. We test the method against simulated Local
Group catalogs extracted from the Millennium Run to confirm that mass
predictions are consistent with actual galaxy halo masses.
