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\subsection{Observed Quiescent Fractions for Satellites}  Figure~\ref{fig:quiescent_fraction} shows, for all satellite galaxies with at  $\mstar\lesssim10^9\msun$ within $300\kpc$  of the MW and/or or  M31, the fraction that are quiescent in 1-dex bins of $\mstar$ \citep[see also][]{Phillips2014, SlaterBell2014}. We do not attempt any correction for observational completeness as a function of $\mstar$, because we measure the \emph{relative fraction} in each bin, which is likely an unbiased metric at these satellites' distances.  %absent significant differential completeness as a function of recent star formation, which is unlikely because star-forming galaxies are generally brighter, but the quiescent fraction is near unity across almost all $\mstar$.  We show fractions for all such satellites (blue circles) as well as separately for those in the MW (violet squares) and M31 (green triangles) halos.