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\subsection{Observed Quiescent Fractions}  Figure~\ref{fig:quiescent_fraction} shows the fraction of all observed satellite dwarf galaxies of the MW or M31 that are quiescent versus $\mstar$.  Blue circles show all satellites, while violet squares show those of the MW and green triangles show those of M31.  The only star-forming/gas-rich satellites are: LMC ($\mstar=1.5\times10^9\msun$) and SMC ($\mstar=4.6\times10^8\msun$) around the MW, LGS 3 ($\mstar=9.6\times10^5\msun$) and IC 10 ($\mstar=9\times10^7$) around M31.  At $\mstar<8\times10^7\msun$, 50 of 51 satellites are quiescent, and at $\mstar<9 \times10^5\msun$ \emph{all} are quiescent.  The error bars show 68\% uncertainty for a beta distribution \citep{Cameron2011} based on the observed counts.  In measuring the fraction of satellites that are quiescent, we group them into 1-dex bins of $\mstar$.  We do not attempt any correction for observational completeness as a function of $\mstar$, because we measure the \emph{relative fraction} that are quiescent in each $\mstar$ bin, which should be unbiased, absent significant differential completeness as a function of recent star formation.  We consider the latter unlikely because star-forming galaxies are generally brighter, but the quiescent fraction is near unity across our range in $\mstar$.