  The relation between galaxies and dark matter halos is of vital importance
for evaluating theoretical predictions of structure formation and galaxy
formation physics. We show that the widely used method of abundance matching
based on dark matter only simulations fails at the low mass end because two of
its underlying assumptions are broken: only a small fraction of low mass (below
10^9.5 solar masses) halos host a visible galaxy, and halos grow at a lower
rate due to the effect of baryons. In this regime, reliance on dark matter only
simulations for abundance matching is neither accurate nor self-consistent. We
find that the reported discrepancy between observational estimates of the halo
masses of dwarf galaxies and the values predicted by abundance matching does
not point to a failure of LCDM, but simply to a failure to account for baryonic
effects. Our results also imply that the Local Group contains only a few
hundred observable galaxies in contrast with the thousands of faint dwarfs that
abundance matching would suggest. We show how relations derived from abundance
matching can be corrected, so that they can be used self-consistently to
calibrate models of galaxy formation.
