  We use measurements of the projected galaxy correlation function w_p and
galaxy void statistics to test whether the galaxy content of halos of fixed
mass is systematically different in low density environments. We present new
measurements of the void probability function (VPF) and underdensity
probability function (UPF) from Data Release Four of the Sloan Digital Sky
Survey, as well as new measurements of the VPF from the full data release of
the Two-Degree Field Galaxy Redshift Survey. We compare these measurements to
predictions calculated from models of the Halo Occupation Distribution (HOD)
that are constrained to match both w_p and the space density of galaxies. The
standard implementation of the HOD assumes that galaxy occupation depends on
halo mass only, and is independent of local environment. For luminosity-defined
samples, we find that the standard HOD prediction is a good match to the
observations, and the data exclude models in which galaxy formation efficiency
is reduced in low-density environments. More remarkably, we find that the void
statistics of red and blue galaxies (at L ~ 0.4L_*) are perfectly predicted by
standard HOD models matched to the correlation function of these samples,
ruling out "assembly bias" models in which galaxy color is correlated with
large-scale environment at fixed halo mass. We conclude that the luminosity and
color of field galaxies are determined predominantly by the mass of the halo in
which they reside and have little direct dependence on the environment in which
the host halo formed. In broader terms, our results show that the sizes and
emptiness of voids found in the distribution of L > 0.2L_* galaxies are in
excellent agreement with the predictions of a standard cosmological model with
a simple connection between galaxies and dark matter halos. (abridged)
