  We present measurements of the void probability function (VPF) at z~1 using
data from the DEEP2 Redshift Survey and its evolution to z~0 using data from
the Sloan Digital Sky Survey (SDSS). We measure the VPF as a function of galaxy
color and luminosity in both surveys and find that it mimics trends displayed
in the two-point correlation function, $\xi$; namely that samples of brighter,
red galaxies have larger voids (i.e. are more strongly clustered) than fainter,
blue galaxies. We also clearly detect evolution in the VPF with cosmic time,
with voids being larger in comoving units at z~0. We find that the reduced VPF
matches the predictions of a `negative binomial' model for galaxies of all
colors, luminosities, and redshifts studied. This model lacks a physical
motivation, but produces a simple analytic prediction for sources of any number
density and integrated two-point correlation function, \bar{\xi}. This implies
that differences in the VPF across different galaxy populations are consistent
with being due entirely to differences in the population number density and
\bar{\xi}. The robust result that all galaxy populations follow the negative
binomial model appears to be due to primarily to the clustering of dark matter
halos. The reduced VPF is insensitive to changes in the parameters of the halo
occupation distribution, in the sense that halo models with the same \bar{\xi}
will produce the same VPF. For the wide range of galaxies studied, the VPF
therefore does not appear to provide useful constraints on galaxy evolution
models that cannot be gleaned from studies of \bar{\xi} alone. (abridged)
