  Using cosmological $N$-body simulations and the void probability function
(VPF), we investigate the statistical properties of voids within a wide range
of initially Gaussian models for the origin of large-scale structure. We pay
particular attention to the ability of the VPF to diagnose `biased galaxy
formation': the preferential formation of galaxies in regions of high
background density and corresponding suppression of galaxy formation in regions
of low background density. Biased models have systematically higher VPFs than
unbiased models, but for a given biasing scheme the VPF is relatively
insensitive to the value of the bias factor $b$. Thus, while the VPF can
distinguish unbiased models from some biased models, it is probably not a
useful way to constrain the bias factor; uncertainties in the appropriate
choice of biasing prescription overwhelm the mild dependence on $b$. We compare
the predictions of our models to the most extensive VPF observations published
to date. These data do {\it not} require strong biasing; Gaussian models in
which galaxies trace mass can reproduce the VPF data to within the errors
expected from the current finite volume fluctuations. Models with the moderate
biasing predicted by cosmological simulations with gas dynamics yield a
slightly better match to the data. Models in which galaxy formation is strongly
suppressed in low density regions produce an excess of large, empty voids.
