  We have analyzed the distribution of void sizes in the two-dimensional slices
of the Las Campanas Redshift Survey (LCRS). Fourteen volume-limited subsamples
were extracted from the six slices to cover a large part of the survey and to
test the robustness of the results against cosmic variance. Thirteen samples
were randomly culled to produce homogeneously selected samples. We then studied
the relationship between the cumulative area covered by voids and the void size
as a property of the void hierarchy. We find that the distribution of void
sizes scales with the mean galaxy separation, $\lambda$. In particular, we find
that the size of voids covering half of the area is given by $D_{med} \approx
\lambda + (12\pm3) \h^{-2}$Mpc. Next, by employing an environmental density
threshold criterion to identify mock galaxies, we were able to extend this
analysis to mock samples from dynamical $n$-body simulations of Cold Dark
Matter (CDM) models. To reproduce the observed void statistics, overdensity
thresholds of $\delta_{th} \approx 0 ... 1$ are necessary. We have compared
standard (SCDM), open (OCDM), vacuum energy dominated ($\Lambda$CDM), and
broken scale invariant CDM models (BCDM): we find that both the void coverage
distribution and the two-point correlation function provide important and
complementary information on the large-scale matter distribution. The
dependence of the void statistics on the threshold criterion for the mock
galaxy indentification shows that the galaxy biasing is more crucial for the
void size distribution than are differences between the cosmological models.
