  We measure the redshift space reduced void probability function (VPF) for
2dFGRS volume limited galaxy samples covering the absolute magnitude range
M_bJ-5logh=-18 to -22. Theoretically, the VPF connects the distribution of
voids to the moments of galaxy clustering of all orders, and can be used to
discriminate clustering models in the weakly non-linear regime. The reduced VPF
measured from the 2dFGRS is in excellent agreement with the paradigm of
hierarchical scaling of the galaxy clustering moments. The accuracy of our
measurement is such that we can rule out, at a very high significance, popular
models for galaxy clustering, including the lognormal distribution. We
demonstrate that the negative binomial model gives a very good approximation to
the 2dFGRS data over a wide range of scales, out to at least 20h-1Mpc.
Conversely, the reduced VPF for dark matter in a LambdaCDM universe does appear
to be lognormal on small scales but deviates significantly beyond \approx
4h-1Mpc. We find little dependence of the 2dFGRS reduced VPF on galaxy
luminosity. Our results hold independently in both the north and south Galactic
pole survey regions.

Astrophysics