  We use the void probability function to compare the redshift--space galaxy
distribution in the Perseus--Pisces survey with artificial samples from N-body
simulations of standard cold dark matter (CDM) and broken scale invariance
(BSI) models. Galaxies are identified as residing in peaks of the evolved
density field in such a way as to reproduce both the observed luminosity and
two--point correlation functions. Using a similar approach, it was recently
shown that the VPF can discriminate between CDM and a cold+hot dark matter
(CHDM) model with cold/hot/baryon fractions = 0.6/0.3/0.1. Our main result is
that both CDM (as expected from a previous analysis) and BSI fit observational
data. The robustness of the result is checked against changing the observer's
position in the simulations and the galaxy identification in the evolved
density field. Therefore, while the void statistics is sensitive to the passage
from CDM to CHDM (different spectrum and different nature of dark matter), it
is not to the passage from CDM to BSI (different spectrum but same dark
matter). On such a basis, we conjecture that the distribution of voids could be
directly sensitive to the nature of dark matter, but scarcely sensitive to the
shape of the transfer function.
