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.

25 pages + 5 figures, AASMS LaTeX, ApJ, 469, in press