  The evolution of galaxy cluster counts is a powerful probe of several
fundamental cosmological parameters. A number of recent studies using this
probe have claimed tension with the cosmology preferred by the analysis of the
Planck primary CMB data, in the sense that there are fewer clusters observed
than predicted based on the primary CMB cosmology. One possible resolution to
this problem is systematic errors in the absolute halo mass calibration in
cluster studies, which is required to convert the standard theoretical
prediction (the halo mass function) into counts as a function of the observable
(e.g., X-ray luminosity, Sunyaev-Zel'dovich flux, optical richness). Here we
propose an alternative strategy, which is to directly compare predicted and
observed cluster counts as a function of the one-dimensional velocity
dispersion of the cluster galaxies. We argue that the velocity dispersion of
groups/clusters can be theoretically predicted as robustly as mass but, unlike
mass, it can also be directly observed, thus circumventing the main systematic
bias in traditional cluster counts studies. With the aid of the BAHAMAS suite
of cosmological hydrodynamical simulations, we demonstrate the potential of the
velocity dispersion counts for discriminating even similar $\Lambda$CDM models.
These predictions can be compared with the results from existing redshift
surveys such as the highly-complete Galaxy And Mass Assembly (GAMA) survey, and
upcoming wide-field spectroscopic surveys such as the Wide Area Vista
Extragalactic Survey (WAVES) and the Dark Energy Survey Instrument (DESI).
