  We aim at an unbiased census of the radio halo population in galaxy clusters
and test whether current low number counts of radio halos have arisen from
selection biases. We construct near-complete samples based on X-ray and
Sunyaev-Zel'dovich (SZ) effect cluster catalogues and search for diffuse,
extended (Mpc-scale) emission near the cluster centers by analyzing data from
the National Radio Astronomy Observatory Very Large Array Sky Survey. We remove
compact sources using a matched filtering algorithm and model the diffuse
emission using two independent methods. The relation between radio halo power
at 1.4 GHz and mass observables is modelled using a power law, allowing for a
'dropout' population of clusters hosting no radio halo emission. An extensive
suite of simulations is used to check for biases in our methods. Our findings
suggest that the fraction of targets hosting radio halos may have to be revised
upwards for clusters selected using the SZ effect: while approximately 60 per
cent of the X-ray selected targets are found to contain no extended radio
emission, in agreement with previous findings, the corresponding fraction in
the SZ selected samples is roughly 20 per cent. We propose a simple explanation
for this selection difference based on the distinct time evolution of the SZ
and X-ray observables during cluster mergers, and a bias towards relaxed,
cool-core clusters in the X-ray selection.
