  Recently, a very large clustering length has been measured for quasars at a
redshift of z~4. In combination with the observed quasar luminosity function we
assess the implications of this clustering for the relationship between quasar
luminosity and dark matter halo mass. Our analysis allows for non-linearity and
finite scatter in the relation between quasar luminosity and halo mass, as well
as a luminosity dependent quasar lifetime. The additional novel ingredient in
our modelling is the allowance for an excess in the observed bias over the
underlying halo bias owing to the merger driven nature of quasar activity. We
find that the observations of clustering and luminosity function can be
explained only if both of the following conditions hold: (i) The luminosity to
halo mass ratio increases with halo mass; (ii) The observed clustering
amplitude is in excess of that expected solely from halo bias. The latter
result is statistically significant at the 99% level. Taken together, the
observations provide compelling evidence for merger driven quasar activity,
with a black-hole growth that is limited by feedback. In difference from
previous analyses, we show that there could be scatter in the luminosity halo
mass relation of up to 1 dex, and that quasar clustering can not be used to
estimate the quasar lifetime.
