  The mechanisms responsible for the production of relativistic jets from
supermassive black holes (SMBHs) accreting at near-Eddington rates are not
well-understood. Simple theoretical expectations indicate that SMBHs in quasars
accrete via thin discs which should produce at most very weak jets. This is
contradicted by observations of powerful jets in flat-spectrum radio quasars
(FSRQs). We use gamma-ray luminosities observed with the \emph{fermi} Large
Area Telescope as a proxy of the jet power for a population of 154 FSRQs.
Assuming typical quasar accretion rates and using black hole mass measurements
from a variety of methods, we find a mean jet production efficiency of about 10
per cent for FSRQs, with values as high as 222 per cent. We find that this is
consistent with FSRQs hosting moderately thin, magnetically arrested accretion
discs around rapidly spinning black holes (BHs). Modeling our observations
using general relativistic magnetohydrodynamic (GRMHD) simulations of jets from
thin discs, we find an average lower limit of $a_* = 0.59$ for the SMBH spins
of FSRQs, with tendency for the spins to decrease as the black hole mass
increases. Our results are consistent with the merger-driven evolution of
SMBHs. 3 per cent of the sample cannot be explained by current GRMHD models of
jet production from Kerr BHs due to the high efficiencies. Along the way, we
find a correlation between BH masses and $L_\gamma$ which may be an useful mass
estimator in blazar gamma-ray studies.
