  We present photometric and polarimetric measurements of gamma-ray burst (GRB)
optical afterglows observed by the RINGO3 imaging polarimeter over its $\sim$7
year lifetime mounted on the Liverpool Telescope. During this time, RINGO3
responded to 67 GRB alerts. Of these, 28 had optical afterglows and a further
ten were sufficiently bright for photometric and polarimetric analysis
($R\lessapprox{17}$). We present high quality multicolour light curves of ten
sources: GRB 130606A, GRB 130610A, GRB 130612A, GRB 140430A, GRB 141220A, GRB
151215A, GRB 180325A, GRB 180618A, GRB 190114C, and GRB 191016A and polarimetry
for seven of these (excluding GRB 130606A, GRB 130610A, and GRB 130612A, which
were observed before the polarimetry mode was fully commissioned). Eight of
these ten GRBs are classical long GRBs, one sits at the short-long duration
interface with a $T_{90}$ $\sim$ 4 seconds and one is a classical short, hard
burst with extended emission. We detect polarization for GRB 190114C and GRB
191016A. While detailed analyses of several of these GRBs have been published
previously, here we present a uniform re-reduction and analysis of the whole
sample and investigation of the population in a broad context relative to the
current literature. We use survival analysis to fully include the polarization
upper limits in the comparison with other GRB properties, such as temporal
decay rate, isotropic energy and redshift. We find no clear correlation between
polarization properties and wider sample properties and conclude that larger
samples of early time polarimetry of GRB afterglows are required to fully
understand GRB magnetic fields.

High Energy Astrophysical Phenomena