  We present a blind time-delay strong lensing (TDSL) cosmographic analysis of
the doubly imaged quasar SDSS 1206+4332. We combine the relative time delay
between the quasar images, Hubble Space Telescope imaging, the Keck stellar
velocity dispersion of the lensing galaxy, and wide-field photometric and
spectroscopic data of the field to constrain two angular diameter distance
relations. The combined analysis is performed by forward modelling the
individual data sets through a Bayesian hierarchical framework, and it is kept
blind until the very end to prevent experimenter bias. After unblinding, the
inferred distances imply a Hubble constant $H_0 = 68.8^{+5.4}_{-5.1}$
kms$^{-1}$Mpc$^{-1}$, assuming a flat Lambda cold dark matter cosmology with
uniform prior on $\Omega_{\rm m}$ in [0.05, 0.5]. The precision of our
cosmographic measurement with the doubly imaged quasar SDSS 1206+4332 is
comparable with those of quadruply imaged quasars and opens the path to perform
on selected doubles the same analysis as anticipated for quads. Our analysis is
based on a completely independent lensing code than our previous three H0LiCOW
systems and the new measurement is fully consistent with those. We provide the
analysis scripts paired with the publicly available software to facilitate
independent analysis. The consistency between blind measurements with
independent codes provides an important sanity check on lens modelling
systematics. By combining the likelihoods of the four systems under the same
prior, we obtain $H_0 = 72.5^{+2.1}_{-2.3}$kms$^{-1}$Mpc$^{-1}$. This
measurement is independent of the distance ladder and other cosmological
probes.
