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.
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