  The cosmic distance duality (CDD) relation (based on the Etherington
reciprocity theorem) plays a crucial role in a wide assortment of cosmological
measurements. Attempts at confirming it observationally have met with mixed
results, though the general consensus appears to be that the data do support
its existence in nature. A common limitation with past approaches has been
their reliance on a specific cosmological model, or on measurements of the
luminosity distance to Type Ia SNe, which introduces a dependence on the
presumed cosmology in spite of beliefs to the contrary. Confirming that the CDD
is actually realized in nature is crucial because its violation would require
exotic new physics. In this paper, we study the CDD using the observed angular
size of compact quasar cores and a Gaussian Process reconstruction of the HII
galaxy Hubble diagram---without pre-assuming any particular background
cosmology. In so doing, we confirm at a very high level of confidence that the
angular-diameter and luminosity distances do indeed satisfy the CDD. We then
demonstrate the potential power of this result by utilizing it in a comparative
test of two competing cosmological models---the R_h=ct universe and LCDM---and
show that R_h=ct is favoured by the CDD data with a likelihood ~82.3% compared
with ~17.7% for the standard model.
