  We consider the implications of the bond valence model (BVM) description of
charge distribution in reduced ceria phases
(CeO$_{2-x}$)\cite{Shoko2009,Shoko2009b} to the models used to describe
electronic and ionic conductivity in these phases. We conclude that the BVM is
consistent with both the small polaron model (SPM) and the atomistic models
which describe the electronic and ionic conductivities respectively. For
intermediate phases, i.e., $x \sim 0.3$, we suggest the possibility of low
temperature metallic conductivity. This has not yet been experimentally
observed. We contrast the BVM results and the conventional description of
charge distribution in reduced ceria phases.
