We report a partial elucidation of the relationship between polymer polarity and ionic conductivity in polymer electrolyte mixtures comprising a homologous series of nine poly(vinyl ether)s (PVEs) and lithium bis(trifluoromethylsulfonyl)imide. Recent simulation studies have suggested that low dielectric polymer hosts with glass transition temperatures far below ambient conditions are expected to have ionic conductivity limited by salt solubility and dissociation. In contrast, high dielectric hosts are expected to have the potential for high ion solubility but slow segmental dynamics due to strong polymer-polymer and polymer-ion interactions. We report results for PVEs in the low polarity regime with dielectric constants of about 1.3 to 9.0. Ionic conductivity measured for the PVE and salt mixtures ranged from about 10-10 to 10-3 S/cm. In agreement with the predictions from computer simulations, the ionic conductivity increased with dielectric constant and plateaued as the dielectric approached 9.0, comparable to the dielectric constant of the widely used poly(ethylene oxide).