Lithium sulphate and a few other compounds have high temperature phases which are both solid electrolytes and plastic crystals (rotor phases). Three types of experiments are here considered in order to test the validity of a "paddle-wheel mechanism" that has been proposed for cation conductivity in these phases. A single-crystal neutron diffraction study has been performed for cubic lithium sulphate. The refinement of the data gives a very complex model for the location of the lithium ions. There is definitely a void at and near the octahedral (1/2, 1/2, 1/2) position. 90% of the lithium ions are located at the tetrahedral 8c-sites (1/4, 1/4, 1/4), although significantly distorted in the directions of the four neighbouring sulphate ions. The remaining 10% of the lithium ions are refined as an evenly distributed spherical shell which is surrounding the sulphate ions. The lithium ions are transported along a slightly curved pathway of continuous lithium occupation corresponding to a distance of about 3.7 angstrom. Thus, lithium transport occurs in one of the six directions , [110BAR],  etc. The electrical conductivity has been studied for solid solutions of lithium tungstate in cubic lithium sulphate. The conductivity is reduced in the one-phase region, while it is increased in a two phase (solid-melt) region. There are pronounced differences between the rotor phases and other phases concerning how partial cation substitution affects the electrical conductivity of solid solutions. Regarding self and interdiffusion, all studied mono- and divalent cations are very mobile in the rotor phases, which lack the pronounced correlation with ionic radii that is characteristic for diffusion in other classes of solid electrolytes. The quoted studies are to be considered as strong evidence against a percolation model proposed by Secco.