The conductivity and heat capacity of CaF2 in the superionic phase are calculated by computer simulation using an ab initio interaction model which includes polarization effects. The results are compared with those obtained in Gillan's classic study of CaF2, where an empirical effective pair potential was used. Despite large differences between the potentials at the pair-wise interaction level, the observable properties predicted by the two models are essentially identical in the crystal, and the reasons for the success of the effective pair potential in recapturing the consequences of the polarization effects are discussed. As further aspects of the study, we clarify the simulation predictions for the magnitude of the heat capacity anomaly at the superionic transition and for the number of defects present in the superionic states-matters on which Gillan's results have been taken to be at variance with the body of experimental evidence on other fluorite-structured materials. (C) 2004 Elsevier B.V. All rights reserved.