The electric-dipole polarizabilities of all the ions in the solid group IV dioxides ZrO₂, CeO₂, ThO₂ and UO₂ are deduced from experimental high-frequency dielectric-constant data. The resulting polarizabilities of 2.76+or-0.15 au, 5.54+or-0.15 au and 8.82+or-0.15 au for Zr⁴⁺, Cd⁴⁺ and Th⁴⁺, being unaffected by the crystalline environment, pertain also to these free cations. The polarizabilities of the O^2- ions are found to depend on their in-crystal environment, as parameterized by the closest cation-anion separation, in the same way as those of the anions in the M₂O alkali oxides. The ionic polarizabilities are used to derive values with an estimated error of 5% for the coefficients governing the dipole-dipole dispersive attractions between all ion pairs in all four crystals. Taken in conjunction with ion wavefunctions calculated elsewhere, these coefficients are used to compute values, with estimated errors of about 20%, for the coefficients governing the dipole-quadrupole dispersive attractions between all the ions in ThO₂ and UO₂. Values are presented for the parameters governing the damping of these dispersive attractions when the overlap between the wavefunctions of the interacting ions is not negligible.