A method which allows for the effects of dipole and quadrupole polarizations on the interparticle interactions in molecular dynamics simulations is described. Multipole induction by both Coulombic and short-range interactions is included. The validity of a description of the interactions in condensed ionic systems with pair potentials supplemented with a description of polarization effects is assessed, and the implications for reliably parameterizing such a model are discussed. The role of cation quadrupole polarization is explored in simulations of solid and liquid AgCl. The effect is to substantially improve the agreement with experiment of properties such as phonon dispersion and liquid structure relative to calculations with a simple pair potential.