Correlated anion and cation motion can significantly reduce the overall ion conductivity in electrolytes versus the ideal conductivity calculated based on the diffusion constants alone. Using coarse-grained molecular dynamics simulations, we calculate the conductivity and the degree of uncorrelated ion motion in salt-doped homopolymers and block copolymers as a function of concentration and interaction strengths. Calculating conductivity from ion mobility under an applied electric field increases accuracy versus the typical use of fluctuation dissipation relationships in equilibrium simulations. In typical electrolytes, correlation in cation-anion motion is often expected to be reduced at low ion concentrations. However, for these polymer electrolytes with strong ion-polymer and ion-ion interactions, we find cation-anion motion is more correlated at lower concentrations when other variables are held constant. We show this phenomenon is related to the slower ion cluster relaxation rate at low concentrations rather than the static spatial state of ion aggregation or the fraction of free ions.