The seismic risk assessment of a structure in performance-based design (PBD) may be significantly affected by the representation of ground motion uncertainty. In PBD, the uncertainty in the ground motion is often represented by a probabilistic description of a scalar parameter, or low-dimensional vector of parameters, known as the intensity measure (IM), rather than a full probabilistic description of the ground motion time history in terms of a stochastic model. In this work, a new procedure employing what we call a relative sufficiency measure is introduced based on information theory concepts in order to quantify the suitability of one IM relative to another in representing ground motion uncertainty. Based on this relative sufficiency measure, several alternative scalar- and vector-valued IMs are compared in terms of the expected difference in information they provide about a predicted structural response parameter, namely, the seismically-induced drift in an existing reinforced-concrete frame structure.