A method of scaling is proposed to estimate the positions of candidates and voters on a common issue dimension. The scaling model assumes that candidates occupy true positions in an issue space and that individual level perceptual data arise from this in a two step process. The first step consists of a stochastic component, satisfying the standard Gauss Markov assumptions, which reflects true misperception. The second step consists of a linear distortion which is introduced in the survey situation. Estimates of the parameters of the model are developed by applying the least squares criterion, and distributions of the estimates are investigated by Monte Carlo methods.The scaling technique is applied to the seven-point issue scales asked in the 1968 and 1972 SRC survey. The resulting ideal point estimates are related to candidate positions in 1968 to test a simple Downsian voting model.