In unidimensional absolute identification tasks, participants identify stimuli that vary along a single dimension. Performance is surprisingly poor compared to discrimination of the same stimuli. Existing models assume that identification is achieved using long-term representations of absolute magnitudes. We propose an alternative relative judgment model (RJM) in which the elemental perceptual units are representations of the differences between current and previous stimuli. These differences are used, together with the previous feedback, to respond. Without using long-term representations of absolute magnitudes, the RJM accounts for (a) information transmission limits, (b) bowed serial position effects, and (c) sequential effects, where responses are biased towards immediately preceding stimuli but away from more distant stimuli (assimilation and contrast).