Efficient coding makes and breaks Weber's law

Weber's law is a rare quantitative regularity in psychology, yet its origins remain debated. Here we provide causal evidence that it arises from the more fundamental principle of efficient coding. This principle posits that representational resources are allocated according to stimulus frequencies: distributions skewed toward smaller stimuli thus result in discriminability decreasing with magnitude, as in Weber's law. Skewing frequencies in the other direction---making large magnitudes more frequent than small ones---enabled us to invert this pattern, and to break Weber's law. In discrimination tasks with three different sensory modalities, human subjects' discriminability across stimuli was sensitive to the stimulus distribution, and this adaptation improved task performance. These findings establish efficient coding as a dynamic, organizing principle, explaining when and why Weber's law holds.