Weighing the importance of different pieces of information is a key determinant of making accurate judgments. In social judgment theory, these weighting processes have been successfully described with linear models. How people learn to make judgments has received less attention. Although the hitherto proposed delta learning rule can perfectly learn to solve linear problems, reanalyzing a previous experiment showed that it does not adequately describe human learning. To provide a more accurate description of learning processes we amended the delta learning rule with three learning mechanisms—a decay, an attentional learning mechanism, and a capacity limitation. An additional study tested the different learning mechanisms in predicting learning in linear judgment tasks. In this study, participants first learned to predict a continuous criterion based on four cues. To test the three learning mechanisms rigorously against each other, we changed the importance of the cues after 200 trials so that the mechanisms make different predictions with regard to how fast people adapt to the new environment. On average, judgment accuracy improved from Trial 1 to Trial 200, dropped when the task environment changed, but improved again until the end of the task. The capacity-restricted learning model, restricting how much people update the cue weights on a single trial, best described and predicted the learning curve of the majority of participants. Taken together, these results suggest that considering cognitive constraints within learning models may help to understand how humans learn when making inferences.