Conditioning experiments probe the ways that animals make predictions about rewards and punishments and use those predictions to control their behavior. One standard model of conditioning paradigms which involve many conditioned stimuli suggests that individual predictions should be added together. Various key results show that this model fails in some circumstances, and motivate an alternative model, in which there is attentional selection between different available stimuli. The new model is a form of mixture of experts, has a close relationship with some other existing psychological suggestions, and is statistically well-founded.