We argue that in many circumstances, human observers evaluate sensory evidence simultaneously under multiple hypotheses regarding the physical process that has generated the sensory information. In such situations, inference can be optimal if an observer combines the evaluation results under each hypothesis according to the probability that the associated hypothesis is correct. However, a number of experimental results reveal suboptimal behavior and may be explained by assuming that once an observer has committed to a particular hypothesis, subsequent evaluation is based on that hypothesis alone. That is, observers sacrifice optimality in order to ensure self-consistency. We formulate this behavior using a conditional Bayesian observer model, and demonstrate that it can account for psychophysical data from a recently reported perceptual experiment in which strong biases in perceptual estimates arise as a consequence of a preceding decision. Not only does the model provide quantitative predictions of subjective responses in variants of the original experiment, but it also appears to be consistent with human responses to cognitive dissonance.