When is coarseness not a curse? Comparative statics of the coarse random utility model

In a variety of choice environments, perception is both noisy and coarse. That is, the agent perceives the true ranking of the objects of choice with error; and, in addition, the perceived values can only be discriminated coarsely. Reasons for coarse perception include limitations in sensory perception, memory function, or the communication technology used by expert advisors.
We model these two sources of error in terms of a random utility model with a discrimination threshold. In the limiting case when values are perceived without noise, finer perception is unambiguously beneficial. We show how this ceases to be true when values are perceived with noise. As a practical implication, our results establish conditions where it is counter-productive for an expert to use a finer communication scheme with a decision-maker.