Approximate Utility Under Perceptual Restrictions

If agents have perceptual limits, and cannot distinguish objects that are sufficiently similar, then immediate problems arise with this notion of rationality. For example, Mas-Colell, Whinston, and Green (1995) provide an example of an agent with limited visual perception, who cannot distinguish a white object from a gray one. Because preferences are assumed to be complete, and because the two objects look the same to the agent, the natural assumption is that the agent must be indifferent between the two alternatives. If the gray object in turn is compared to an otherwise identical black object, the agent may again be incapable of distinguishing the two alternatives. If indifference is transitive, this means that the agent must be indifferent between the black and the white objects, even if the two do not look alike to the agent. That is, complete and transitive preferences make agents with perceptual limits indifferent to everything.1