We introduce a rational choice theory that allows for many forms of imperfect perception, including failures of memory, selective attention, and adherence to simplifying rules of thumb. Despite its generality, the theory has strong, simple, and intuitive implications for standard choice data and for more enriched choice data. The central assumption is rational expectations: decision makers understand the relationship between their perceptions, however limited they may be, and the (stochastic) consequences of their available choices. Our theory separately identifies two distinct “framing" effects: standard effects involving the layout of the prizes (e.g. order in a list) and novel effects relating to the information content of the environment (e.g. how likely is the first in the list to be the best). Simple experimental tests both affirm the basic model and confirm the existence of information-based framing effects.