We provide a full behavioral characterization of the standard Shannon model of rational inattention. The key axiom is "Invariance under Compression", which identifies this model as capturing an ideal form of attention-constrained choice. We introduce tractable generalizations that allow for many of the known behavioral violations from this ideal, including asymmetries and complementarities in learning, context effects, and low responsiveness to incentives. We provide an even more general method of recovering attention costs from behavioral data. The data set in which we characterize all behavioral patterns is "state dependent" stochastic choice data.
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