A vibrant literature incorporates elements of bounded rationality into choice theory. We survey this work, discussing five central ways in which the literature has modeled departures from the rational choice procedure. We discuss the variety of purposes axiomatic choice characterizations serve for these positive theories, delve into experimental tests, synthesize the welfare debate, and assess important future directions.

We propose relaxing the first-order conditions in optimization to approximate rational consumer choice. We assess the magnitude of departures with a new, axiomatically founded measure that admits multiple interpretations. Standard inequality tests of rationality for any given reference class of preferences can be conveniently repurposed to measure goodness-of-fit with that class. Another advantage of our approach is that it is applicable in any context where the first-order approach is meaningful (e.g., convex budget sets arising from progressive taxation). We apply these ideas to shed new light on existing portfolio-choice data.