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Bounded rationality is a paradigmatic example. Early criticisms of rationality from people like Herbert Simon were broad ranging criticisms of the idea that people could even begin to behave in the way depicted by the standard utility-maximising model given that they had neither the information, the capacity to process that information, nor the ability to act upon it that would be required. Thus they would use rules of thumb, `satisfice' instead of `optimise', and and so forth.
`Imperfect information' in mainstream economics is another example: in a sense individuals have more information than under perfect information, since they know all the probabilities and possible states of the world instead of just one of the latter. And as I have previously argued, this point applies even to the name of macroeconomic models -- which claim to be Dynamic, Stochastic, General and Equilibrium, but are not really the first 3 in any meaningful sense. Critics would like to see their issue at the core of theories instead of bolted on at the end.
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