Rational expectation of mistakes and a measure of error-proneness

We characterize axiomatically a stochastic choice model, the consistent-mistakes model (CMM), that describes an error-prone decision maker's choices. In contrast to random utility models, CMMs generate closed-form choice probability. Under the axioms, we uniquely identify from the choices an expected utility function that represents the decision maker's true preference and a propensity function that describes how likely an alternative is to be chosen. We introduce a measure of error-proneness and show that the logit model of mistakes is a CMM with a constant measure of error-proneness, characterized by a strong version of the independence axiom from expected utility theory. We analyze the properties of models of mistakes.