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.