Measuring Stochastic Rationality

We develop a partial ordering approach toward comparing stochastic choice functions on the basis of their rationality. We do this by assigning to any stochastic choice function a one-parameter class of deterministic choice correspondences, and then checking for the rationality (in the standard sense of revealed preference) of these correspondences for each parameter value. Similar to the classical notion of deterministic rationality, our rationality ordering detects violations of (stochastic) transitivity as well as inconsistencies between choices from nested menus. We obtain an easy-to-use characterization of this ordering, and then use that characterization to introduce an index of stochastic rationality. We apply our ordering and index to some well-known stochastic choice models and provide an empirical application using a famous experiment by Amos Tversky.