We introduce a flexible framework to study probabilistic choice that accommodates heterogeneous types and bounded rationality. We provide a novel progressive structure for the heterogeneous types to capture heterogeneity due to varying levels of a behavioral trait. Given an order of alternatives, our progressive structure sorts the types by the extent to which they align with this order. Unlike the random-utility model, our model uniquely identifies the heterogeneity, allowing policy makers to perform an improved welfare analysis. As a showcase, we provide characterization of a well-studied type of bounded rationality: “less-is-more.” In addition, we provide conditions for unique identification of the underlying order for the less-is-more structure.

This paper illustrates how one can deduce preference from observed choices when attention is both limited and random. We introduce a random attention model where we abstain from any particular attention formation and instead consider a large class of nonparametric random attention rules. Our intuitive condition, monotonic attention, captures the idea that each consideration set competes for the decision maker’s attention. We then develop a revealed preference theory and obtain testable implications. We propose econometric methods for identification, estimation, and inference for the revealed preferences. Finally, we provide a general-purpose software implementation of our estimation and inference results and simulation evidence.