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 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 a 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.