The theoretical literature on (non-random) choice largely follows the route of Richter (1966) by working in abstract environments and by stipulating that we see all choices of an agent from a given feasible set. On the other hand, empirical work on consumption choice using revealed preference analysis is done following the approach of Afriat (1967), which assumes that we observe only one (and not necessarily all) of the potential choices of an agent. These two approaches are structurally different and they are treated in the literature in isolation from each other. This paper introduces a framework in which both
approaches can be formulated in tandem. We prove a rationalizability theorem in this framework that simultaneously generalizes the fundamental results of Afriat and Richter,
along with many of their variants.