A Boolean structural model is proposed to represent individual judgments of subjects about the admissibility of choice options. The model includes a set of latent criteria. Each judge is assumed to use an individual subset of these criteria and to select those and only those options that meet all criteria of this subset. The model is illustrated with an analysis of student housing data. The discussion highlights distinctive features of the latent criteria model, and considers more in general the strengths, limitations and validity of the Boolean structural modelling approach to decision making.