Abstract
A decision maker chooses alternatives from menus by proceeding sequentially through a checklist of properties. In contrast to the standard framework her ranking of properties is not necessarily complete. We characterize the model in terms of observed choices. As another main result of the paper we show that an important special case of our model is exactly equivalent to the maximization of an incomplete preference relation. We also relate the model to the choice model resulting from the maximization of a multi-utility (also called multi-criteria) function. Our results suggest a close relationship between the degree of completeness of the order by which properties in a checklist are looked at, and the degree of completeness of the revealed preference relation maximizing the corresponding choice function.