Limited consideration model with a trigger or a capacity

When making a choice from a menu, individuals sometimes consider only a subset of the menu and choose one alternative according to their preferences from the subset. We provide a unified model that formalizes two aspects of such consider-then-choose procedures: the circumstances under which individuals have limited consideration and the structures that are imposed on consideration sets in the presence of limited consideration. Full consideration is guaranteed when the size of a menu does not exceed a cutoff number. Limited consideration may occur or must occur when the size of a menu exceeds the cutoff number, which is correspondingly interpreted as the trigger of initiating limited consideration or the capacity of full consideration. We also assume that the consideration function from a menu to its consideration set satisfies an intuitive property that captures a range of real-world heuristics to form consideration sets. We provide a characterization of the model.