We model the choice behaviour of an agent who suffers from imperfect attention but is otherwise von Neumann Morgenstern rational. We define inattention axiomatically through preference over menus and endowed alternatives: an agent is inattentive if it is better to be endowed with an alternative a than to be allowed to pick a from a menu in which a is is the best alternative. This property and vNM rationality on the domain of menus and alternatives imply that the agent notices each alternative with a given menu-dependent probability (attention parameter) and maximises a menu independent utility function over the alternatives he notices. Preference for flexibility restricts the model to menu independent attention parameters as in Manzini and Mariotti [17]. Our theory explains anomalies (e.g. the attraction effect) that other prominent stochastic choice theories cannot accommodate.
