Stochastic choice and consideration sets

We model a boundedly rational agent who suffers from limited attention. The agent considers each feasible alternative with a given (unobservable) probability, the attention parameter, and then chooses the alternative that maximises a preference relation within the set of considered alternatives. Both the preference and the attention parameters are identified uniquely by stochastic choice data. The model is the only one for which the impact of removing any alternative a on the choice probability of any other alternative b is non-negative, asymmetric (either a impacts b or vice-versa), menu independent, neutral (the same on any alternative in the menu), and consistent with the impacts on a and b by a common third alternative.