In the context of choice with limited consideration, where the decision-maker may not pay attention to all available options, the consideration function of a decision maker is path-independent if her choice cannot be manipulated by the presentation of the choice set. This paper characterizes a model of choice with limited consideration with path independence, which is equivalent to a consideration function that satisfies both the attention filter and consideration filter properties from Masatlioglu et al. (2012) and Lleras et al. (2017), respectively. Despite the equivalence of path-independent consideration with the consideration structures from these two papers, we show that, to have a choice with limited consideration that is path-independent, satisfying both axioms on the choice function that characterize choice limited consideration with attention and consideration filters unilaterally (from Masatlioglu et al. (2012) and Lleras et al. (2017)) is necessary but not sufficient.
Choice Function-Based Two-Sided Markets: Stability, Lattice Property, Path Independence and Algorithms