Congruence relations on a choice space

A choice space is a finite set of alternatives endowed with a map associating to each menu a nonempty subset of selected items. A congruence on a choice space is an equivalence relation that preserves its structure. Intuitively, two alternatives are congruent if the agent is indifferent between them, and, in addition, her choice is influenced by them in exactly the same way. We give an axiomatic characterization of the notion of congruence in...