Separable joint choices

We introduce a novel choice dataset, called joint choice, in which options and menus are multidimensional. In this general setting, we define a notion of choice separability, which requires that selections from some dimensions are never affected by those performed on the remaining dimensions. This generalizes the classical definition of separability for discrete preference relations and utility functions, to encompass a class of choice behaviors that may lack a preference or utility representation. We thoroughly investigate the stability of separability across dimensions, and then suggest effective tests to check whether a joint choice is separable. Upon defining rationalizable joint choices as those explained by the maximization of a relation of revealed preference, we examine the interplay between the notions of rationalizability and separability. Finally, we show that the rationalizability of a separable joint choice can be tested by verifying the rationalizability of some derived joint choices over fewer dimensions.