Before revision:  Next, for general multinomial choice that allows for income-effects, we provide global shape restrictions on choice probability functions, which are shown to be sufficient for rationalizability. Finally, we outline nonparametric identification of preference distributions using these results .
After revision:  Next, for general multinomial choice that allows for income-effects, we provide global shape restrictions on choice probability functions, which are shown to be necessary and sufficient for the canonical Additive Random Utility Model (ARUM). The sufficiency-proof is constructive, and facilitates nonparametric identification of preference distributions using these results .