Before revision: In multinomial choice settings with additive heterogeneity, Daly-Zachary (1978) and Armstrong-Vickers (2015) provided closed-form conditions, under which choice probability functions can be rationalized via random utility models . A key condition is Slutsky symmetry. We first show that in the multinomial context, Daly-Zachary's Slutsky symmetry is equivalent to absence of income-effects.
After revision: In multinomial choice settings with additive heterogeneity, Daly-Zachary (1978) and Armstrong-Vickers (2015) provided closed-form conditions, under which choice probability functions can be rationalized via random-utility models with nonparametric heterogeneity and general income-effects.