Before revision:  This is confirmed by our data-driven theoretical results which show that random forests can predict the choice probability of any discrete choice model consistently , with its splitting criterion capable of recovering preference rank lists .
After revision:  This is confirmed by our data-driven theoretical results which show that random forests can predict the choice probability of any discrete choice model consistently . Moreover, our algorithm predicts unseen assortments with mechanisms and errors that can be theoretically analyzed. We also prove that the splitting criterion in random forests, the Gini index, is capable of recovering preference rank lists .