A class of random utility models yielding the exploded logit

Abstract

We reexamine a family of distributions introduced within the framework of random utility models by David Strauss. This family generates ranking probabilities of the exploded logit model and, de facto, the choice probabilities of the multinomial logit model. We explore the necessary and sufficient conditions for its validity within the copula theory. By specifying the minimal assumptions required for the support of the marginal utility distributions, we clarify and reinforce the fundamental structure of the model, proving that it relies on strict archimedean copulas. Additionally, we provide a new mathematical proof by induction on the number of alternatives confirming that these utility distributions indeed generate the exploded logit model.