Mixed models,random utilities,and the triangle inequality

A new probabilistic binary choice model, which we call the mixed model is proposed. This model is used to give an interpretation of probabilistic choice behavior in terms of complete and partial orders. The model is used as a guide to disprove Jacob Marschak's conjecture that the binary random utility model is equivalent to the triangle inequality. Another result is presented concerning the relation between moderate stochastic transitivity and the triangle inequality.