Identification in the Random Utility Model

The random utility model is known to be unidentified. However, there are times when a data set is uniquely rationalizable by the random utility model. We ask the question for which data sets does the random utility model have a unique representation. Our first result characterizes which data sets admit a unique representation. Our second result provides a finite test which determines if a distribution of preferences is observationally equivalent to some other distribution of preferences. We then explore the implications of our results in the context of other random utility models.