  The random utility model is known to be unidentified, but there are times
when the model admits a unique representation. We offer two characterizations
for the existence of a unique random utility representation. Our first
characterization puts conditions on a graphical representation of the data set.
Non-uniqueness arises when multiple inflows can be assigned to multiple
outflows on this graph. Our second characterization provides a direct test for
uniqueness given a random utility representation. We also show that the support
of a random utility representation is identified if and only if the
representation itself is identified.
