Content deleted Content added
Line 17:
=== Uniqueness ===
Block and [[Jacob Marschak|Marschak]]<ref name=":1" /> proved that, when there are at most 3 alternatives, the random utility model is unique ("identified"); however, when there are 4 or more alternatives, the model may be non-unique.<ref name=":3" /> For example,<ref>{{cite conference |title=Stochastic Choice |first1=Tomasz |last1=Strzalecki
|conference=Hotelling Lectures in Economic Theory, Econometric Society European Meeting |___location=Lisbon |date=25 August 2017 |url=https://scholar.harvard.edu/files/tomasz/files/lisbon32-post.pdf }}{{pn}}</ref> we can compute the probability that the agent prefers w to x (w>x), and the probability that y>z, but may not be able to know the probability that both w>x and y>z. There are even distributions with disjoint supports, which induce the same set of choice probabilities.
Some conditions for uniqueness were given by [[Jean-Claude Falmagne|Falmagne]].<ref name=":2" /> Turansick<ref name=":0">{{cite journal |last1=Turansick |first1=Christopher |title=Identification in the random utility model |journal=Journal of Economic Theory |date=July 2022 |volume=203 |pages=105489 |doi=10.1016/j.jet.2022.105489 |arxiv=2102.05570 }}</ref> presents two characterizations for the existence of a unique random utility representation.
| |||