The Limits of Identification in Discrete Choice

TL;DR

This paper establishes tight bounds on the number of preferences allowed in identified random utility models, showing that as the number of choices grows, the admissible preferences diminish rapidly, and introduces a weaker sufficient condition for identification.

Contribution

It provides a new, weaker sufficient condition for identification in discrete choice models, extending the understanding of when preferences can be uniquely determined.

Findings

Admissible preferences decrease rapidly with more alternatives.

A new sufficient condition for identification is proposed.

The Latin Square example is shown to be identified using the new condition.

Abstract

This paper uncovers tight bounds on the number of preferences permissible in identified random utility models. We show that as the number of alternatives in a discrete choice model becomes large, the fraction of preferences admissible in an identified model rapidly tends to zero. We propose a novel sufficient condition ensuring identification, which is strictly weaker than some of those existing in the literature. While this sufficient condition reaches our upper bound, an example demonstrates that this condition is not necessary for identification. Using our new condition, we show that the classic ``Latin Square" example from social choice theory is identified from stochastic choice data.