Revealed Stochastic Preference: A One-Paragraph Proof and Generalization

TL;DR

This paper provides a concise proof of the Revealed Stochastic Preference theorem and extends it to set-valued choices, requiring a new axiom for the latter case.

Contribution

It offers a simplified proof of the core theorem and generalizes the result to set-valued choices with a different axiom.

Findings

Simplified proof of the Revealed Stochastic Preference theorem.

Extension of the theorem to set-valued choice models.

Identification of a new axiom for set-valued choice rationalizability.

Abstract

McFadden and Richter (1991) and later McFadden (2005) show that the Axiom of Revealed Stochastic Preference characterizes rationalizability of choice probabilities through random utility models on finite universal choice spaces. This note proves the result in one short, elementary paragraph and extends it to set valued choice. The latter requires a different axiom than is reported in McFadden (2005).