Counterexamples to "Transitive Regret"

TL;DR

This paper presents counterexamples to a key proposition in regret-based preference theory, challenging the assumption that transitivity and continuity imply equivalence of random variables with the same distribution.

Contribution

It provides counterexamples to a previously claimed equivalence between transitive regret-based preferences and expected utility, clarifying limitations of the theory.

Findings

Counterexamples to Proposition 1 in Bikhchandani & Segal (2011)

Transitivity and continuity do not imply equivalence of distributions in regret preferences

Challenges the characterization of regret-based preferences as expected utility

Abstract

Theorem 1 in Bikhchandani & Segal (2011; Theoretical Economics) suggests that a complete, transitive, monotonic, and continuous preference is regret based if and only if it is expected utility. Their Proposition 1 suggests that transitivity and continuity of a regret-based preference implies an equivalence condition: if random variables $X$ and $Y$ have the same distribution, then $X\sim Y$. We give counterexamples to Proposition 1.