Continuity and Monotonicity of Preferences and Probabilistic Equivalence

TL;DR

This paper demonstrates that a weak form of continuity and monotonicity in preferences over random variables ensures probabilistic equivalence in regret-based preference models.

Contribution

It establishes a theoretical link between continuity, monotonicity, and probabilistic equivalence in preference relations.

Findings

Probabilistic equivalence follows from weak continuity and monotonicity.

Provides a theoretical foundation for regret-based preference models.

Highlights conditions under which preferences are probabilistically equivalent.

Abstract

We show that probabilistic equivalence of a regret-based preference relationship over random variables is implied by a weak form of continuity and monotonicity.