Ordered Surprises and Conditional Probability Systems

TL;DR

This paper introduces the Ordered Surprises (OS) model, a complete belief updating framework that handles conditioning on null events, and clarifies its relationship with existing belief systems like Conditional Probability Systems.

Contribution

It characterizes the OS representation of beliefs, showing its equivalence to Conditional Probability Systems and its behaviorally consistent updating rule for null events.

Findings

OS provides well-defined conditional beliefs for any event.

OS is behaviorally equivalent to Conditional Probability Systems.

OS extends Bayesian updating to null events.

Abstract

We study conditioning on null events, or surprises, and behaviorally characterize the Ordered Surprises (OS) representation of beliefs. For feasible events, our Decision Maker (DM) is Bayesian. For null events, our DM considers a hierarchy of beliefs until one is consistent with the surprise. The DM adopts this prior and applies Bayes' rule. Unlike Bayesian updating, OS is a complete updating rule: conditional beliefs are well-defined for any event. OS is (behaviorally) equivalent to the Conditional Probability System (Myerson, 1986b) and is a special case of Hypothesis Testing (Ortoleva, 2012), clarifying the relationships between the various approaches to null events.