Dutch book in simple multivariate normal prediction: Another look

TL;DR

This paper presents an elementary method to demonstrate the existence of a Dutch book in multivariate normal prediction by deriving a special predictive distribution based on invariance principles.

Contribution

It introduces a novel, simple approach to establish Dutch book existence using a nonstandard predictive distribution motivated by invariance.

Findings

Demonstrates the existence of Dutch books in multivariate normal prediction

Introduces a new predictive distribution satisfying an important identity

Provides an elementary proof method for Dutch book existence

Abstract

In this expository paper we describe a relatively elementary method of establishing the existence of a Dutch book in a simple multivariate normal prediction setting. The method involves deriving a nonstandard predictive distribution that is motivated by invariance. This predictive distribution satisfies an interesting identity which in turn yields an elementary demonstration of the existence of a Dutch book for a variety of possible predictive distributions.