Dutch book against some `objective' priors

Abstract

`Dutch book' and `strong inconsistency' are generally equivalent: there is a system of bets that makes money for the gambler, whatever the state of nature may be. As de Finetti showed, an odds-maker who is not a Bayesian is subject to a Dutch book, under certain highly stylized rules of play - a fact often used as an argument against frequentists. However, so-called `objective' or `uninformative' priors may also be subject to a Dutch book. This note explains, in a relatively simple and self-contained way, how to make Dutch book against a frequently recommended uninformative prior for covariance matrices.