Dutch Book against some "Objective" Priors
"Dutch book," "incoherence," and "strong inconsistency" are generally equivalent: there is a system of bets which is expected to make money for the gambler, whatever the state of nature may be. As de Finetti showed, a bookie 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. 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.