Objectifying subjective probabilities: Dutch book arguments for principles of direct inference

Abstract

A Principle of Direct Inference licenses an inference from the frequency of the occurrence of attributes in a population to the probability of particular occurrence of 8 an attribute in a sample. From a Bayesian point of view, such a Principle requires 9 that if we have knowledge of the relative frequency of an attribute in a population, our degree of belief in the occurrence of that attribute in the population be 11 equal to this frequency (or that this knowledge should somehow constrain our de- 12 grees of belief about the occurrence in a sample).1 This might seem so painfully 13 self-evident as to not need any justification. However, Bayesian justifications for 14 constraining degrees of belief are usually based on Dutch Book arguments, and in- 15 deed several such arguments for Principles of Direct inference have been offered. 16 I will discuss three, and find them wanting. Subjective probabilities therefore re- 17 main subjective even when conditioned on knowledge of objective probabilities.