Dutch books, dutch strategies and what they show about rationality

Abstract

Bayesians typically appeal to the so-called Dutch Book argument to justify their claim that a rational agent’s degrees of belief must obey the axioms of probability. The argument has also been extended in support of two other Bayesian principles: the rule of conditionalization, which states that when the evidence E is learned the new probability (degree of belief ) for the proposition A should be equal to the old probability of A given E, and the principle of reflection which states that an agent’s current subjective probability for A, conditional on the supposition that she will later attach a probability to A equal to r, must equal r. 2 Considerable attention has been focused on the structure of the basic argument to show that degrees of belief must satisfy the probability axioms and on whether it established this claim. Recently, a number of authors have suggested that what the basic argument really shows is that degrees of belief which fail to satisfy the axioms suffer from a form of inconsistency and because of this are defective. In his paper, “Clever Bookies and Coherent Beliefs”, David Christensen not only endorses this view, but further argues that on this reading of the basic Dutch Book argument, it follows that the argument cannot adequately be extended to justify belief change by conditionalization nor to justify the principle of reflection. 3 In this paper, I argue that Christensen’s criticisms of the Dutch Book arguments for conditionalization and reflection are unsatisfactory. Nevertheless, I agree that the arguments do not show that an agent who violates these principles must be irrational. In the final section of the paper, I suggest that the Dutch Book arguments for conditionalization and reflection do lend support for these principles as ideals of certain sorts, although they do not show that they are requirements of rationality.