Dutch book

Abstract: A central part of Bayesianism is the doctrine that the decision maker's knowledge in a given situation can be represented by a subjective probability measure defined over the possible states of the world. This measure can be used to determine the expected utility for the agent of the various alternatives open to him. The basic decision rule is then that the alternative which has the maximal expected utility should be chosen. A fundamental assumption for this strict form of Bayesianism is that the decision maker's knowledge can be represented by a unique probability measure. The adherents of this assumption have produced a variety of arguments in favor of it, the most famous being the so-called Dutch book arguments. A consequence of the assumption, in connection with the rule of maximizing expected utility, is that in two decision situations which are identical with respect to the probabilities assigned to the relevant states and the utilities of the various outcomes the decisions should be the same. It seems to us, however, that it is possible to find decision situations which are identical in all the respects relevant to the strict Bayesian, but which nevertheless motivate different decisions. As an example to illustrate this point, consider Miss Julie who is invited to bet on the outcome of three different tennis matches. 1 As regards match A, she is very well-informed about the two players - she knows everything about the results of their earlier matches, she has watched them play several times, she is familiar with their present physical condition and the setting of the match, etc. Given all this information, Miss lulie predicts that it will be a very even match and that a mere chance will determine the winner. In match B, she knows nothing whatsoever about the relative strength of the contestants (she has not even heard their names before) and she has no other information that

Abstract: Since the 1930s, "Dutch Book" arguments have been used to support the view that one's degrees of belief should conform to the probability calculus. These arguments show that if an agent's degrees of belief violate the probability calculus, then a clever bookie, knowing nothing beyond what the agent's degrees of belief are, can offer the agent a set of bets with the following two properties: (1) each of the bets in the set will be fair, given the agent's degrees of belief; and (2) the set of bets taken together guarantees that the agent will end up losing money overall. Such a set of bets is called a "Dutch Book." Clearly, there is something unattractive about a belief state which leaves one open to this sort of exploitation.1 Closely related arguments have also been given in support of further conditions on rational degrees of belief, conditions which go well beyond probabilistic consistency. Some of these arguments support popular "Conditionalization" principles, which describe the way an agent's degrees of belief should change when she is confronted with new evidence. (The probability calculus itself provides no guidance in such matters, so Conditionalization principles fill an important gap in probabilistic accounts of rationality.)2 Sim-

Abstract: Four important arguments for probabilism—the Dutch Book, representation theorem, calibration, and gradational accuracy arguments—have a strikingly similar structure. Each begins with a math...

Abstract: Bayesians have traditionally taken a dim view of the Inference to the Best Explanation (IBE), arguing that, if IBE is at variance with Bayes' rule, then it runs afoul of the dynamic Dutch book argument. More recently, Bayes' rule has been claimed to be superior on grounds of conduciveness to our epistemic goal. The present paper aims to show that neither of these arguments succeeds in undermining IBE.