Dutch book

A set of beliefs held with various degrees of confidence is open to a Dutch book if, were a subject forced to bet in accordance with these degrees of confidence, he could be made to lose whatever happens. For example, if I am confident that p but also confident that not-p, then in acting out that confidence I should accept a small stake from you in return for a large payout if not-p, thereby acting out my confidence that p, and similarly accept a small stake in return for a large payout if p, acting out my confidence that not-p . I then lose whatever happens. A semi-Dutch book is sometimes defined as a combination of bets where the subject may lose, but cannot win. For personalists following de Finetti and Ramsey, avoiding a Dutch book is the key conception of coherence, on which the logic and mathematics of probability judgements depends. A problem in developing the approach has been that of extending the notion of coherence to dynamic situations, in which an adjustment to previous confidences must be made in the light of new evidence. See conditional probability.