Dutch book theorem the proposition that anyone who (a) counts a bet on a proposition p as fair if the odds correspond to his degree of belief that p is true and who (b) is willing to make any combination of bets he would regard individually as fair will be vulnerable to a Dutch book provided his degrees of belief do not conform to the axioms of the probability calculus. Thus, anyone of whom (a) and (b) are true and whose degree of belief in a disjunction of two incompatible propositions is not equal to the sum of his degrees of belief in the two propositions taken individually would be vulnerable to a Dutch book. R.Ke.