 A Dutch Book argument can be constructed for the principle by extending the Dutch Book for finite additivity (Adams 1962; Jeffrey 2004; Williamson 1999) by appealing to an infinite set of bets that each pay $1 if \(W_i\) is true for the price \(\pr(W_i)\). In the case of the Dutch Book argument for countable additivity, there is an additional reason beyond those for the basic argument to favor the interpretation of it, as Jeffrey does, as establishing the principle as a consistency constraint, since the loss is purely theoretical. There is no threat of an actual loss to an agent since this would require an infinite series of bets, which cannot all be made and settled. However, the principle itself is controversial, making the Dutch Book argument for countable additivity highly provocative. Both de Finetti (1972) and Savage (1954) argued that the principle should not be invoked as a constraint on rational degrees of belief.  A consequence of the principle is that it prohibits positive credences that are uniformly distributed over a countably infinite partition, and yet it seems at least acceptable, in the absence of a reason to favor some possibilities over others, to adopt such a distribution. Intuitively, a uniform distribution ought to count as consistent, which puts pressure on the idea, at least when it comes to countable additivity, that Dutch Books reveal a defect that is substantially analogous to inconsistency. In the background, as with the basic argument, the Dutch Book argument for countable additivity makes significant assumptions about how degrees of belief are linked with preference and assessments of value. For details concerning how these relate to the demand that an agent’s degrees of belief satisfy countable additivity, see (Seidenfeld and Schervish 1983).  For a recent critical discussion of the argument, see Pettigrew (2020).