 The traditional answer is that an agent that violates the axioms of probability opens herself up, in some sense, to a system of bets that guarantee a sure loss. Answers of this flavor are called Dutch Book arguments. The pragmatic version of the argument posits a tight connection between degrees of belief and betting behavior. The argument concludes by proving a theorem to the effect that an agent would enter into a system of bets guaranteeing a sure loss iff her degrees of belief violate the probability calculus. But, as we have seen, there are reasons to doubt that the connection between degrees of belief and betting behavior is really so tight as required by the pragmatic Dutch book argument. That renders the argument less convincing. The depragmatized version of the argument posits a connection between degrees of belief and dispositions to consider systems of bets fair, without necessarily entering into them (Armendt 1993 Christensen 1996, Ramsey 1926, Skyrms 1984). It concludes by proving an essentially identical theorem to the effect that an agent would consider fair a system of bets guaranteeing a sure loss iff her degrees of belief violate the probability calculus. The depragmatized Dutch Book Argument is a more promising justification for probabilism. See, however, Hájek (2005; 2008). For a much more extensive discussion see the entry on  Dutch book arguments.  