Levi on money pumps and diachronic dutch books

In Erik J. Olsson (ed.), Knowledge and Inquiry: Essays on the Pragmatism of Isaac Levi. Cambridge University Press (2006)
Abstract
The paper's focus is on pragmatic arguments for various ‘rationality constraints’ on a decision maker’s state of mind: on his beliefs or preferences. An argument of this kind purports to show that a violator of a given constraint can be exposed to a decision problem in which he will act to his guaranteed disadvantage. Dramatically put, he can be exploited by a clever bookie who doesn’t know more than the agent himself. Examples of pragmatic arguments of this kind are synchronic Dutch Books, for the standard probability axioms, diachronic Dutch Books, for the more controversial principles of reflection and conditionalization, and Money Pumps, for the transitivity requirement on preferences. The proposed exploitation set-ups share a common feature. If the violator of a given constraint is logically and mathematically competent, he can be exploited only if he is disunified in his decision-making. Exploitation is possible only if the agent makes decisions on various issues he confronts one by one, rather than on all of them together. Unity in decision making may be quite costly and is often inconvenient, especially when it concerns opportunity packages that are spread over time. Therefore, pragmatic arguments should be seen as delivering conditional conclusions: “To afford being disunified as a decision maker, you’d better satisfy these constraints.” Arguments of this kind fail to establish the inherent rationality of the constraints under consideration. Levi’s view of the status of pragmatic arguments (cf. Levi 2002) is diametrally opposed. According to him, only synchronic pragmatic arguments are valid (indeed, categorically valid). The diachronic ones, he argues, lack any validity at all. This line of reasoning is questioned in the paper.
Keywords pragmatic arguments  dutch books  money pumps  dynamic inconsistency  unified choice  Levi, Isaac
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