REFLECTING ON DIACHRONIC DUTCH BOOKS

Conditionalization governs how to reallocate credence in light of new evidence. One prominent argument in favor of Conditionalization holds that an agent who violates it is vulnerable to a diachronic Dutch book: a series of acceptable bets offered at multiple times that inflict a sure loss. van Fraassen argues that an agent who violates the Principle of Reflection is likewise vulnerable to a diachronic Dutch book. He concludes that agents should conform to both Conditionalization and Reflection. Some authors reply that Reflection is implausible and hence that there must be something wrong with diachronic Dutch book arguments. Other authors try to isolate a principled difference between the Dutch book argument for Conditionalization and the Dutch book argument for Reflection, such that the former argument may succeed even though the latter fails. I pursue a version of this strategy. I contend that, once we properly elucidate the notion of sure loss, non-reflectors are not vulnerable to a sure loss. An agent who violates Reflection is not thereby subject to a diachronic Dutch book. Appearances to the contrary result from an unmotivated focus upon an overly narrow set of gambling scenarios. §1. Conditionalization and Reflection