Reflecting on diachronic Dutch books

Abstract

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.

Reflection and conditionalization: Comments on Michael Rescorla

“…With examples from a previous debate in the 70s and results about Reflection and Conditionalization in the 80s, I propose a way of seeing the epistemic enterprise in the light of practical requirements to be met by demands for synchronic coherence and probability updating policies. This includes a defense of principles rejected by Rescorla, while allowing for the value of his results in the borderland between theories of cognition and formal epistemology.Rescorla is entirely right that the original Dutch Book argument for Reflection assumed knowledge on the bookie's side, equal to the bettor's relevant knowledge (Rescorla, 2023). It is fascinating to see this exploration of possible updating policies when that assumption is not made, that is, if what is counted as relevant is a thus widened set of gambling scenarios.…”

“…Rescorla is entirely right that the original Dutch Book argument for Reflection assumed knowledge on the bookie's side, equal to the bettor's relevant knowledge (Rescorla, 2023). It is fascinating to see this exploration of possible updating policies when that assumption is not made, that is, if what is counted as relevant is a thus widened set of gambling scenarios.…”