The Dutch Book Argument

This book is under contract with Cambridge University Press to appear in their series Cambridge Elements in Decision Theory and Philosophy (edited by Martin Peterson). It should appear in December 2019.


Here’s the current overview:

Our beliefs come in degrees. I’m 70% confident that it will rain tomorrow, and 0.001% sure that my lottery ticket will win. What’s more, we think that these degrees of belief should abide by certain principles if they are to be rational. You shouldn’t believe that a person’s taller than 6ft more strongly than you believe that they’re taller than 5ft, since the former entails the latter. You shouldn’t be very confident that a coin is fair, whilst also being very confident that it will land heads when it’s next tossed. We use these degrees of belief when we decide what we should do. When I decide whether or not to take my umbrella when I go outside, I need to decide how much I dislike getting wet, how much I dislike being encumbered by an umbrella, and so on. But I also need to decide how likely I think it is that it will rain. So I appeal not just to the strengths of my desires and tastes and values concerning the outcomes of my actions, but also the strengths of my beliefs about the world. In Dutch Book arguments, we try to establish the principles of rationality for degrees of belief by appealing to their role in guiding decisions. In particular, we show that degrees of belief that don’t satisfy the principles will always guide action in some way that is bad or undesirable. In Part I of this book, we will formulate, critique, and reformulate the Dutch Book argument for Probabilism, offered first by Frank P. Ramsey and Bruno de Finetti. In Part II, we will consider Dutch Book arguments for other principles of rationality, such as Bayesian Conditionalization and the Reflection Principle, Jeffrey’s Probability Kinematics, the Principal Principle, the Principle of Indifference, and principles of group judgment aggregation. In Part III, we will consider how the Dutch Book arguments might be applied in different settings, such as in the imprecise credences framework and in the presence of non-classical logic.


As I immerse myself in the literature and start writing the book, I’ll be putting down some thoughts in blogposts at M-Phi. Here they are so far: