The Dutch Book Argument

This book is now out with Cambridge University Press. It appears in their series Cambridge Elements in Decision Theory and Philosophy, which is edited by Martin Peterson. It was published in July 2020. Here is the CUP webpage for the book.

Draft of the book

Here is the current draft of the book PDF.


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 Chapters 1-3, we formulate, critique, and reformulate the Dutch Book arguments for Probabilism, Countable Additivity, Regularity, and the Principal Principle. Our critique of the argument for Countable Additivity leads us to abandon it. In Chapter 4, we investigate the Dutch Strategy arguments for Bayesian Conditionalization and the Reflection Principle. In Chapters 5 and 6, we raise objections to our formulations of the arguments. And in Chapter 7 we generalize those arguments by lifting certain assumptions we’ve been making so far. Chapter 8 presents the mathematical results that underpin these arguments.


As I immersed myself in the literature and started to write the book, I put down some thoughts in blogposts at M-Phi. Here they are so far:

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