# Sami Petersen comments on Closed Limelike Curves’s Shortform

• I think it’ll be helpful to look at the object level. One argument says: if your beliefs aren’t probabilistic but you bet in a way that resembles expected utility, then you’re succeptible to sure loss. This forms an argument for probabilism.[1]

Another argument says: if your preferences don’t satisfy certain axioms but satisfy some other conditions, then there’s a sequence of choices that will leave you worse off than you started. This forms an agument for norms on preferences.

These are distinct.

These two different kinds of arguments have things in common. But they are not the same argument applied in different settings. They have different assumptions, and different conclusions. One is typically called a Dutch book argument; the other a money pump argument. The former is sometimes referred to as a special case of the latter.[2] But whatever our naming convensions, it’s a special case that doesn’t support the vNM axioms.

Here’s why this matters. You might read assumptions of the Dutch book theorem, and find them compelling. Then you read a article telling you that this implies the vNM axioms (or constitutes an argument for them). If you believe it, you’ve been duped.

1. ^

(More generally, Dutch books exist to support other Bayesian norms like conditionalisation.)

2. ^

This distinction is standard and blurring the lines leads to confusions. It’s unfortunate when dictionaries, references, or people make mistakes. More reliable would be a key book on money pumps (Gustafsson 2022) referring to a key book on Dutch books (Pettigrew 2020):

“There are also money-pump arguments for other requirements of rationality. Notably, there are money-pump arguments that rational credences satisfy the laws of probability. (See Ramsey 1931, p. 182.) These arguments are known as Dutch-book arguments. (See Lehman 1955, p. 251.) For an overview, see Pettigrew 2020.” [Footnote 9.]

• I mean, I think it would be totally reasonable for someone who is doing some decision theory or some epistemology work, to come up with new “dutch book arguments” supporting whatever axioms or assumptions they would come up with.

I think I am more compelled that there is a history here of calling money pump arguments that happen to relate to probabilism “dutch books”, but I don’t think there is really any clear definition that supports this. I agree that there exists the dutch book theorem, and that that one importantly relates to probabilism, but I’ve just had dozens of conversations with academics and philosophers and academics and decision-theorists, where in the context of both decision-theory and epistemology question, people brought up dutch books and money pumps interchangeably.

• I agree that there exists the dutch book theorem, and that that one importantly relates to probabilism

I’m glad we could converge on this, because that’s what I really wanted to convey.[1] I hope it’s clearer now why I included these as important errors:

• The statement that the vNM axioms “apart from continuity, are often justified using the Dutch book theorems” is false since these theorems only relate to belief norms like probabilism. Changing this to ‘money pump arguments’ would fix it.

• There’s a claim on the main Dutch book page that the arguments demonstrate that “rationality requires assigning probabilities to events [...] and having preferences that can be modeled using the von Neumann–Morgenstern axioms.” I wouldn’t have said it was false if this was about money pumps.[2] I would’ve said there was a terminological issue if the page equated Dutch books and money pumps. But it didn’t.[3] It defined a Dutch book as “a set of bets that ensures a guaranteed loss.” And the theorems and arguments relating to that do not support the vNM axioms.

Would you agree?

1. ^

The issue of which terms to use isn’t that important to me in this case, but let me speculate about something. If you hear domain experts go back and forth between ‘Dutch books’ and ‘money pumps’, I think that is likely either because they are thinking of the former as a special case of the latter without saying so explicitly, or because they’re listing off various related ideas. If that’s not why, then they may just be mistaken. After all, a Dutch book is named that way because a bookie is involved!

2. ^

Setting asside that “demonstrates” is too strong even then.

3. ^

It looks like OP edited the page just today and added ‘or money pump’. But the text that follows still describes a Dutch book, i.e. a set of bets. (Other things were added too that I find problematic but this footnote isn’t the place to explain it.)