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.

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

- ^
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 appreciate the intention here but I think it would need to be done with considerable care, as I fear it may have already led to accidental vandalism of the epistemic commons. Just skimming a few of these Wikipedia pages, I’ve noticed several new errors. These can be easily spotted by domain experts but might not be obvious to casual readers.

^{[1]}I can’t know exactly which of these are due to edits from this community, but some very clearly jump out.^{[2]}I’ll list some examples below, but I want to stress that this list is not exhaustive. I didn’t read most parts of most related pages, and I omitted many small scattered issues. In any case,

I’d like to ask whoever made any of these edits to please reverse them, and to triple check any I didn’t mention below.^{[3]}Please feel free to respond to this if any of my points are unclear!^{[4]}## False statements

The page on Independence of Irrelevant Alternatives (IIA) claims that IIA is one of the vNM axioms, and that one of the vNM axioms “generalizes IIA to random events.”

Both are false. The similar-sounding Independence axiom of vNM is neither equivalent to, nor does it entail, IIA (and so it can’t be a generalisation). You can satisfy Independence while violating IIA. This is a not a technicality; it’s a conflation of distinct and important concepts. This is repeated in several places.

The mathematical statement of Independence there is wrong. In the section conflating IIA and Independence, it’s defined as the requirement that

for any p∈[0,1] and any outcomes

Bad,Good, andNsatisfyingBad≺Good. This mistakes weak preference for strict preference. To see this, set p=1 and observe that the line now readsN≺N. (The rest of the explanation in this section is also problematic but the reasons for this are less easy to briefly spell out.)The Dutch book page states that the argument demonstrates that “

rationality requires assigning probabilities to events [...] and having preferences that can be modeled using the von Neumann–Morgenstern axioms.” This is false. It is an argument for probabilistic beliefs; it implies nothing at all about preferences. And in fact, the standard proof of the Dutch book theoremassumessomething like expected utility (Ramsey’s thesis).This is a substantial error, making a very strong claim about an important topic. And it’s repeated elsewhere, e.g. when stating that the vNM axioms “apart from continuity, are often justified using the Dutch book theorems.”

The section ‘The theorem’ on the vNM page states the result using strict preference/inequality. This is a corollary of the theorem but does not entail it.

## Misleading statements

The decision theory page states that it’s “

a branch of applied probability theory and analytic philosophy concerned with the theory of making decisions based on assigning probabilities to various factors and assigning numerical consequences to the outcome.” This is a poor description. Decision theorists don’t simply assume this, nor do they always conclude it—e.g. see work on ambiguity or lexicographic preferences. And besides this, decision theory is arguably more central in economics than the fields mentioned.The IIA article’s first sentence states that IIA is an “axiom of decision theory and economics” whereas it’s classically one of social choice theory, in particular voting. This is at least a strange omission for the context-setting sentence of the article.

It’s stated that IIA describes “a necessary condition for rational behavior.” Maybe the individual-choice version of IIA is, but the intention here was presumably to refer to Independence. This would be a highly contentious claim though, and definitely not a formal result. It’s misleading to describe Independence as necessary for rationality.

The vNM article states that obeying the vNM axioms implies that agents “behave as if they are maximizing the expected value of some function defined over the potential outcomes at some specified point in the future.” I’m not sure what ‘specified point in the future’ is doing there; that’s not within the framework.

The vNM article states that “the theorem assumes nothing about the nature of the possible outcomes of the gambles.” That’s at least misleading. It assumes all possible outcomes are known, that they come with associated probabilities, and that these probabilities are fixed (e.g., ruling out the Newcomb paradox).

Besides these problems, various passages in these articles and others are unclear, lack crucial context, contain minor issues, or just look prone to leave readers with a confused impression of the topic. (This would take a while to unpack, so my many omissions should absolutely not be interpreted as green lights.) As OP wrote: these pages are a mess. But I fear the recent edits have contributed to some of this.

So, as of now, I’d strongly recommend against reading Wikipedia for these sorts of topics—even for a casual glance. A great alternative is the Stanford Encyclopedia of Philosophy, which covers most of these topics.

I checked this with others in economics and in philosophy.

E.g., the term ‘coherence theorems’ is unheard of outside of LessWrong, as is the frequency of italicisation present in some of these articles.

I would do it myself but I don’t know what the original articles said and I’d rather not have to learn the Wikipedia guidelines and re-write the various sections from scratch.

Or to let me know that some of the issues I mention were already on Wikipedia beforehand. I’d be happy to try to edit those.