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:
Would you agree?
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!
Setting asside that "demonstrates" is too strong even then.
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.)
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.]
check the edit history yourself by just clicking on the "View History" button and then pressing the "cur" button
Great, thanks!
I hate to single out OP but those three points were added by someone with the same username (see first and second points here; third here). Those might not be entirely new but I think my original note of caution stands.
Scott Garrabrant rejects the Independence of Irrelevant Alternatives axiom
*Independence, not IIA. Wikipedia is wrong (as of today).
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]
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 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 theorem assumes something 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.”
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.
Two nitpicks and a reference:
an agent’s goals might not be linearly decomposable over possible worlds due to risk-aversion
Risk aversion doesn't violate additive separability. E.g., for we always get whether (risk neutrality) or (risk aversion). Though some alternatives to expected utility, like Buchak's REU theory, can allow certain sources of risk aversion to violate separability.
when features have fixed marginal utility, rather than being substitutes
Perfect substitutes have fixed marginal utility. E.g., always has marginal utilities of 1 and 2.
I'll focus on linearly decomposable goals which can be evaluated by adding together evaluations of many separate subcomponents. More decomposable goals are simpler
There's an old literature on separability in consumer theory that's since been tied to bounded rationality. One move that's made is to grant weak separability accross goups of objects---features---to rationalise the behaviour of optimising accross groups first, and within groups second. Pretnar et al (2021) describe how this can arise from limited cognitive resources.
It may be worth thinking about why proponents of a very popular idea in this community don't know of its academic analogues, despite them having existed since the early 90s[1] and appearing on the introductory SEP page for dynamic choice.
Academics may in turn ask: clearly LessWrong has some blind spots, but how big?
I argued that the signal-theoretic[1] analysis of meaning (which is the most common Bayesian analysis of communication) fails to adequately define lying, and fails to offer any distinction between denotation and connotation or literal content vs conversational implicature.
In case you haven't come accross this, here are two papers on lying by the founders of the modern economics literature on communication. I've only skimmed your discussion but if this is relevant, here's a great non-technical discussion of lying in that framework. A common thread in these discussions is that the apparent "no-lying" implication of the analysis of language in the Lewis-Skyrms/Crawford-Sobel signalling tradition relies importantly on common knowledge of rationality and, implicitly, on common knowledge of the game being played, i.e. of the available actions and all the players' preferences.
In your example, DSM permits the agent to end up with either A+ or B. Neither is strictly dominated, and neither has become mandatory for the agent to choose over the other. The agent won't have reason to push probability mass from one towards the other.
You can think of me as trying to run an obvious-to-me assertion test on code which I haven't carefully inspected, to see if the result of the test looks sane.
This is reasonable but I think my response to your comment will mainly involve re-stating what I wrote in the post, so maybe it'll be easier to point to the relevant sections: 3.1. for what DSM mandates when the agent has beliefs about its decision tree, 3.2.2 for what DSM mandates when the agent hadn't considered an actualised continuation of its decision tree, and 3.3. for discussion of these results. In particular, the following paragraphs are meant to illustrate what DSM mandates in the least favourable epistemic state that the agent could be in (unawareness with new options appearing):
It seems we can’t guarantee non-trammelling in general and between all prospects. But we don’t need to guarantee this for all prospects to guarantee it for some, even under awareness growth. Indeed, as we’ve now shown, there are always prospects with respect to which the agent never gets trammelled, no matter how many choices it faces. In fact, whenever the tree expansion does not bring about new prospects, trammelling will never occur (Proposition 7). And even when it does, trammelling is bounded above by the number of comparability classes (Proposition 10).
And it’s intuitive why this would be: we’re simply picking out the best prospects in each class. For instance, suppose prospects were representable as pairs that are comparable iff the -values are the same, and then preferred to the extent that is large. Then here’s the process: for each value of , identify the options that maximise . Put all of these in a set. Then choice between any options in that set will always remain arbitrary; never trammelled.
I don't apprecaite the hostility. I aimed to be helpful in spending time documenting and explaining these errors. This is something a heathy epistemic community is appreciative of, not annoyed by. If I had added mistaken passages to Wikipedia, I'd want to be told, and I'd react by reversing them myself. If any points I mentioned weren't added by you, then as I wrote in my first comment:
The point of writing about the mistakes here is to make clear why they indeed are mistakes, so that they aren't repeated. That has value. And although I don't think we should encourage a norm that those who observe and report a problem are responsible for fixing it, I will try to find and fix at least the pre-existing errors.