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, and N satisfying Bad≺Good. This mistakes weak preference for strict preference. To see this, set p=1 and observe that the line now reads N≺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 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.”
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 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.
None of these changes are new as far as I can tell (I checked the first three), so I think your basic critique falls through. You can check the edit history yourself by just clicking on the “View History” button and then pressing the “cur” button next to the revision entry you want to see the diff for.
Like, indeed, the issues you point out are issues, but it is not the case that people reading this have made the articles worse. The articles were already bad, and “acting with considerable care” in a way that implies inaction would mean leaving inaccuracies uncorrected.
I think people should edit these pages, and I expect them to get better if people give it a real try. I also think you could give it a try and likely make things better.
Edit: Actually, I think my deeper objection is that most of the critiques here (made by Sammy) are just wrong. For example, of course Dutch books/money pumps frequently get invoked to justify VNM axioms. See for example this.
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.
Well, thinking harder about this, I do think your critiques on some of these is wrong. For example, it is the case that the VNM axioms frequently get justified by invoking dutch books (the most obvious case is the argument for transitivity, where the standard response is “well, if you have circular preferences I can charge you a dollar to have you end up where you started”).
Of course, justifying axioms is messy, and there isn’t any particularly objective way of choosing axioms here, but in as much as informal argumentation happens, it tends to use a dutch book like structure. I’ve had many conversations with formal academic experience in academia and economics here, and this is definitely a normal way for dutch books to go.
I’ve pretty consistently (by many different people) seen “Dutch Book arguments” used interchangeably with money pumps. My understanding (which is also the SEP’s) is that “what is a money pump vs. a dutch book argument” is not particularly well-defined and the structure of the money pump arguments is basically the same as the structure of the dutch book arguments.
This is evident from just the basic definitions:
“A Dutch book is a set of bets that ensures a guaranteed loss, i.e. the gambler will lose money no matter what happens.”
Which is of course exactly what a money pump is (where you are the person offering the gambles and therefore make guaranteed money).
The money pump Wikipedia article also links to the Dutch book article, and the book/paper I linked describes dutch books as a kind of money pump argument. I have never heard anyone make a principled distinction between a money pump argument and a dutch book argument (and I don’t see how you could get one without the other).
A pattern of intransitive or cyclic preferences causing a decision maker to be willing to pay repeated amounts of money to have these preferences satisfied without gaining any benefit. [...] Also called a Dutch book [...]
(Edit: It’s plausible that for weird historical reasons the exact same argument, when applied to probabilism would be called a “dutch book” and when applied to anything else would be called a “money pump”, but I at least haven’t seen anyone defend that distinction, and it doesn’t seem to follow from any of the definitions)
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.
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.
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!
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.)
We certainly are, which isn’t unique to either of us; Savage discusses them all in a single common framework on decision theory, where he develops both sets of ideas jointly. A money pump is just a Dutch book where all the bets happen to be deterministic. I chose to describe things this way because it lets me do a lot more cross-linking within Wikipedia articles on decision theory, which encourages people reading about one to check out the other.
You can check the edit history yourself by just clicking on the “View History” button and then pressing the “cur” button next to the revision entry you want to see the diff for.
Note that if the edit history is long or you are doing a lot of checks, there are tools to bisect WP edit histories: at the top of the diff page, “External tools: Find addition/removal (Alternate)”
Edit: Actually, I think my deeper objection is that most of the critiques here (made by Sammy) are just wrong. For example, of course Dutch books/money pumps frequently get invoked to justify VNM axioms. See for example this.
Sami never mentioned money pumps. And “the Dutch books arguments” are arguments for probabilism and other credal norms[1], not the vNM axioms.
I broadly agree with all of Sami’s points. However, on this terminological issue I think it is a bit less clear cut. It is true that many decision theorists distinguish between “dutch books” and “money pumps” in the way you are suggesting, and it seems like this is becoming the standard terminology in philosophy. That said, there are definitely some decision theorists that use “Dutch book arguments” to refer to money pump arguments for VNM axioms. For example, Yaari writes that “an agent that violates Expected Utility Theory is vulnerable to a so-called Dutch book”.
Now, given that the entry is called “dutch book theorems” and mostly focuses on probabilism, Sami is still right to point out that it is confusing to say that these arguments support EUT. Maybe I would have put this under “misleading” rather than under “false” though.
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:
...let me know that some of the issues I mention were already on Wikipedia beforehand. I’d be happy to try to edit those.
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.
I’m not annoyed by these, and I’m sorry if it came across that way. I’m grateful for your comments. I just meant to say these are exactly the sort of mistakes I was talking about in my post as needing fixing! However, talking about them here isn’t going to do much good, because people read Wikipedia, not LessWrong shortform comments, and I’m busy as hell working on social choice articles already.
From what I can tell, there’s one substantial error I introduced, which was accidentally conflating IIA with VNM-independence. (Although I haven’t double-checked, so I’m not sure they’re actually unrelated.) Along with that there’s some minor errors involving strict vs. non-strict inequality which I’d be happy to see corrected.
Thanks. Let me end with three comments. First, I wrote a few brief notes here that I hope clarify how Independence and IIA differ. Second, I want to stress that the problem with the use of Dutch books in the articles is a substantial one, not just a verbal one, as I explained here and here. Finally, I’m happy to hash out any remaining issues via direct message if you’d like—whether it’s about these points, others I raised in my initial comment, or any related edits.
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, and N satisfying Bad≺Good. This mistakes weak preference for strict preference. To see this, set p=1 and observe that the line now reads N≺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 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.”
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.
None of these changes are new as far as I can tell (I checked the first three), so I think your basic critique falls through. You can check the edit history yourself by just clicking on the “View History” button and then pressing the “cur” button next to the revision entry you want to see the diff for.
Like, indeed, the issues you point out are issues, but it is not the case that people reading this have made the articles worse. The articles were already bad, and “acting with considerable care” in a way that implies inaction would mean leaving inaccuracies uncorrected.
I think people should edit these pages, and I expect them to get better if people give it a real try. I also think you could give it a try and likely make things better.
Edit: Actually, I think my deeper objection is that most of the critiques here (made by Sammy) are just wrong. For example, of course Dutch books/money pumps frequently get invoked to justify VNM axioms. See for example this.
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.
Well, thinking harder about this, I do think your critiques on some of these is wrong. For example, it is the case that the VNM axioms frequently get justified by invoking dutch books (the most obvious case is the argument for transitivity, where the standard response is “well, if you have circular preferences I can charge you a dollar to have you end up where you started”).
Of course, justifying axioms is messy, and there isn’t any particularly objective way of choosing axioms here, but in as much as informal argumentation happens, it tends to use a dutch book like structure. I’ve had many conversations with formal academic experience in academia and economics here, and this is definitely a normal way for dutch books to go.
For a concrete example of this, see this recent book/paper: https://www.iffs.se/media/23568/money-pump-arguments.pdf
You are conflating the Dutch book arguments for probabilism (Pettigrew, 2020) with the money-pump arguments for the vNM axioms (Gustafsson, 2022).
I’ve pretty consistently (by many different people) seen “Dutch Book arguments” used interchangeably with money pumps. My understanding (which is also the SEP’s) is that “what is a money pump vs. a dutch book argument” is not particularly well-defined and the structure of the money pump arguments is basically the same as the structure of the dutch book arguments.
This is evident from just the basic definitions:
“A Dutch book is a set of bets that ensures a guaranteed loss, i.e. the gambler will lose money no matter what happens.”
Which is of course exactly what a money pump is (where you are the person offering the gambles and therefore make guaranteed money).
The money pump Wikipedia article also links to the Dutch book article, and the book/paper I linked describes dutch books as a kind of money pump argument. I have never heard anyone make a principled distinction between a money pump argument and a dutch book argument (and I don’t see how you could get one without the other).
Indeed, the Oxford Reference says explicitly:
(Edit: It’s plausible that for weird historical reasons the exact same argument, when applied to probabilism would be called a “dutch book” and when applied to anything else would be called a “money pump”, but I at least haven’t seen anyone defend that distinction, and it doesn’t seem to follow from any of the definitions)
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 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’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?
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.)
We certainly are, which isn’t unique to either of us; Savage discusses them all in a single common framework on decision theory, where he develops both sets of ideas jointly. A money pump is just a Dutch book where all the bets happen to be deterministic. I chose to describe things this way because it lets me do a lot more cross-linking within Wikipedia articles on decision theory, which encourages people reading about one to check out the other.
Note that if the edit history is long or you are doing a lot of checks, there are tools to bisect WP edit histories: at the top of the diff page, “External tools: Find addition/removal (Alternate)”
so eg https://wikipedia.ramselehof.de/wikiblame.php?user_lang=en&lang=en&project=wikipedia&tld=org&article=Von+Neumann–Morgenstern+utility+theorem&needle=behave+as+if+they+are+maximizing+the+expected+value+of+some+function&skipversions=0&ignorefirst=0&limit=500&offmon=7&offtag=23&offjahr=2024&searchmethod=int&order=desc&start=Start&user= identifies in 10s the edit https://en.wikipedia.org/w/index.php?title=Von_Neumann–Morgenstern_utility_theorem&diff=prev&oldid=1165485303 which turns out to be spurious but then we can restart with the older text.
Sami never mentioned money pumps. And “the Dutch books arguments” are arguments for probabilism and other credal norms[1], not the vNM axioms.
Again, see Pettigrew (2020) (here is a PDF from Richard’s webpage).
I broadly agree with all of Sami’s points. However, on this terminological issue I think it is a bit less clear cut. It is true that many decision theorists distinguish between “dutch books” and “money pumps” in the way you are suggesting, and it seems like this is becoming the standard terminology in philosophy. That said, there are definitely some decision theorists that use “Dutch book arguments” to refer to money pump arguments for VNM axioms. For example, Yaari writes that “an agent that violates Expected Utility Theory is vulnerable to a so-called Dutch book”.
Now, given that the entry is called “dutch book theorems” and mostly focuses on probabilism, Sami is still right to point out that it is confusing to say that these arguments support EUT. Maybe I would have put this under “misleading” rather than under “false” though.
Yes, these Wikipedia articles do have lots of mistakes. Stop writing about them here and go fix them!
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.
I’m not annoyed by these, and I’m sorry if it came across that way. I’m grateful for your comments. I just meant to say these are exactly the sort of mistakes I was talking about in my post as needing fixing! However, talking about them here isn’t going to do much good, because people read Wikipedia, not LessWrong shortform comments, and I’m busy as hell working on social choice articles already.
From what I can tell, there’s one substantial error I introduced, which was accidentally conflating IIA with VNM-independence. (Although I haven’t double-checked, so I’m not sure they’re actually unrelated.) Along with that there’s some minor errors involving strict vs. non-strict inequality which I’d be happy to see corrected.
Thanks. Let me end with three comments. First, I wrote a few brief notes here that I hope clarify how Independence and IIA differ. Second, I want to stress that the problem with the use of Dutch books in the articles is a substantial one, not just a verbal one, as I explained here and here. Finally, I’m happy to hash out any remaining issues via direct message if you’d like—whether it’s about these points, others I raised in my initial comment, or any related edits.