Talk:Two envelopes problem/Archive 7

A common resolution
Although Richard has now changed this section so that it makes some kind of mathematical sense it is clearly not now a resolution of the paradox, which requires us to find the flaw in the proposed line of reasoning. The 'resolution' now simply shows that there is no point in swapping, which is something that everybody finds obvious at the start, indeed, without this natural assumption there would be no paradox. That is the problem with the 'common resolution, it can either be a mathematically sound statement which fails to address the problem at hand or it can be a confused and non-mathematical rambling which is worse than the paradox itself. Martin Hogbin (talk) 09:32, 16 February 2012 (UTC)


 * This solution claims that step 7 in the line of reasoning is wrong. It doesn't claim "simply that there is no point in swapping." You have used this pointless argument yourself in our discussions on these talk pages but the defenders of this view hasn't. Please show me a single source for your claim. It is obvious that you haven't understood this solution at all and that you have created your very own interpretation of it, which might very well be absurd. iNic (talk) 10:46, 16 February 2012 (UTC)
 * Yes, you are quite right, there are two unrelated attempts at a resolution in this section. The first is as shown below. Note carefully Richards wording which I have put in bold.


 * 'A common way to resolve the paradox, both in popular literature and in the academic literature in philosophy, is to observe that A stands for different things at different places in the expected value calculation, step 7 above. In the first term A is the smaller amount while in the second term A is the larger amount. To mix different instances of a variable in the same formula like this is said to be illegitimate, so step 7 is incorrect, and this is the cause of the paradox.'


 * This is Richard's way of trying to express the vague notion about using one thing being used to be be two different things. It is there because such vague thoughts often appear in some literature.  If you can find some clear explanation of exactly what is being claimed by these authors then please replace the paragraph with that.  You need to start with defining exactly what kind of quantity 'A' is supposed to be.


 * The rest of the section merely states the obvious. Martin Hogbin (talk) 11:07, 16 February 2012 (UTC)


 * The reason I inserted "said to be" is because we're reporting the claim of the typical writer who supports this solution. We wikipedia editors are not endorsing any particular solution, just reporting what's in the literature, and as far as possible trying to do that so that our readers will understand it. I don't find these resolutions satisfactory at all. But they are common. I also made an attempt to convert this vague solution into a careful mathematical analysis, which at least mathematicians hopefully would find meaningful. In the mathematical analysis I adopt what seems to be the interpretation of these solutions, namely that we are after an unconditional expectation, and I explain where the writer then derails, under this interpretation. Personally I don't like this solution at all - I find the interpretation far fetched, I find the vague resolution unsatisfactory. Moreover it misses one of the errors which the writer is making, according to this interpretation. He is also confusing random variables and their expectation values. So the mathematically precise version of this resolution is just as complicated as that of the second resolution. I hope our readers will do their best to understand the second interpretation and the standard resolution which goes with it. Finally we must leave our readers to judge for themselves. We are merely reporters, not judges. Richard Gill (talk) 15:44, 16 February 2012 (UTC)


 * I agree 100% that we are only reporters of opinions and if we agree or not, think the ideas are silly or not, worthless or not, brilliant or not, pointless or not, complicated or not, ridiculous or not, far fetched or not, satisfactory or not, vague or not, meaningful or not, erroneous or not, stupendous or not or even dangerous or not, should not make a damn difference. And we should not "hope our readers will do their best to understand the second interpretation and the standard resolution" because there is no "standard resolution." If you have this agenda you should back off from WP and not edit a single page from now on. The ideas you happen to like doesn't automatically transform into any "standard resolution." That is just BS. iNic (talk) 16:17, 16 February 2012 (UTC)


 * By the way, I can tell you the real difference between a philosopher and a mathematician. A philosopher can grasp more than one idea at the same time. iNic (talk) 16:17, 16 February 2012 (UTC)

Tools required to be a mathematician: pencils, paper, waste paper basket. Tools required to be a philosopher: pencils, paper. Martin Hogbin (talk) 17:16, 16 February 2012 (UTC)


 * I think I will do the same as you Richard and leave this page entirely and let the vandals take over. I have done that before and the result was a disaster. Then you came along and I started to believe in making a fun, short, readable and yet accurate page about TEP again. But now I have lost hope in this project once again. It's kind of sad but I will leave the corpse to the hyenas again. iNic (talk) 22:24, 16 February 2012 (UTC)


 * Your offensive tone to other editors will not be missed. Martin Hogbin (talk) 23:03, 16 February 2012 (UTC)


 * Yes leaving this page will leave both you and me happier. It's a true win-win. Who said that two opponents can't both win when playing a game? iNic (talk) 00:24, 17 February 2012 (UTC)

iNic, when I said hat I hoped the readers would come to their own conclusions, I did not mean they should come to my conclusion. Maybe the neutrally and clearly presented, and well sourced material, will lead them finally to your opinion, or to Martin's, or to mine, or to yet another, I think the article, though not perfect, does honestly survey what's in the literature. The "vandalism" which previously plagued the article was that editors who thought they understood TEP wrote up their own solution. I think the amount of vandalism will go down strikingly in the future; we have set some "academic standards" which will encourage serious editing. Maybe the properties "fun, short readable" are mutually inconsistent. Or more precisely, the resulting article would strongly depend on the point of view of the writer. Wikipedia is not there for that purpose. We give references to articles which some readers will find short, fun, readable. The lead of the article should be short, fun and readable. I think that present lead and intro are pretty good.Richard Gill (talk) 06:56, 17 February 2012 (UTC)


 * The current article is already strongly dependent on the point of view of the writer(s). For example, the logical version isn't mentioned in the new fabulous introduction at all, despite it's one of the very first versions. Why? Because of biased editors. When the logical version is presented in the article the first comment about it is from two probabilists who knows nothing at all about logic(!). Then their silly idea is presented that the problem can be dismissed because the non-probabilistic version doesn't include probability(!). This is a very biased way to present, or rather suppress, a topic in WP. It is moreover in perfect accordance with your own personal view of this topic. Wikipedia is not here for your purpose. iNic (talk) 15:02, 17 February 2012 (UTC)


 * (1) Smullyan's version is not mentioned explicitly in the introduction because of its relative lack of notability. (2) The present discussion of it presents in an unbiased way the points of view of Albers et al., Chase, and Li, and moreover points out that they are consistent with one another. In particular the logician Li agrees 100% with the mathematicians Albers et al.: without any probability there are no reasons to switch or not to switch; both of Smulyan's arguments are wrong. Chase adds probability and shows that there now is a good reason why switching is pointless: one of Smulyan's arguments is correct, the other is incorrect. (3) As far as the article reflects any editors' editorial (rather than substantive) opinions, it seems to me to be a decent compromise between those of the three currently active editors. Richard Gill (talk) 11:05, 18 February 2012 (UTC)


 * iNic, you say, 'the logical version isn't mentioned in the new fabulous introduction at all'. One reason for this is that this is not the version described at the top of the article.  One thing you must agree on is that different versions of the problem can have different resolutions. The is absolutely no point in carefully describing one version of the paradox (as we currently do) and then giving the resolution to another version.


 * Why not add a new section at the end called 'Variations of the problem' or similar in which you describe the less notable variants of the paradox and their resolutions? Martin Hogbin (talk) 12:54, 18 February 2012 (UTC)


 * It's obvious that the intro violates the NPOV policy, from the first sentence to the last. You are both of you so totally into your own way of thinking about this problem that you are unable to write a neutral and unbiased introduction. Richard, who has decided that the logical version has a "lack of notability"? No one has. That is just nonsense. You are simply violating one of the fundamental rules of WP wich is neutrality. And Martin, you think that all versions except the logical is explicitly mentioned at the top of the article? This is obviously not true. Your argument to justify a biased intro is equally much nonsense as Richard's argument. (Interesting to note that while you have a silent agreement that the logical version should be abandoned from the intro, when forced to speak about it you totally disagree on why it should be abandoned...) Martin, different writers differ when it comes to how many distinct versions they think there are, and which versions they think are only different wordings of one and the same version. This is the problem with both of you. You are both convinced that you know the real resolution(s) to this problem(s) and how many different versions there really are and which versions are less important and thus can be dismissed. Then in the name of enlightening the masses of the correct interpretations and their solutions you bias the article to fit your "true" views. That is POV editing, resulting in a POV article. Let's take the first sentence of the intro as an illustration: "The ways in which the paradox can be resolved depend to a large degree on the assumptions that are made about the things that are not made clear in the setup and the proposed argument for switching." This is simply not true. It's not the case that all authors of papers complain over lacking information in the setup or history of events leading to the situation. The writers with a Bayesian approach typically do that, but not all solutions are written from a Bayesian standpoint, or even can be written from a Bayesian standpoint. So even if you are both convinced Bayesians you need to be able to take off your Bayesian glasses, just for a little while, and view your personal standpoint as one among others when editing this page. If you can't do that you are simply not suited to edit this page. Right now you are both too much engaged in the battle to be able to be neutral reporters of the battle. iNic (talk) 11:22, 19 February 2012 (UTC)


 * What exactly is the POV that you believe is missing? Martin Hogbin (talk) 11:34, 19 February 2012 (UTC)


 * The missing POV is the NPOV. iNic (talk) 11:52, 19 February 2012 (UTC)
 * You are not being particularly helpful. You clearly believe that one POV is being pushed at the expense of one or more others. What is the POV you believe is being excluded and where can I find a reference to it? Martin Hogbin (talk) 12:17, 19 February 2012 (UTC)


 * As I have already said above, not all writers blame on a not well enough specified set up of the problem as stated. This is however stated as a fact without any reservations in the very first sentence of your intro. The whole intro also takes the Bayesian view for granted. Without even mentioning the Bayesian view with one word. Instead exclusively Bayesian concepts like priors, or rather improper priors, are blamed at just like that. No explanation of context. No explanation of what a prior is to start with and why some authors talk about these for some of the versions of TEP. All we get is a silly and wrong reason why a thing called "prior" should be called "improper." Extremely unhelpful and biased text. iNic (talk) 13:11, 19 February 2012 (UTC)
 * Please stop complaining and tell me what it is you would like to see.Martin Hogbin (talk) 18:11, 19 February 2012 (UTC)


 * The intro would have to be rewritten entirely to live up to NPOV standards. But what's the point having an intro in the first place? Better to make the article itself easier to read, then we can skip having intros. iNic (talk) 19:01, 19 February 2012 (UTC)


 * Are you suggesting that it is possible to give a clear resolution of a paradox without knowing either the setup or what the claimed paradox is? Martin Hogbin (talk) 11:39, 19 February 2012 (UTC)


 * Please read the sources. This is the Talk page, not the Arguments page, so I'm not suggesting anything about the problem. This is precisely the problem with you and Richard. You treat this Talk page as if it's the Arguments page (I've moved tons of your contributions here to the Arg page) and you treat the article as if it's the Talk page. iNic (talk) 11:56, 19 February 2012 (UTC)


 * Is there a particular source you would like me to read? The article as it is represents the sources, in particular the closest that we have to a general review, the Nalebuff paper. Martin Hogbin (talk) 12:08, 19 February 2012 (UTC)


 * Nalebuff writing in 1989 can't possibly give an overview of all the papers written after 1989. Since then the number of papers has exploded. The sources page lists 111 different papers/contributions after 1989 and just a handful before 1989. iNic (talk) 13:11, 19 February 2012 (UTC)


 * If you are not going to say what view you think is not properly represented here and what sources propose this view, please stop putting POV tags on the article. Martin Hogbin (talk) 18:11, 19 February 2012 (UTC)


 * I have said that. The logical view is never mentioned and Bayesianism introduced as a fact when it's not a fact, only a point of view some have in some contexts. iNic (talk) 18:56, 19 February 2012 (UTC)


 * The logical view clearly does not address the paradox described at the start of the article. Why do you not do as I suggest and add a section on this variant and its resolution?


 * There is nothing specifically Bayesian about the section in question except that it mentions the term improper prior. The resolutions referred to apply equally to the frequentist interpretation of probability as at least one source says.  I will try to find a reference and add it.  Martin Hogbin (talk) 20:36, 19 February 2012 (UTC)


 * If you classify the papers written since Nalebuff's paper you will find that most of them repeat material that is already in his paper. Several use it to invent new paradoxes inspired by the original (cf. the Broome variants, already in Nalebuff) or go more deeply into some technical aspects, or wander off on some tangent seeing connections to other problems (e.g., Saint Petersburg paradox, already in Nalebuff). The more mathematical literature almost exclusively takes the point of view that the TEP argument is about a computation of the conditional expectation value of the contents of Envelope B given some hypothesized amount in Envelope A. It takes for granted that the reader has some basic understanding either of the Bayesian point of view, or of the frequentist point of view, in both cases seeing the pair of amounts in the two envelopes a priori as random variables. The philosophical literature almost exclusively takes the point of view that TEP is about a computation of the unconditional expectation value of the contents of Envelope B. It is also highly repetitive. Many of the papers are very long and difficult to read and aimed at an academic audience in philosophy interested in particular technical issues in philosophy (problems of how to name things). Smullyan's little paradox is a breath of fresh air in the philosophy literature. He separates the issues of how to name things from the issues of probability calculation. There are several resolutions of his paradox since there are several ways to interpret his problem statement, but they are all discussed in the wikipedia article and there is no mutual contradiction between them. The literature on his TEP is rather small. My opinion is therefore that the present introduction to the paper represents the literature in a rather fair way, and in a way which makes it maximally accessible to the lay person. Specialists will also find in the article a discussion of all the notable specialist (academic) issues. The field is complex and messy, many of the publications are not very high quality, so it is quite a challenge to give a comprehensive overview. But that is what we have done. Richard Gill (talk) 09:27, 20 February 2012 (UTC)


 * There are three main categories of solutions to TEP in the literature. One of them, the one you call the philosophers' solution, is satisfied with how the problem is stated. No information is lacking but no information is superflous either. This is the one currently called the "A common solution" in the article. Then there is the class of solutions which I call Bayesian and you call the mathematicians' solution. In their view the problem as stated doesn't contain sufficient information; the problem as stated is underdetermined. So to be able to solve the problem they first have to fill in the missing parts. This can be done in different ways leading to quite different types of arguments and solutions. Here we find the bounded prior game, the unbounded Broome type prior game, my bounded ticket game and so on. Then the third category of solutions we could call the logicians' solution. Their view is that the problem as stated contain superflous information. According to this view we can reduce the problem to a logical problem without any probabilities. Your intro is not NPOV because already in the first sentence it states the middle POV that the problem id underdetermined. Why don't we call these three main interpretations "The philosophers solution", "The mathematicians solutions" and "The logicians solutions" in the article? I think that would be an enhancement. iNic (talk) 10:06, 20 February 2012 (UTC)

An interesting argument but let me ask whether this particular analysis of the literature is your own or if you have source which analyses the literature in this way. Martin Hogbin (talk) 10:42, 20 February 2012 (UTC)


 * There are no neutral surveys of the literature yet, probably because this is still an ongoing debate. Richard agrees with me on this point. How many of the sources have you read? Only Nalebuff? Maybe our different views of TEP as a subject is due to different views of the TEP history. To you and Richard TEP as a field of research essentially ended in 1989 with the Nalebuff paper. In my view it on the contrary took off for real in 1989 with the Nalebuff paper. I think that just a glance at the sources page supports my view. iNic (talk) 12:09, 20 February 2012 (UTC)


 * I disagree, iNic, that the mathematicians think the mathematician's version of TEP is incomplete. Whatever prior distribution is put over the possible amounts of money in the two envelopes, as long as it is proper, the TEP argument deriving the conditional expectation of B given A=a is incorrect and one can clearly state where it fails. It simply can't be the case that B is equally likely a/2 as 2a for all possible values of a. For ordinary folk, the example where we assume an upper bound to the sums of money makes this clear enough. Improper priors are dealt with by remarking that they are improper. Littlewood uses the word "monstrous". Broome's paradox is a new paradox. Interesting for mathematicians, not too interesting for ordinary folk, I suspect. Regarding Smulyan's paradox, I am not aware of any logician who thinks that Smulyan's problem is "the only true" TEP problem because it is somehow more pure to leave out the probability ingredients altogether. It is simply considered a new paradox. It is obvious that the usual (standard) statement of basic TEP (as presented in the article) is incomplete, and needs extra information before it can be resolved: the philosophers and the mathematicians fill in key missing steps in different ways: the missing information being what is thought to be random and what is thought to be fixed, hence also implicitly whether a conditional or unconditional expectation is being taken. Both common interpretations have simple resolutions if one is familiar with elementary probability calculus. However it is all rather heavy going for those who do not have any familiarity with elementary probability concepts. Richard Gill (talk) 17:41, 20 February 2012 (UTC)
 * The problem with the simple solutions given by some philospohers and others is that they are mathematical nonsense, just as bad as the problem itself. Unfortunately, there do not seem to be any reliable sources which point this out, maybe someone needs to write one.


 * Let me try - It is strange for a logician such as Smulyan to start with an falacious thinking that you already have something at the start of the game; either (A or A/2) or (2X or X). In fact you have nothing (0) in both cases, so it is not true that you can lose anything. You always gain, either (A/2 or A) or (2X or X). You can't "lose" neither A/2 nor X.

I assume the same logical fallacy forms the basis in other mathematical solutions. comment added by Activeco (talk • contribs) 10:19, 8 September 2012 (UTC)
 * The logicians solution is, obviously, to a different variant of the problem, which could be added at the end of the article. Martin Hogbin (talk) 10:04, 21 February 2012 (UTC)


 * The logician's problem and two logician's solutions are already in the article "non probabilistic variant". iNic was complaining that it is not mentioned in the introduction. I think it is not notable enough for this. Only three or four articles out of the hundred, I think. It is the case however that it focusses on the confusion of wording ("equivocation") which the philosophers concentrate on, in their interpretation of TEP. In that sense it is, In my opinion, a better paradox than the philosopher's version. Richard Gill (talk) 12:48, 21 February 2012 (UTC)


 * Perhaps we should just change the name of the introduction to, 'Introduction to the solutions using probability theory' or the like. It was never intended to be a summary of the whole subject, that is the purpose of the lead.  Martin Hogbin (talk) 17:42, 21 February 2012 (UTC)

Introduction to resolutions based on probability theory
Although we may not all agree with it, the version of the 25 February represents some kind of consensus. I would like to completely remove the erroneous and unreferenced 'Common resolution' section; iNic would like to move the 'Introduction' section. As we cannot agree we should leave it as it was. Martin Hogbin (talk) 13:27, 19 March 2012 (UTC)


 * We never reached a "consensus" on February 25. It's a violation of NPOV to remove sections you don't like or think is wrong. And the section you hate is not unreferenced as you claim. The 'Introduction to resolutions' section you have written only cover the Bayesian probability cases, and can consequently only function as an introduction to the Bayesian probability cases. I pointed out this flaw over and over and over again, but to deaf ears. You never understood what I said. Since February 25 the page has erroneously pretended that your introduction covered the 'Common resolution' as well as the non-probabilistic cases, none of which it mentions with a single word. Simple as that! IQ 50 should suffice to understand this. As each and every edit I do at the page is immediately reverted by you and you don't understand (or want to understand) what I say about the reasons for the edits we have indeed a difficult situation for this page. At least as long as you are policing this page, which probably will be until the end of days. iNic (talk) 18:07, 19 March 2012 (UTC)


 * The 'common resolution' is, quite obviously, not a resolution at all, it is just a reason not to swap, which we all knew. Martin Hogbin (talk) 20:52, 19 March 2012 (UTC)


 * Why don't you move along and spend your time at some other page that you do understand? iNic (talk) 00:35, 20 March 2012 (UTC)


 * That is a good point. I guess this is your page where you make all the decisions and attack any one who disagrees with you. Martin Hogbin (talk) 19:30, 20 March 2012 (UTC)


 * I think the article is looking pretty good now. A lot of the "reliable sources" contain what in my opinion is obviously nonsense. The article gives such nonsense solutions reasonable prominence, but does not actually endorse them. People who are really interested, and smart enough to appreciate the technicalities, will read on and find some decent resolutions. Interestingly though, Thomas Bruss' article does not endorse the philosophers "equivication" solution at all. And he later wrote a second article which takes the Bayesian approach (and conditional expectation interpretation). It's clear that a lot of the Wikipedia article was written by editors with insufficient mathematical background to actually understand papers like that of Bruss. Richard Gill (talk) 15:34, 24 March 2012 (UTC)


 * Actually, non-familiarity with philosophy is much more of a handicap for an editor of this page than unfamiliarity with mathematics. iNic (talk) 22:30, 29 March 2012 (UTC)

I am not so sure that we are supposed to give obvious nonsense reasonable prominence; we are supposed to be writing an encyclopedia not a literature review. Martin Hogbin (talk) 16:51, 24 March 2012 (UTC)


 * Why don't you move along and spend your time at some other collaborative Internet site where you do understand the rules? iNic (talk) 23:26, 24 March 2012 (UTC)

One of the fundamental rules of WP is to discus the content not attack the editor, please stop doing this.

Also please note that the discussion that I have restored is about improving this article by not having sections that do not address the stated problem. Please leave other people's comments alone. This is not your page. Martin Hogbin (talk) 23:55, 24 March 2012 (UTC)


 * What individual editors think is nonsense or not nonsense is completely irrelevant for Wikipedia and for the Wikipedia readers. That's a very basic WP rule and if you don't understand this rule there are plenty of other forums, both online and offline, where you can spend your precious time instead. Please see this as a friendly suggestion, not as a personal attack. iNic (talk) 16:26, 27 March 2012 (UTC)

Thanks for your kind advice. You might like to review your own understanding of WP rules; obvious nonsense can be removed, especially when it is not supported by a single source. Remember also that any sources cited must actually support what is said on the page without undue interpretation or synthesis. Martin Hogbin (talk) 17:39, 27 March 2012 (UTC)


 * No, what you think is "obvious nonsense" can not be removed from Wikipedia. PLEASE READ THIS. The "Common resolution" is published in many papers. This does not, however, mean that everyone must agree that this is the correct resolution. On the contrary, in philosophy it is often the case that there are different conflicting opinions in the literature. If you are totally unfamiliar with philosophy, please move on to some other simpler page that does not contain any philosophy. A math page for example. What a good WP article in philosophy should do is to list all the different opinions in a neutral way. It's never up to an individual editor to start to delete well published ideas and opinions the editor personally happen to dislike. In philosophy that is obvious nonsense. iNic (talk) 22:22, 29 March 2012 (UTC)

Why not then have the generally agreed mathematical resolutions first and then the philosophical musings later? The article currently reads as though there is a simple, mathematically acceptable resolution to the paradox put forward at the start of the article. As you seem to agree, this is simply not the case. Martin Hogbin (talk) 09:52, 30 March 2012 (UTC)


 * Because WP is not a forum for propaganda. NPOV is a very basic principle. You should know, as every editor of this page, that there is no "generally agreed mathematical resolution" (and no generally agreed philosophical resolution either, for that matter). I don't know why you are so engaged in this page while you have a very shallow familiarity with the literature and, more importantly, don't even know what philosophy is. Please tell me which of the papers in the list of sources you have read and understood. Of course, we should not claim that any of the proposed solutions is the "final" or the "correct" one. I will support any changes making this even more clear. So if you feel that the "Common resolution" is currently written in a way that could fool some readers into believing that this is the "simple, mathematically acceptable resolution," please change the text in that paragraph so we avoid that kind of reading. Delete the paragraph is, however, not an option. iNic (talk) 15:43, 30 March 2012 (UTC)

The mathematical resolution of this paradox is simple, agreed, and given in the article.

Deleting a paragraph that does not have a single reference and does not refer to the paradox given at the start of the article most certainly is an option, in fact it is how WP works, unreferenced material should be removed. Martin Hogbin (talk) 20:25, 30 March 2012 (UTC)


 * So please tell me who discovered this "simple and agreed mathematical resolution" that you believe exist? What paper are you referring to? Have you read other papers as well? Which ones? You didn't answer my question which papers you have read. Please do. iNic (talk) 12:08, 1 April 2012 (UTC)

The mathematically sound resolutions are in the article, as are the papers that they are based on. Martin Hogbin (talk) 16:06, 3 April 2012 (UTC)


 * I can't find any mathematically sound resolutions in the article. You have to tell me which ones you mean. You still haven't answered which papers you have read. Please do. iNic (talk) 08:20, 4 April 2012 (UTC)

A common resolution
INic please tell us exactly what paradox this, completely unreferenced, section resolves. Martin Hogbin (talk) 09:17, 25 March 2012 (UTC)


 * Please take the time to read the whole section and you will discover that it is not unreferenced. The paradox is often called "The two-envelope paradox," but other names has been used as well. iNic (talk) 16:13, 27 March 2012 (UTC)

The first section has no references whatever and does not even address the stated paradox, it should be removed. The 'Mathematical details' is Richards attempt to restore some mathematical integrity to the article. Martin Hogbin (talk) 09:55, 30 March 2012 (UTC)


 * This is getting really silly. The paragraph as a whole has references. Deleting the main paragraph while keeping its sub-paragraph containing some in-depth explanations of the main paragraph is simply vandalism. Trying to justify your vandalism at the talk page is either a silly joke or completely brain dead. iNic (talk) 15:58, 30 March 2012 (UTC)

The second section does not in any way justify the first. Martin Hogbin (talk) 20:28, 30 March 2012 (UTC)


 * Are you dumb for real? The sub-section starts "Let us rewrite the preceding calculations in a more detailed notation..." After your removal of the main section what "preceding calculations" do you think the sub-section then refers to? iNic (talk) 11:46, 1 April 2012 (UTC)

INic, please do not attack editors by using phrases like, "Are you dumb for real?". If you want to discus the content that is fine but I will not respond to personal attacks. Martin Hogbin (talk) 13:26, 1 April 2012 (UTC)


 * Sorry, it was not meant as a personal attack. It is a serious question. iNic (talk) 15:21, 1 April 2012 (UTC)

What exactly do you say is the relation of the second section to the first? Is it an explanation, a justification, a criticism, or what? Martin Hogbin (talk) 21:56, 1 April 2012 (UTC)


 * It starts "Let us REWRITE THE PRECEDING CALCULATIONS IN A MORE DETAILED NOTATION..." But you want to delete the PRECEDING CALCULATIONS. This means that after your vandalism the sub-section DOESN'T REFER TO ANYTHING AT ALL. Is this difficult logic for you? How old are you? iNic (talk)

Perhaps that section should go too then. You still have not answered my question. What exactly do you say is the relation of the second section to the first? Is it an explanation, a justification, a criticism, or what? Martin Hogbin (talk) 16:03, 3 April 2012 (UTC)


 * So that is the logic of a vandal? Scary. I will revert any vandalism you do. Please ask Richard who created the sub-section if you need help interpreting it. iNic (talk) 08:17, 4 April 2012 (UTC)

I do not care enough about this page or this problem to argue with you. I do not think that Wikipedia should contain obvious nonsense but I will leave it up to you. The whole problem is essentially a self-inflicted injury. Martin Hogbin (talk) 14:07, 4 April 2012 (UTC)

Resolution based upon time constraints
I didn't want to just edit this in since it's my own idea but there seems to be a simple resolution of this coming from a slightly different direction. Namely: The process of swapping envelopes must take a finite amount of time. Even if this time is very small, any answer which results in continuous swapping will take infinite time. Since our lives are of finite length such answers will therefore lead to no actual benefit (and quite a lot of loss since we will have missed out on our whole life). Since any answer which results in opening an envelope within your lifetime will have a definite positive benefit this is always a better solution. Obviously there's other directions you can take based on this line of reasoning, such as considering the actual time values for swapping and opening the envelope and actual values held within the envelopes and trying to ascertain how much time it's actually worth spending on the problem. But i'm pretty sure that the eventual answer would be, "Just open the damn thing and get on with your life."

This resolution seems to be hinted at in the article but not expressed explicitly. Should it be? Is it a valid argument? Has anyone else considered this before? Do i have to actually write a paper on this and get it published for it to be included? Please discuss...Biasoc (talk) 14:01, 20 March 2013 (UTC)


 * I have not seen this idea in the literature, so you will have to work out the details, get it published, get other people to take notice of it! Personally, though, I am happy with existing resolutions of the paradox. Richard Gill (talk) 17:22, 26 March 2013 (UTC)

Attribution of common (philosopher's) solution
I have just received copies of two papers by Thomas Bruss on TEP. The first one is cited as approving of the philosopher's solution "The preceding resolution was first noted by Bruss in 1996". Interestingly, Bruss writes in this paper that he finds the Sobel (1994) and Rawling (1994) solutions somewhat inadequate. He writes "Rawling's feeling about the 'rigid designator' problem was close to this, but the correct conclusion was missing". Bruss also writes that a perfectly adequate resolution is given in section 3 of Christensen and Utts (1992), which according to him should have completely closed the discussion. Unfortunately, he suggests, the title of that section "some frequentist calculations" has mislead readers since these simple calculations are purely mathematical and independent of any particular interpretation (frequentist or Bayesian) of the probabilities being manipulated in TEP.

Bruss's conclusion is that there is no paradox but only a simple fallacy.

Amusingly, after writing his 1996 paper which he hoped would at last definitively close TEP, by bringing Christensen and Utts' section 3 comments out of hiding, he wrote another paper in 2000 together with L. Rüschendorf "The switching problem and conditionally specified distributions" (same journal as Bruss 1966: The Mathematical Scientist). This paper takes up the Broome type examples, which Bruss yet again relates to the Saint Petersburg paradox. Of course there is no error in the calculations leading to the recommendations to switch in the Broome example. The advice to switch is however not waranted, because of the infinite expectation values involved. The Broome paradox is a paradox, not a fallacy, in Bruss' understanding of these words. Richard Gill (talk) 21:06, 28 February 2012 (UTC)


 * Can you please put these papers in the dropbox? I put the Zabell paper there, if you haven't noticed that yet. iNic (talk) 09:15, 29 February 2012 (UTC)

"Can you please put these papers in the dropbox? I put the Zabell paper there" I have been trying to find the Zabell article without success. Can you please give the details on accessing this dropbox? ---Dagme (talk) 04:48, 29 March 2013 (UTC)

Great work
The article is much more clear and sensible than it was 2 years ago, when I had a crack at it. Congratulations on the great work. Dilaudid (talk) 08:43, 3 October 2012 (UTC)

I agree with this assessment. I visited the article today after several years and found it vastly improved. I now think I can find some valuable information in it. I want to spend some time going over it carefully. ---Dagme (talk) 04:55, 29 March 2013 (UTC)

Formatting error
Several times on the page, red text. Can anyone fix this? Shiningroad (talk) 17:11, 8 February 2014 (UTC)

Recent edit warring
On the face of it, the recently added material seems to be supported by a reliable source. Martin Hogbin (talk) 14:06, 2 October 2014 (UTC)


 * Wikipedia shall primarily be based on secondary sources where the most accepted theories in published papers are presented. However, secondary sources are hard to find for this article. In the absence of secondary sources the editors of this article need to do much of the work a secondary source would have done. It means that we as editors need to include ideas and theories that are noteworthy because it has many followers or because many other authors refer to that work. We should not include a summary of a theory, with no followers at all and no citations at all, inserted between two random paragraphs of the WP article. This is comparable to vandalism. I put the text we now discuss at the Arguments page where all other ideas without followers are gathered. Interested readers will find it there. iNic (talk) 19:39, 2 October 2014 (UTC)
 * iNic please read WP:vandal, where it says, 'Even if misguided, willfully against consensus, or disruptive, any good-faith effort to improve the encyclopedia is not vandalism. Edit warring over content is not vandalism', and do not accuse good-faith contributors of actions comparable to vandalism.


 * Whether you agree or not the added content was supported by a reliable source. You do not WP:own this page and all discussion of article content should take place here. Martin Hogbin (talk) 20:39, 2 October 2014 (UTC)


 * If it would have been good faith edits the contributor would have discussed his contribution here at the talk page long ago. instead he just reverts back again and again. There are literally hundreds of ideas for a solution more prominent than this one so if you think we should keep this edit we should allow for executive summaries of every paper ever written inserted randomly within the existing article. Then we better delete this article altogether from Wikipedia. As you think this contribution is so brilliant and well placed why don't you revert it back yourself? Why wait for mr anonymous to do it for you? iNic (talk) 03:31, 3 October 2014 (UTC)


 * It would be good to discuss changes on the talk page and I look forward to hearing from our IP editor here. Martin Hogbin (talk) 09:42, 7 October 2014 (UTC)


 * Because I use my IP address and you use your username (INic) doesn't mean that your opinion is more reliable than mine. I am not more anonymous than you are.


 * If you type four tildes (like this ~ after your post, the system will automatically sign and date it for you. Martin Hogbin (talk) 22:32, 7 October 2014 (UTC)

In a mess again
The body of the article used to start with, 'Here the ways the paradox can be resolved depend to a large degree on the assumptions that are made about the things that are not made clear in the setup and the proposed argument for switching'. This key statement has been moved down the page with attempts at 'resolutions' being placed before it.

It is quite clear that one of the principal problems with resolving this paradox is the uncertainty in what is meant by the question. Without a clear understanding of this fact, all attempts at resolutions are meaningless. Martin Hogbin (talk) 12:51, 16 June 2014 (UTC)

There are some simple and uncontroversial fundamental principles, that can be applied before we attempt any resolutions.

The setup must be well defined
It must be clear exactly what the rules of the game are. For example, are there any restrictions on the sums that might be in the envelopes and does the player look inside his envelope before making a choice?


 * There are authors that think that the problem is underdetermined, others that the problem is overdetermined and still others that the problem is neither underdetermined nor overdetermined. Your view that the problem is underdetermined is not globally correct. It is only one of the views put forward by some of the authors. Also, if it matters for the player to look inside the first envelope or not is also a matter of controversy. Some authors think that it matters while others think that it doesn't matter. Even if it is advantageous or not to swap is a mater of controversy as some authors claim that is is indeed a good idea to switch envelope whatever is found in the first one selected, and they try to avoid a paradox by reinterpreting or limit other concepts like expected value and so on. You should really try to read some papers by authors of which you disagree. iNic (talk) 10:34, 7 October 2014 (UTC)


 * I am not arguing about whether the problem is what you call underdetermined or overdetermined. If sources use that terminology so should we in the article, clearly stating the sources' views on that subject, their reasons for their choices, the line (or lines) of argument) in which they find a flaw, and what that flaw is.


 * Which sources in this article support the view that it is indeed a good idea to switch envelope whatever is found in the first one selected? Martin Hogbin (talk) 19:10, 10 October 2014 (UTC)


 * You have been editing this page for many years and you are still totally clueless what the sources say in general, except for six papers that you claim you have read but ask me all the time about the remaining 96% of the sources. As you are apparently very interested in this topic and want to participate in editing this Wikipedia article why don't you read more of the sources? This is very puzzling to me. Most of the sources are quite easily accessible on the Internet. The rest you can access via your local library. I'm not here to tell you what's in the sources. Find out for yourself and then we can discuss it, okay? iNic (talk) 07:40, 11 October 2014 (UTC)


 * As you apparently have a very different view regarding how this page should be organized, what sections it should contain, what names the sections should have, in what order the sections should appear, which sources the article should be based upon and in general what message the article should give to the world about the general state of this problem, I have a suggestion to you. Why don't you write an article from scratch exactly along the lines you want? I think the only way for you to really show me and everyone else how you envisage this page is to actually create the page you have in mind. You are free to do that and when it is finished you can challenge this page and if your page is better we will simply delete this page and use your page instead. This has already happened once in the past so for a short while Wikipedia had two separate articles about this problem. The current page is the result of a merge of the contents of these two pages, after which one of the pages were deleted. We can do this again, no problem. I mean this as a 100% sincere suggestion. iNic (talk) 01:02, 12 October 2014 (UTC)


 * INic, I suggest you to write a new article about the topic. You could name it "INic's view about the two envelopes problem". There, we promise to let you do whatever you want. Imagine how great would that be! Caramella1 (talk) 05:34, 13 October 2014 (UTC)


 * I have no need to do that. As long as the article is based on the most common views in the sources I'm happy. This page can still be improved, no doubt about that. Some quite common views on how to resolve the problem is still missing in the article for example. But as I've said before I don't edit this page anymore. iNic (talk) 14:23, 13 October 2014 (UTC)

The full basis of the argument to switch must be made clear at some point
One problem with this paradox is that intuitively there is no paradox. Most people intuitively think that the correct thing to do is not to bother switching and, unlike the Monty Hall problem for example, their intuition turns out to be correct. As far as I know, there are no sources that say it is sensible to switch for any version of the paradox.

For there to be a paradox at all, a convincing line of reasoning needs to be presented to the reader to support switching. Without this there is no paradox to be resolved. The resolution of the paradox therefore requires the fault (or possibly just ambiguity) in the proposed argument for switching to be found, thus confirming the readers original intuition and the mathematically correct fact that switching is pointless.

A mathematical argument which shows that there is nothing to be gained by switching is not a resolution of the paradox it is merely a confirmation of the obvious.Martin Hogbin (talk) 14:41, 16 June 2014 (UTC)

In the argument I ignore the Ali Baba variation, where there is still no paradox. In this case it is intuitively obvious that you should swap, a simple argument can be proposed for swapping, and it is easy to show that swapping is advantageous, but it is a different problem. Martin Hogbin (talk) 15:17, 16 June 2014 (UTC)


 * As nobody seems to care about this I guess I should just be wp:bold and edit the page to fix the problems noted above. Martin Hogbin (talk) 20:40, 2 October 2014 (UTC)


 * Your analysis above is simply not correct. Your analysis is based on your own Bayesian opinion about how one should approach this paradox and it is currently placed correctly within the article at the introduction to the Bayesian attempts to solve the paradox. I know since earlier discussions with you that you want to delete all other approaches than the Bayesian ones from this article. I will not allow this to happen. Yes, I am annoying at times. iNic (talk) 03:49, 3 October 2014 (UTC)


 * Please read what I have written. It has nothing to do with Bayesian or any other analysis is about making clear what problem is being solved.  No one can sensibly give any kind of argument unless it is clear exactly what problem is being solved.


 * You say, 'I will not allow this to happen'. Let me repeat, you do not WP:own this page and it is not up you you alone to decide what goes here. Martin Hogbin (talk) 17:07, 3 October 2014 (UTC)


 * There are different views on how to solve this problem. Very different views. Please read the sources. Our job as editors is NOT to promote our own views (if we have one) and put that view to the front. What you have just done is creating a mess of the article again. No one, exactly no one, is helped by knowing which solution you think is the best one. No one cares about your opinion as an editor. Please try to understand that. iNic (talk) 06:04, 7 October 2014 (UTC)


 * You still seem not to have read what I have written under the two headings above. There is no source or rational view which says that we must solve a problem that is not well defined. All the sources that I have read discuss a particular version of the problem. In this article we talk about 'the problem' as if there is one well-defined version; this approach is not supported by the sources.


 * Secondly, the problem is not, 'should you swap?'. We all know that in the most versions of this problem the answer is 'no, of course not'.  The problem, as stated in the article, is to find the error in the presented line of reasoning for swapping.  These two issues are presented under the two headings above, where I ask you to respond.  Martin Hogbin (talk) 09:23, 7 October 2014 (UTC)


 * There are three main groups of solutions found in the sources. According to one of the groups the problem as stated is underdetermined and more information is needed. This group all use some kind of Bayesian view to attack the problem and what is lacking in their view is typically the prior probability distributions describing the prior belief a certain amount should be found in an envelope. According to another view the problem in neither underdetermined nor overdetermined and can be solved by a careful analysis of how 'constants' and 'variables' are used in the problem. According to the third approach the problem is overdetermined because it is possible to do away with all probability talk altogether. The authors having this view typically solve the problem via some logical analysis of the situation. To claim that one of these approaches is the correct one by putting it first under the heading "Resolution" is dishonest and incorrect. If you are unable to separate your role as an editor from your own personal convictions regarding this topic you should really refrain from edit this article. iNic (talk) 10:02, 7 October 2014 (UTC)


 * The section that I moved to the top was the one supported by 6 good quality sources but I shall ignore your accusations of dishonesty because at last you seem to be discussing how to improve the article.


 * Provided that it is supported by good quality reliable sources, what you say above would seem to make a good introduction to the subject and I would be happy to work with you to write such an introduction. At the moment we have a collection of solution with no indication of what they are solutions to.  Starting with a summary of the way the problem has been interpreted would seem a good idea to me.  We can than group the solutions according to the understanding of the problem that they solve.


 * There is still an issue that you have not addressed which is that there are no good quality sources that state that it is a good idea to endlessly exchange envelopes. This means that no version of the problem requires us to show that swapping envelopes endlessly is a bad idea; this is obvious and correct.  All solutions must therefore, as well as making clear their understanding of the problem, make clear exactly what argument for switching they are addressing. Martin Hogbin (talk) 12:49, 8 October 2014 (UTC)


 * I totally agree that the article can be improved and I would love to collaborate with you of some other editor to improve it. But as long as you make changes which sole purpose is to promote your own favorite understanding of the problem you are not acting as the NPOV editor every serious Wikipedia editor should be. In the process of placing your own favorite views at the top you obscure the structure of the page making it inconsistent. You can't just fiddle around with paragraphs in the way you do. This just creates a mess and a totally unreadable article. In addition, you claim that your favorite view is the "Resolution" as if this problem has a well established resolution that everyone agrees is the correct resolution. You know this is not true and when your edits contain these kinds of blatant lies, me calling your edit dishonest is just a nice way of putting it. In addition I think your actions for promoting your own understanding of this problem are counterproductive. Making the article into a mess will not make more people reading it, including your own favorite ideas. Much better to have a clear structure of the article where the different takes on how to tackle the problem are presented. In this way your own views will be much more read and respected. iNic (talk) 15:43, 8 October 2014 (UTC)


 * I have no idea what you are talking about when you refer to 'your own favorite views'. I moved the section because it was supported by 6 good sources.  My view are not included in the article anywhere.


 * Ok but there are currently 148 articles written about this topic. Your six good sources are thus merely 4% of all articles written. How many of the remaining 142 sources have you read? iNic (talk) 22:47, 8 October 2014 (UTC)
 * If you believe a majority of reliable sources support a different view the it is up to you to cite them here. Martin Hogbin (talk) 09:05, 9 October 2014 (UTC)


 * No they are already cited in the article by editors that read more than 4% of the papers. You have tried to delete them from the article before and you will probably try to delete them again but so far they have survived. iNic (talk) 10:33, 10 October 2014 (UTC)


 * Nevertheless it is necessary for a proposed solution to clearly state what problem it solves. It is also necessary for a solution to make clear what line of reasoning is presented for swapping.  These simple facts apply to all solutions. Martin Hogbin (talk) 16:36, 8 October 2014 (UTC)


 * If you mean that all authors must think that the problem as stated is underdetermined you are simply wrong. For some authors the problem is clearly stated, for others it isn't. iNic (talk) 22:47, 8 October 2014 (UTC)


 * No this is not what I mean.


 * For there to be a solution to any problem there must be a problem to solve, even if it is ambiguously stated.  What exactly do you claim is the problem statement?  Is it the unsourced statement at the beginning of this article?


 * The section called "Problem" is a good first statement of the problem in my view and it is not unsourced. The paragraph called "The problem" in the lead was added by an anonymous editor (you?) and is indeed unsourced. I removed that when it was added because it was redundant, unsourced and it didn't state the problem in a sufficiently accurate way. However you reverted it back immediately with the comment "The lead should be a summary of the article and subject. It must state what the problem is." So please feel free to remove this unsourced statement of the problem in the lead if it now suddenly annoys you. iNic (talk) 10:33, 10 October 2014 (UTC)


 * That is correct, the lead should contain a summary of the article itself. It is not necessary for a source to be cited in the lead if the subject is covered, with a source, in the body of the article.  If you believe that the sentence in the lead inaccurately summarises the problem as stated in the body of the article then you are welcome to improve it.  I always edit under my real name (except if I forget to log in).


 * So it was you that added this anonymously? iNic (talk) 16:46, 11 October 2014 (UTC)


 * The section, 'The switching argument:' cites no sources. Are you saying that is the single definitive statement of the problem that all solutions answer? Martin Hogbin (talk) 08:42, 11 October 2014 (UTC)


 * Come on! The citation is directly before the section which is common practice. But move it if it bothers you. Sometimes I wonder why you are here editing this topic year after year when you are still so totally clueless what this topic is all about. Anyone merely reading the lead of this article would be able to answer the question you have now. iNic (talk) 16:46, 11 October 2014 (UTC)


 * Forget the insults, perhaps you could answer my two questions. Are you saying that the 'Problem' section gives the exact problem that all solutions answer?  Must a solution find the flaw in the line of reasoning given? Martin Hogbin (talk) 17:40, 11 October 2014 (UTC)


 * This is what I said: "The section called "Problem" is a good first statement of the problem in my view and it is not unsourced." I also directed you to the lead of the article where you can find the answer to both your questions. So I did answer your questions. iNic (talk) 18:08, 11 October 2014 (UTC)


 * Is 'the problem' finding 'the flaw in the very compelling line of reasoning above', as stated in this article? Martin Hogbin (talk) 09:05, 9 October 2014 (UTC)


 * You say above, 'There are three main groups of solutions found in the sources'. Can you provide a source for this statement?  It would provide a good starting point for the article.


 * There are very few secondary sources in this topic unfortunately. Not a single one actually. I wish there were but this is the cold facts. This means that we as editors must do much of the work a secondary source would have done for us. First of all we should read the primary sources. If not all so most of them. iNic (talk) 22:47, 8 October 2014 (UTC)


 * As there are no sources supporting this grouping it is your own WP:OR. I agree that it is up to editors here to decide how to organise the article but please note the plural 'editors'. There is no consensus to organise the article the way that you want. Martin Hogbin (talk) 09:05, 9 October 2014 (UTC)


 * By all means please suggest another way to organize the 148 sources that you find is a better way to do it! You haven't exactly done anything in this direction so far. On the contrary your main goal in the past has been to remove sourced sections describing whole classes of solutions. I can't see how that would constitute a new and fresh grouping of the sources. But if you have come up with one now please let us all know! iNic (talk) 10:33, 10 October 2014 (UTC)


 * Your three groups of solution are listed below. Can we list the sources associated with each group and make clear exactly what problem each source addresses. Martin Hogbin (talk) 16:36, 8 October 2014 (UTC)


 * The article already has this structure! "Common resolution" in the article is your type 2 below and is presented first because it is the least complex solution. "Alternative interpretation" is the name in the article for your type 1 below. "Non-probabilistic variant" is the name of your type 3 below. iNic (talk) 22:47, 8 October 2014 (UTC)


 * You seem to be claiming the right to decide on your own how to group the solutions, what names these groups have, and what order they should be presented in. This must be decided by consensus. Martin Hogbin (talk) 09:05, 9 October 2014 (UTC)


 * The grouping and order has indeed already been decided by consensus by editors in the past. By the way, I have for sure not invented the names of these groups. Other editors came up with these names. In fact I haven't contributed to this article in any substantial way for many many years. My focus has been to try to keep this article in such a shape that it doesn't contradict itself (which it usually does when you rearrange paragraphs) and remove vandalism, POV edits and other unhelpful additions or deletions to the article. So I don't really know what you are talking about. If you want other names of the groups, other groups and another ordering among these groups please speak out about that. You have done nothing in that direction in the past. At least not in a consistent way that also is in accordance with the contents of the sources. I really look forward to learn what you suggest as a new grouping of the sources! This will be very interesting. iNic (talk) 10:33, 10 October 2014 (UTC)


 * I have never seen a consensus emerge about this page. I do not follow your argument for putting what is called a "Common resolution".  I will start a new section on this below. Martin Hogbin (talk) 08:45, 11 October 2014 (UTC)


 * There is in fact currently a consensus among editors who have read a substantial part of the sources. That people like mr anonymous and you will never be satisfied is a different thing. iNic (talk) 16:46, 11 October 2014 (UTC)


 * Which editors to you say support this grouping? Martin Hogbin (talk) 17:42, 11 October 2014 (UTC)


 * Please consult the View history tab of the article to see who have been involved in the past. iNic (talk) 18:08, 11 October 2014 (UTC)

Types of solution
1) The problem as stated is underdetermined and more information is needed. This group all use some kind of Bayesian view to attack the problem and what is lacking in their view is typically the prior probability distributions describing the prior belief a certain amount should be found in an envelope.

I imagine that sources promoting this view would include Nalebuff (1989), Christensen and Utts (1992), Falk and Konold (1992), Blachman, Christensen and Utts (1996),[14] Nickerson and Falk (2006).


 * Correct, but there are others as well but I don't remember which ones right now. iNic (talk) 22:47, 8 October 2014 (UTC)

2) The problem in neither underdetermined nor overdetermined and can be solved by a careful analysis of how 'constants' and 'variables' are used in the problem.

What sources do we have supporting this view apart from Eckhardt?


 * The sources mentioned in the article are Schwitzgebel and Dever, Bruss, Falk, but I know there are others as well, but again I have to re-read articles to find them. iNic (talk) 22:47, 8 October 2014 (UTC)

3) According to the third approach the problem is overdetermined because it is possible to do away with all probability talk altogether. The authors having this view typically solve the problem via some logical analysis of the situation.

I assume the sources supporting this view are: Smullyan, Knopf, Chase, Katz, and Byeong-Uk Martin Hogbin (talk) 16:36, 8 October 2014 (UTC)


 * Yes correct, and in this case I think this list is exhaustive. At least for now. iNic (talk) 22:47, 8 October 2014 (UTC)