Talk:Info-gap decision theory/Archive 1

Uncertain function?

Added title. —Nils von Barth (nbarth) (talk) 17:55, 6 April 2009 (UTC)

I am a mathematician not an economist. The section of this article entitled Info-gap models does not make mathematical sense to me. The section talks about an "uncertain function u(x)". This should more correctly be "uncertain function u". It is u that is a function between two sets, say, u maps points in a set X to points in a set Y. The notation u(x) means the point in Y that x in X is mapped to by u.

Then the first displayed equation should be

U={u:X\rightarrow Y : for all x \in X ... }

What typically are the sets X and Y? Is Y most of the time the real numbers? Are there typically any other restrictions on the functions u allowed? Then the article talks about an "unbounded family of sets". Does this just mean an infinite family of sets? All the sets are contained in the the set of all functions mapping X into Y i.e. in {u:X\rightarrow Y}. In that sense they are all bounded. —The preceding unsigned comment was added by 86.10.223.162 (talk • contribs) 15:38 UTC, 27 June 2007.

Dear mathematician,

Thanks for your comments. I have added "for all x" in the info-gap model, hoping this makes it a bit clearer. I've not added clarification regarding the phrase "unbounded family of sets". It seems adequate for the level of mathematical detail of this brief article.

Yours,

Ybenhaim 18:49, 27 June 2007 (UTC)ybenhaim

Similarities with Minimax

Info-gap seems to share many similarities with minimax decision-making, a point identified by a researcher at the university of melbourne. I've identified this in the introduction. I don't mean to state that info-gap is specific case of minimax (as Prof. M. Snidovich does), but simply that their approach to uncertainty is analogous.

Also, the referencing of this article is non-wiki-standard.220.238.65.174 06:51, 13 August 2007 (UTC)

I think it is fair to say that info-gap and minimax decision theories have some similarities, as well as some differences. Your statement of this is more or less NPOV. The link you added, however, is just a link to an unpublished essay making claims that, as far as I can tell, have never been published. This does not meet Wikipedia criteria for inclusion. From WP:NOR: "[A]ny facts, opinions, interpretations, definitions, and arguments published by Wikipedia must already have been published by a reliable publication." --Zvika 15:16, 13 August 2007 (UTC)

Your point is well made. However, the linking of this article was primarily focussing on the proof that info-gap could be written as a maximin problem (see page 25 and 26 of the article). This proof seems sound, even if the tone of the article is non-standard. Also, WP:NOR doesn't exclude unpublished information if it comes from a Reliable source. Reliable sources include "authors or publications regarded as trustworthy or authoritative in relation to the subject at hand." The author of that paper, Moshe Sneidovich, is a Reader at the University of Melbourne, and has done a large amount of relevant research in that area - I think his comments on the method are relevant. 128.250.102.46 06:51, 14 August 2007 (UTC)

Not being too familiar with the subject, I don't want to start an argument here. However, if Dr. Sneidovich has indeed done a large amount of relevant research in this area, it shouldn't be a problem to find a published source with the relevant proof. I would have no objection to that. The link you gave reads more like a vendetta than an academic paper, and I do not think it belongs here. Indeed, given the large amount of published work on info-gap, this seems like a case of WP:REDFLAG. --Zvika 09:35, 14 August 2007 (UTC)

I added a section dealing with this aspect of Info-Gap. It is based on a peer-reviewd article (Sniedovich 2007). Sniedo (talk) 22:12, 26 December 2007 (UTC)

NPOV and cleanup

I have made a number of modifications of the article on info-gap theory, which I summarize here:

1. In several places the style of the exposition was inconsistent with Wikipedia's NPOV policy, so I've changed the style without altering the basic assertions.
2. I've added a new section elaborating on the relation between info-gap robust-satisficing and max-min. In particular, this section explains two ideas:
   1. "Observational equivalence" between these strategies asserts that either can be used to describe the other.
   2. "Behavioral difference" between these strategies asserts that an actual decision maker with specific beliefs may not be indifferent between these two strategies, and in some situations may prefer the robust-satisficing strategy.
3. I have modified the first example slightly. The derivation of the robustness function is correct only for values of the parameter b for which $|b|>=2$. This does not alter the basic import of the example, so I've simply indicated this restriction, and adjusted the text slightly to accommodate this restriction. (In case you're interested, the complete robustness function, for arbitrary $b$ and $r_{c}$, has three branches, of which the solution in the article shows one branch.)
4. I have removed the second example entirely since there is a basic problem here. The performance function $R(q,u)$ is stated to be unknown over a particular region. This is perfectly okay from an info-gap point of view, but would seem to suggest the need to include that lack of knowledge in an info-gap model of uncertainty. In any case, the robustness function from the previous example cannot be directly applied since the performance function is different. Finally, the point of the example is well made in a subsequent section without the example in any case.
5. Finally, in the spirit of NPOV, I've added an additional point of view about the utility of info-gap theory in dealing with severe uncertainty. There are indeed multiple points of view, and the NPOV policy is to present them in a balanced manner. The original online summary was unbalanced so I removed it, and this exchange constitutes a good summary and conclusion of the article.

Ybenhaim (talk) 09:07, 31 December 2007 (UTC)

G'day.

The following is a summary of my latest update.

1. Since the statement "is a simple instance of is much more informative than is related to and is perfectly neutral, the correction made in the first paragraph was not justified and even counter productive. I therefore restored the previous version, indicating clearly that Info-Gap's robustness model is a simple instance of Wald's famous Maximin model.
2. The assertion that ... Info-gap robustness analysis is a method for evaluating each feasible decision by asking: how wrong can this estimate be, and the decision under consideration will still yield an acceptable outcome? is groundless. Since the true value of the estimate is unknown, the gap is not a measure of how wrong the estimate can be and the decision under consideration will still yield an acceptable outcome. Rather, Info-Gap's robustness analysis is a method for evaluating each feasible decision by asking: how much can we deviate from the estimate so that the performance over the respective region of uncertainty surrounding the estimate is acceptable? In other words, the robustness is a measure of the size of the area around the poor estimate over which the performance is acceptable. Since under severe uncertainty the estimate is a wild guess, why should we be interested exclusively in such a neighborhood of the region of uncertainty? I adjusted the introductory text accordingly.
3. I fixed the typo in the expression for the robustness in first example.
4. I expanded the section Relation to Wald's Maximin model" which now also provides a Maximin model for the opportuneness model. I do not regard this section as criticism. It simply states a fact.
5. The new subsection "The Maximin Connection explains why the two new concepts "Observational equivalence" and "Observational equivalence" are counter-productive.
6. The section on "Observational equivalence" and "Observational equivalence" is not relevant to the discussion on the Maximin model formulated in the section "Relation to Maximin. In fact, the Maximin model alluded to in this section is not defined explicitly and, in any case, is not the same as the model used in the section "Relation to Wald's Maximin Model". So what is the purpose of the analysis in this section? In my opinion this section is counter productive because it does not deal with a proper Maximin model that is supposed to subsume Info-Gap as an instance. However, I left this section as is, simply pointing out the distinction between the Maximin model alluded to in this section and the specific Maximin model defined in the section "Relation to Wald's Maximin Model". They are not the same and should not be confused. If the author of this section insists on keeping it intact, he/she should provide a formal mathematical description of the Maximin model used in the comparison. I suspect that it is the model I formulated in the new subsection The Maximin Connection. However, I believe that it would be best to delete this section. Should this be done I shall be happy to delete the discussion on the counter-productive nature of the two new concepts in the new subsection "The Maximin Connection".
7. The removal of the second example was totally unjustified. The ? is used as an effective tool to vividly illustrate the flaw in the Info-Gap model. It simply indicates that Info-Gap's robustness model does not depend on the specific value represented by ?. I therefore restored this example and elaborated a bit more on the role of ? in the exposition. This is a perfectly NPOV example. Furthermore, I am confident that many readers will find this example much more reader-friendly than the abstract technical discussion.
8. I created a number of new sections where I formalize the discussion on the flaw in the Info-Gap robustness model.
9. For the benefit of the readers I added a short NPOV summary. Sniedo (talk) 11:16, 6 January 2008 (UTC)

Sniedo (talk) 08:02, 10 January 2008 (UTC)

Proposal

I would like to offer my view as someone without very much knowledge of info-gap, but with some experience in resolving Wikipedia disputes. Wikipedia is based on the assumption that people with very different beliefs can work together to create a repository of knowledge which describes all notable viewpoints in a fair and balanced manner. For this to work, the crucial point is to rise above our personal beliefs (including things that we are entirely sure are true), and try to write instead about what the scientific community as a whole thinks about a topic. With this in mind, and with good faith on all sides, it is usually possible to reach an article which all parties see as acceptable.

I would like to propose that we discuss what should happen with this article here on the talk page, rather than reverting each other's edits, which just gets everybody annoyed. I urge everyone involved to take a look at Wikipedia's core policies, especially WP:NOR and WP:UNDUE (which is part of WP:NPOV). One point which seems relevant to me is: "Articles that compare views should not give minority views as much or as detailed a description as more popular views, and may not include tiny-minority views at all."

Now, again, I am not an expert on info-gap, but from the article is seems that there is quite a wide range of published material supporting info-gap (two editions of a book from a reputable publisher, and quite a few peer-reviewed articles by many different authors), whereas there is only one published paper criticizing info-gap. By contrast, the Wikipedia article currently contains 9122 words, of which 4087 words (almost half) are in the "Critique" section. This strikes me as inappropriate. If there are additional researchers or papers describing the difficulties with info-gap, then these should be added to make the critique section more convincing. If not, then clearly the critique is a minority view and should be given appropriately limited coverage in the article: perhaps a one-sentence mention in the lead and a couple of paragraphs within the text.

I'd be glad to hear what the others think about this. --Zvika (talk) 07:32, 7 January 2008 (UTC)

G'day:

This is just a quick response to your proposal.

1. As indicated in my last communication there is plenty of scope here to streamline the debate and present the public with a much shorter and less contentious article.
2. It would definitely be much better to attempt to reach a consensus via a "behind the scenes" discussion than by repeatedly re-reediting the article.
3. I shall have to think about how to proceed from here in the best possible way.

I shall respond to the content of your proposal in a few days. Sniedo (talk) 23:48, 7 January 2008 (UTC)

G'day:

Here is my response to the content of the Proposal:

Wikipedia is no doubt a "democratic" enterprise, but it is still an Encyclopedia. As such it must strive to ensure that the material published under its aegis is factual, valid, correct and accurate.

Thus, in the case of mathematically oriented articles, Wikipedia must apply the same criteria that the scientific community has adopted since the dawn of modern science. In particular, the validity of mathematical propositions must be established on grounds of solid/sound argument (proof). That is, the validity of such propositions is not judged a-priori on grounds of number of proponents, popularity, or number of publications propounding them.

A scientific/mathematical thesis may well be in the minority at a given time -- they all are. However, once its validity is substantiated by means of formal proofs; furthermore, once it is established by means of formal proofs that the majority position is invalid, incorrect, inaccurate, etc., the minority position overrides that of the majority. This is how science works.

Info-gap is indeed propounded in many publications, held by many proponents, and is at present a majority position. However, this fact in itself neither vouches for its validity, correctness and accuracy nor does it give it a privileged position. It must still be able to withstand any amount of close scrutiny.

The situation is that two formal theorems -- whose validity is established by formal proofs that can be easily ascertained by inspection -- completely undermine the foundation of Info-Gap decision theory and prove the majority wrong.

The length of the Critique section in the current version of the article is an expression of the need to explain in detail, to the majority and the public at large, the extent to which the majority is wrong. But the length is not an issue: once the theorems and their implications are accepted by WIKIPEDIA for what they are, the criticism can be shortened significantly.

The issue here is that the argument (theorems) put forward by the opposing minority position must be judged on its on merits and the right conclusions must be drawn accordingly. This done, the length issue can be easily resolved.

So what's next?

I shall send you a plan based on this position that hopefully will resolve the dispute quickly and satisfactorily. This may take a few days. Sniedo (talk) 00:15, 10 January 2008 (UTC)

I am glad to hear that you accept the fact that your view is a minority. It should be emphasized that the info-gap community is not currently in a state of limbo and confusion following your recent publication. Rather, the majority view on info-gap has not changed, and indeed there are several responses to the criticism you raised, some of which appear in the article text. Also, many info-gap-based studies continue to be performed (and published) despite your arguments. In short, while the validity of your proofs is not questioned, the interpretation that they "completely undermine the foundation of info-gap" (as you say) is a value judgement held by a small minority (which includes, to the best of my understanding, only yourself).

I sympathize with your feeling that "the king is naked" and that everybody else is wrong. As you say, overturning majority opinions is not uncommon in the history of science, and I wish you the best of luck in doing so. However, this should be done through proper academic discussion -- in peer-reviewed academic journals -- and not in an encyclopedia. As I said in my previous post, the purpose of Wikipedia (and, for that matter, any encyclopedia) is to report the current scientific understanding and consensus. It is an integral part of this policy that the majority opinion is represented as such, and that dissenting opinions be presented briefly while clearly stating that they are a minority view. To this end, the article as it currently stands will have to be changed drastically.

The power of Wikipedia is that if and when the consensus changes, the content here can be updated to reflect that. However, it is not our goal to update the content here in order to change scientific consensus. --Zvika (talk) 07:46, 10 January 2008 (UTC)

G'day:

As I indicated earlier, I shall send you a simple plan to resolve the issue in a few days. Sniedo (talk) 08:02, 10 January 2008 (UTC)

Hello:

I agree with Zvika's proposal. There is clearly wide consensus which constitutes a "standard interpretation" of info-gap theory. There is also a small minority interpretation represented by Sniedo. The latter should be mentioned by one sentence in the lead and a short criticism section of probably one paragraph. This is consistent with Wikipedia's policy and the general concept of an encyclopedia. Ybenhaim (talk) 08:29, 10 January 2008 (UTC)

Hello,

I'm glad to read that a détente may be expected: it is unhealthy to the Wikipedia to have debates take place in the article pages. Not to mention that the open nature of Wikipedia makes it practically impossible to impose an opinion.

As to the resolving of this debate, I would like to emphasize the need to distinguish between "mathematical truths" and their interpretation. For example, while it cannot be denied that the robustness function can be expressed in a maximin form, the novelty in the info-gap approach is a question of subjective interpretation. In the encyclopedic spirit of Wikipedia, the article should focus on the widely accepted interpretation, while noting different (minority) views.

Lior Davidovitch (talk) 09:32, 10 January 2008 (UTC)

When the Spin Goes marching in

G'day:

I can see that Info-Gap cannot take the heat and resorts to rhetoric and spin. Three examples will make the point.

1. Maximin Connection

In his two Info-Gap books Ben-Haim (2001, 2006) presents Info-Gap decision theory as a new theory that is radically different from all current theories of decision under uncertainty.

As we all agree now, this is not so: the fact is that Info-Gap's robustness model is a simple Maximin model. Furthermore, on several occasions Ben-Haim (eg. Ben-Haim 2005, FAQ paper) claimed that Info-Gap's robustness model is not a Maximin model.

We can argue forever about the difference between "mathematical truths" and their interpretation, we can even write a script for a play on this interesting subject.

The fact remains that Info-Gap's robustness model is a simple Maximin model and this should be made crystal clear in the WIKIPEDIA article.

And what are we to conclude from the fact that Ben-Haim does not even mention Maximin in his three Info-Gap books?

The point is this: Info-Gap's robustness model is a simple Maximin model and therefore Ben-Haim is wrong in presenting Info-Gap as a new decision theory that is radically different from all current theoreies for decision under uncertainty.

No amount of spin can change this fact.

So why don't we simply tell the public what all of us here know only too well, namely that contrary to the claims in the Info-Gap literature, Info-Gap is not a new theory that is radically different from all current decision theories? Why is Info-Gap trying to hide this important fact from the public?

2. Local vs global robustness

On many occasions Ben-Haim argued that Info-Gap robustness analysis is not local in nature. Suddenly in this WIKIPEDIA article, in response to Sniedovich's criticism, there is a complete change in direction. Ben-Haim now agrees -- in the WIKIPEDIA article -- that Info-Gap robustness analysis is indeed local in nature.

So how is it that in his recent FAQs paper on his website Ben-Haim still claims the opposite: (FAQ paper, page 2):

2. An info-gap analysis is not based on an estimate of the true horizon of uncertainty. That is, the info-gap model of uncertainty is not a single set, $\displaystyle U(\alpha ,{\tilde {u}})$. Rather, an info-gap model is a family of nested sets, $\displaystyle U(\alpha ,{\tilde {u}}){\text{ for all }}\alpha >0$ . The family of sets is usually boundlessly as the unknown horizon of uncertainty, $\ \alpha$, grows. Thus an info-gap model is not a “local analysis of risk” since the family of sets expands, usually boundlessly, as the unknown horizon of uncertainty, $\alpha$, grows. Info-gap theory is not a worst-case analysis, since there is no known worst case in an info-gap model of uncertainty.

And the spin goes on and on and on ....

3. Treatment of severe uncertainty

Info-Gap is presented and promoted as a theory for decision under severe uncertainty, Yet, Sneidovich's Invariance Theorem shows that actually Info-Gap's robustness model does not deal with severe uncertainty, it simply ignores it.

No amount of spin can change this fact.

So why don't we tell the public what all of us here know only too well, namely that Info-Gap actually does not deal with severe uncertainty, it simply ignores it? Is Info-Gap trying to hide this important fact from the public?

---

So what exactly is Info-Gap's contribution to the state of the art in decision-making under severe uncertainty?

Ben-Haim summarizes the answer to this question very eloquently in the last sentence of this paragraph taken from the current version of the WIKIMEDIA article:

The problem is that in situations of severe uncertainty these gaps are deviations from a poor estimate of the true (but unknown) value of the parameter of interest. Info-Gap's robustness analysis is thus conducted in the neighborhood of an estimate that is likely to be substantially wrong. Consequently, the results obtained are equally likely to be substantially wrong. On the other hand, the estimate is the best one has, so it is sometimes useful to know if it can err greatly and still yield an acceptable outcome.

No amount of spin can change this fact.

In short, what emerges from this discussion is that Info-Gap is new and radically different in the sense that it was not aware of its being based on a Maximin model and that although it is supposed to be a methodology for decision under severe uncertainty, it actually ignores severe uncertainty.

The rest, unfortunately, is mostly spin.

The Plan

I am working on the final details of a constructive plan to resolve the dispute. I shall post it here either on Saturday or on Sunday (Melbourne Time). Sniedo (talk) 02:23, 11 January 2008 (UTC)

Response to Sniedo

1. Please refrain from making uncivil remarks. Sarcastic comments such as "we can even write a script for a play on this interesting subject" do not contribute to the discussion, and may result in your user being blocked.
2. As I have tried to explain several times already, we are not trying to agree on whether or not info-gap is a novel theory. We are only trying to ascertain what the scientific consensus about info-gap is. As you said yourself: "Info-gap is indeed propounded in many publications, held by many proponents, and is at present a majority position." Yours is a minority view and should be treated as such.
3. The claim that info-gap theorists were unaware of the relation to minimax before you came along is historically incorrect. See, for example, this 2005 publication where an info-gap-based estimator is shown to be "mathematically equivalent" to the corresponding minimax estimator. From that article: "Similarities notwithstanding, minimax and MPS [info-gap] estimators differ qualitatively in the type of information on which their design is based." Thus, the relation to minimax has not gone unnoticed, nor has the info-gap community been silent about its meaning.
4. I have proposed above a method for resolving this dispute, namely, making the majority of the article describe the consensus view of info-gap, and having a short section describing your criticism, plus a one-sentence mention of this criticism in the lead. The other contributors to this page have agreed to this proposal, so I hope the "plan" you are preparing will be along these lines. The article we end up with should reflect the Wikipedia consensus.

Zvika (talk) 08:48, 11 January 2008 (UTC)

Response to Zvika

G'day:

1. I address your remark on civility below.

2. Aren't you basically saying that facts about Info-Gap (theorems, examples) provided by the Minority will be excluded from the article even though their validity is not questioned by the majority? Isn't this tantamount to presenting to the public an inaccurate, biased depiction of Info-Gap?

3. As for your reference to your 2005 Info-Gap paper. Your statement that the paper's existence shows that:

The claim that info-gap theorists were unaware of the relation to minimax before you came along is historically incorrect.

is a misrepresentation of my position. In the article I state the following:

Although none of the three Info-Gap books (Ben-Haim, 1996, 2001, 2006) either refers to Maximin, or discusses its relation to Info-Gap's robustness model, claims have been made in other publications (eg. Ben-Haim 2005) that Info-Gap's robustness model is related to Maximin, but is not a Maximin model.

So it is patently clear that, contrary to your claim, I am well aware that "Info Gap theorists" examined around 2005 the Info-Gap - Maximin connection.

My point was that the conclusion reached, namely that Info-Gap's robustness model is not Maximin, was erroneous.

Indeed, isn't it clear from your 2005 paper that its authors were unaware that their MPS robustness model is not just similar to but different from maximin? That it is in fact a simple exercise to show formally that your Info-Gap inspired MPS robustness model is a simple instance of Wald's Maximin model?

Rather, the question that I have been calling attention to over the last few years and which I raised in this discussion is this:

And what are we to conclude from the fact that Ben-Haim does not even mention Maximin in his three Info-Gap books?

So, I repeat, the question is:

what are we to conclude from the fact that over a period of 10 years, none of the three books that introduced and expounded Info-Gap so much as hinted at the existence of Maximin, let alone discussed its relationship to Info-Gap?

4. Regarding the plan to revise the article. The identities of "the other contributors to this page" who "have agreed to this proposal" are of interest. As the record shows, they are Yakov Ben-Haim the (creator of Info-gap), Zvika Ben-Haim, and Lior Davidovitch.

For the record, I am posting my counter-plan.

---

Now back to civility.

Is it civil to give the public and contributors to this article/discussion the impression that you are acting as an impartial "arbitrator" not too familiar with the subject under discussion, yet when it suits you, you present yourself as an "info-gap theorist" with a track record on the Info-Gap - Maximin connection?

On August 14, 2007 you stated:

Not being too familiar with the subject, I don't want to start an argument here.

And on January 7, 2008:

I would like to offer my view as someone without very much knowledge of info-gap, but with some experience in resolving Wikipedia disputes.

Now, again, I am not an expert on Info Gap, but from the article it seems that there is quite a wide range of published material supporting Info Gap (two editions of a book from a reputable publisher, and quite a few peer reviewed articles by many different authors) ...

Yet, now you position yourself as an "Info Gap Theorist", citing your 2005 paper.

Indeed, for this and other reasons, is it civil that an arbitrator does not disclose at the outset a possible conflict of interest?

Please note that these questions are rhetorical. Sniedo (talk) 07:13, 13 January 2008 (UTC)

I never said I was an impartial arbitrator. In fact, as you can see below, I am actively trying to get an impartial arbitrator to be involved here so that we can end this dispute once and for all. I simply offered what I think is a fair resolution to this conflict. Like you, I have contributed substantially to this article, so I think neither of us is impartial. I have one publication related to info-gap, and I don't think that makes me an expert on the subject. I guess that's a difference between the two of us. --Zvika (talk) 08:45, 13 January 2008 (UTC)

Sniedo's Counter Proposal

Rationale

The current state of Info-Gap is utterly different from that of two years ago. This is due to our better understanding of Info-Gap and its relationship to classical decision theory and robust optimization.

It is therefore imperative that the new version of the article give the public an accurate and up to date account of Info-Gap and its role and place in decision theory.

Whereas in 2006 Info-Gap was portrayed as a new theory for decision under severe uncertainty that is radically different from all current theories for decision under uncertainty, today Info-Gap has to contend with two relatively new theorems, namely the Maximin Theorem and the Invariance Theorem.

The first refutes the assertion that Info-Gap's robustness model is new and radically different. The second refutes the contention that Info-Gap is a methodology for decision under severe uncertainty and it alerts us to the fact that Info-Gap is subject to the Wrong-in Wrong-out Axiom.

In short, these two theorems indicate that as a methodology for decision under severe uncertainty Info-Gap is fundamentally flawed.

While the Majority does not question the validity of these theorems, it does not accept their obvious implications that Info-Gap is thoroughly unsuitable for severe uncertainty. In other words, the Info-Gap majority does not subscribe to the Wrong-in Wrong-out Axiom. It believes that, somehow, a local analysis in the neighborhood of an estimate that is likely to be substantially wrong can generate robust solutions under severe uncertainty.

This, it should be noted, is incongruent with Ben-Haim's current position. Ben-Haim now concedes (see article) that Info-Gap's robustness analysis is local thereby implicitly accepting the Wrong-in Wrong-out Axiom.

The entire debate is summarized clearly in the following paragraph (from the Preview of the current article):

The problem is that in situations of severe uncertainty these gaps are deviations from a poor estimate of the true (but unknown) value of the parameter of interest. Info-Gap's robustness analysis is thus conducted in the neighborhood of an estimate that is likely to be substantially wrong. Consequently, the results obtained are equally likely to be substantially wrong. On the other hand, the estimate is the best one has, so it is sometimes useful to know if it can err greatly and still yield an acceptable outcome.

The last sentence was written by Ben-Haim.

So the plan I propose below is based on the idea that Info-Gap's prescription for the treatment of severe uncertainty cannot be accepted unless it is shown to be capable of neutralising the Wrong-in Wrong-out Axiom.

The Plan

1. Content

The content of the current version of the article is more or less adequate. It covers all the essential issues, including two related simple illustrative examples.

2. Organization

A radical re-organization of the article's current structure is a must. The topics listed under Critique should not be classified as such. In particular, the Invariance Theorem is not criticism as such. It is a simple mathematical truth. And so is the observation that Info-Gap's robustness analysis is inherently local. The same is true about the existence of pathological cases. These are facts.

All these are properties of the basic Info-Gap paradigm and should be retained. The second example must also be retained. It is not criticism. It illustrates Info Gap in action.

Criticism comes into the picture when these mathematical facts are given concrete practical meanings.

So my suggestion is that the revision of this article be done in two stages. The first should be criticism-free: it should present the facts for what they are: facts.

This done the next stage should be devoted to the practical implications and interpretations of the facts. Here we shall have to deal with the dispute between Sniedovich and Ben-Haim on this matter. An attempt should be made to find a way to deal with the discrepancy between the two positions so as to be able to document it properly in the article. This should be done on a point by point basis.

Summary

Sneidovich's criticism is informative as it is based on a detailed rigorous analysis of the basic facts about Info-Gap's generic model. These facts are not discussed in the Info-Gap literature even though their validity is not questioned by the Majority. The proposed plan is based on the idea of separating facts from criticism: retaining the facts for the next version of the article and taking care of the criticism in future updates.

Practically speaking, the revision can be done rapidly and effortlessly by removing small segments of text from some of the sections and renaming some of the sections/subsections. Sniedo (talk) 07:13, 13 January 2008 (UTC)

RfC: Relative emphasis of different views

I believe the following facts are agreed upon:

• Info-gap decision theory is "propounded in many publications, held by many proponents, and is at present a majority position."
• A recent publication by Sniedovich (User:Sniedo) demonstrates that info-gap-based decisions can be formulated as minimax problems.

The point of contention is the following:

• User:Sniedo claims that his recent publication "completely undermine[s] the foundation of Info-Gap decision theory and prove[s] the majority wrong" and wants the article to state as much, in order to convince the majority of their error.
• User:Zvika claims that the majority of the relevant scientific community interprets Sniedovich's results differently, and that the Wikipedia article should give the most emphasis to the majority's view.

Further details and discussion can be found above.

Comment: Fundamentally, User:Sniedo has no standing to push his own results in wikipedia article editing, per WP:COI. It's OK for him to bring his results to the attention of other editors here on the talk page, but then he must recuse himself from the decision of whether to include those results, or how much emphasis to put on them, in the article. Furthermore, while wikipedia has a policy of representing all points of view, that includes not putting undue weight on minority points of view; so if there's a new result that contradicts the whole field, that should be mentioned, but until the field is somewhat converted it should probably be treated as a minority viewpoint. This comment is based only on the summary above; I have not looked at his publications or the article at all, so if I've got the premises wrong please correct me. Dicklyon (talk) 09:05, 13 January 2008 (UTC)

Having read more of the discussion above, it now appears that maybe all of the editors have a WP:COI problem. Are there any editors who do not have a professional or academic stake in this topic? Dicklyon (talk) 09:20, 13 January 2008 (UTC)

We are all people with some experience with info-gap. I don't think that disqualifies us from editing the article, but we all need to be careful from pushing our POV. From WP:COI:

Editing in an area in which you have professional or academic expertise is not, in itself, a conflict of interest. Using material you yourself have written or published is allowed within reason, but only if it is notable and conforms to the content policies. Excessive self-citation is strongly discouraged. When in doubt, defer to the community's opinion.

This is primarily why I am seeking outside opinion -- to get an objective opinion on what the extent of info-gap criticism should be in the article. --Zvika (talk) 09:37, 13 January 2008 (UTC)

OK, first, I should have read more before commenting. I agree with the COI section quoted above, that a COI does not rule out the ability to contribute; but it does mean that one should not drive decisions in areas in which they have a conflict, which is going to make it hard for all of you. In this case, unless we get some editors here with significant understanding of the top, but without COI, it's going to be hard to converge. Still, I agree with Zvika that the emphasis in the article should not be too different from the emphasis in the literature. The trouble with Sniedo's suggestion is likely that there will be disagreement on what the simple "facts" are. Facts that he derives may not be accepted as facts by others, which seems to be the crux of the disagreement. Am I right? Dicklyon (talk) 18:20, 13 January 2008 (UTC)

I sympathize with an editor who faces the daunting task of wading through the volume of this discussion. However, careful reading will distinguish personal interpretation from fact. I will present a few examples. The crux of the issue is adherence to NPOV and "due balance". Sniedo makes various claims which are in fact interpretations. For instance, consider the following quotes from Sniedo's contribution:

• "This means that the Info-Gap methodology does not deal with severe uncertainty, it simply ignores it and ... hopes for the best!"

This is an inaccurate interpretation of info-gap decision theory, based on a very fragmentary understanding of the theory. Among other evidence, is the fact that many applications of info-gap theory have been successfully made, and published, in situations of difficult decisions under severe uncertainty. But most importantly, this interpretation is in no way a fact; it is Sniedo's opinion, and not the opinion of the many authors who have used and are using info-gap theory.

• "Its [info-gap theory's] generic robustness model is a simple instance of Wald's famous maximin model."

Sniedo's statement is an inaccurate and superficial conclusion from the fact that the info-gap robustness function can be represented in a maximin form. However, Sniedo's conclusion is not consistent with the fact the info-gap robust decisions sometimes agree with maximin decisions, and sometimes do not. As decision theories, maximin and robust-satisficing are not the same. Once again, Sniedo has an opinion which is not a fact. The representation is the fact; the behavioral difference between info-gap the maximin is a fact; but info-gap being subsumed in maximin is Sniedo's (mistaken) interpretation.

• "Differently put, Info-Gap's robustness model is based on a definition of robustness that is local in nature so that the robustness analysis is conduted [conducted] in the locale of a bad (wrong) estimate. We thus have to assume -- methodologically speaking -- that the results are also bad (wrong)."

The conclusion is fallacious, and ignores the issue of how one uses the robustness function. Most importantly, the "fact" here -- that "the results are also bad (wrong)" is not a fact at all. It is Sniedo's preference, perhaps, for other decision methodologies.

• Finally, the vast proportion of the article which is devoted to Sniedo's opinions does not represent a balanced picture of the scientific consensus as expressed in numerous publications by many authors. Ybenhaim (talk) 21:26, 13 January 2008 (UTC)

If there's a published retutation of his incorrect "facts", that could be referenced, that might be useful. Otherwise, let's just say who says what, and not make claims for one or another thing being "fact". I agree that Sniedo's part of the article should be kept to a modest proportion. Dicklyon (talk) 22:20, 13 January 2008 (UTC)

Response to Ben-Haim

1. As Sniedo explains in the article, Ben-Haim's claim that Maximin Theorem is not accurate is wrong. The decisions generated by Sniedo's Maximin model always -- I repeat always -- agree with the Info-Gap robust decisions. As Sniedo clearly explains in the article, it is Ben-Haim's model that is not always equivalent to the Info-Gap robustness model (see further explanation in a new section below).
2. Does Ben-Haim really claim that Info-Gap's robustness model has a cure for the Wrong-in Wrong-out Axiom? If so, can he please spell it out: can he please explain how Info-Gap local robustness analysis in the neighborhood of a poor estimate that is likely to be substantially wrong produces results that are guaranteed not to be substantially wrong? How do we know, for example, that a decision that is not robust in the neighborhood of the estimate is also not robust in other parts of the total region of uncertainty? There is nothing in the Info-Gap robustness model that addresses this issue. Can Ben-Haim indicate in what page of the 2006 book it is proved that the robustness model cures the difficulty associated with the Wrong-in Wrong-out Axiom?
3. Ben-Haim should also address the issues that Sniedo has repeatedly raised:
   1. Given the close relationship between Info-Gap and Maximin, how is it that none of the three Info-Gap books mention Maximin, let alone discuss its relation to Info-Gap?
   2. Given the close relationship between Info-Gap and Maximin, on what grounds does Ben-Haim (2001, 2006) claim that Info-Gap theory is radically different from all current theories for decision under uncertainty? Sniedo (talk) 01:39, 15 January 2008 (UTC)

Second Response to Zvika

1. As clearly indicated by the history of this discussion, in the early stages Zvika presented himself as a person "Not being too familiar with the subject" and as "someone without very much knowledge of info-gap". Later on Zvika considers himself as an "Info-Gap theorist". So how should we classify Zvika now: as "not being too familiar with the subject", as an "Info-Gap theorist", or as "someone without very much knowledge of info-gap"?
2. For the record, it looks like Zvika's attempt to bring in an impartial arbitrator began only after Sniedo's raised the possibility of a conflict of interest.
3. In any case, the conflict of interest issue is not related to your familiarity with Info-Gap. It is related to you very close personal (family) relationship with Yakov Ben-Haim.
4. One does not have to be an Info-Gap theorist to conclude and show formally that Info-Gap's robustness model is (a) a Maximin model and (b) fundamentally flawed under severe uncertainty. Sniedo (talk) 01:39, 15 January 2008 (UTC)

Response to Dick Lyon

1. Sniedo is not trying to push his own results into the article.
2. Sniedo is trying to convince the contributors to this discussion that all important FACTS about Info-Gap should be included in the article, even those provided by the minority. Facts are facts.
3. There are many facts that are not disputed by the majority. Sniedo's Counter-Proposal proposes that only undisputed facts should be incorporated in the new version of the article.
4. The possible COI issue that Sniedo raised was not with regard to Zvika's academic interest/expertise in Info-Gap. This was a CIVILITY issue (see Sniedo's responses to Zvika).
5. The COI issue is the very close personal (family) relationship between Zvika and Ben-Haim.
6. WIKIPEDIA's guidelines are very clear on this matter. Sniedo (talk) 01:39, 15 January 2008 (UTC)

Why does Sniedo always talk about himself in the third person and state as facts things that are clearly only his own POV? Even the statement "WIKIPEDIA's guidelines are very clear on this matter" is rather cryptic, since it doesn't say which guideline, or which matter, and in my experience they're never all that clear. Anyway, you guys have a mess here, and I don't think I have any good way to help. Dicklyon (talk) 04:32, 15 January 2008 (UTC)

This is Sniedo's style. So what you are saying, Dick, is that you are not familiar with Wikipedia's guidelines for WP:COI? Is this a FACT? If so, I suggest that you read it. Sniedo (talk) 06:01, 15 January 2008 (UTC)

More on the Info-Gap Maximin Connection

In the article Sniedo explains in detail why Ben-Haim's assertion that Info-Gap's robustness model is not a Maximin model is wrong. But Ben-Haim keeps raising this issue.

So here is a clarification of the flaw in Ben-Haim's argument. To make the point crystal clear I incorporate $\ q$ as a decision variable in the maximin models so that it is easier to compare Ben-Haim's model with Sniedo's model.

There are two different claims here, namely:

Sniedo's Maximin Theorem:

(1) $\quad \max _{q\in {\mathcal {Q}}}\max \left\{\alpha :\ {r_{\rm {c}}}\leq \min _{u\in {\mathcal {U}}(\alpha ,{\tilde {u}})}R(q,u)\right\}=\max _{q\in {\mathcal {Q}},\alpha \geq 0}\min _{u\in {\mathcal {U}}(\alpha ,{\tilde {u}})}f(q,\alpha ,u)$

where

(2)$\quad f(q,\alpha ,u):=\left\{{\begin{matrix}\alpha &,&{r_{\rm {c}}}\leq R(q,u)\\-\infty &,&{r_{\rm {c}}}>R(q,u)\end{matrix}}\right.\ ,\ \alpha \geq 0,u\in {\mathcal {U}}(\alpha ,{\tilde {u}})$

Ben-Haim's Claim:

(3) $\quad \max _{q\in {\mathcal {Q}}}\max \left\{\alpha :\ {r_{\rm {c}}}\leq \min _{u\in {\mathcal {U}}(\alpha ,{\tilde {u}})}R(q,u)\right\}{\stackrel {\text{not always}}{=}}\max _{q\in {\mathcal {Q}}}\min _{u\in {\mathcal {U}}(\alpha ^{\circ },{\tilde {u}})}R(q,u)$

The "not-always" clause in Ben-Haim's claim refers to the value of $\alpha ^{\circ }$ used. For some values the equation holds for others it does not hold.

Now, the obvious thing to note is that the Maximin model deployed by Ben-Haim is significantly different from the Maximin model deployed by Sniedo. That is,

(4) Sniedo's Maximin model:   $\quad \max _{q\in {\mathcal {Q}},\alpha \geq 0}\min _{u\in {\mathcal {U}}(\alpha ,{\tilde {u}})}f(q,\alpha ,u)$

(5)   Ben-Haim's  Maximin Model:    $\quad \max _{q\in {\mathcal {Q}}}\min _{u\in {\mathcal {U}}(\alpha ^{\circ },{\tilde {u}})}R(q,u)$

where $\displaystyle \alpha ^{\circ }$ denotes an estimate of $\displaystyle \alpha$.

Hence, the validity of Ben-Haim's claim does no refute the validity of Sniedo's claim. Ben-Haim's claim indicates the obvious, namely that HIS Maximin model is not equivalent to Info-Gap's robustness model.

This does not refute the FACT that Info-Gap's robustness model is a simple instance of Wald's Maximin model, that is the instance deployed by the Maximin Theorem.

In short, Ben-Haim's claim that Info-Gap's robustness model is not an instance of Wald's Maximin model is, plainly speaking, wrong.

The decisions generated by the Maximin model deployed by the Maximin Theorem are always -- I repeat always -- the same as those generated by Info-Gap's robustness model, that is

Corollary 15/01/08

(6) $\quad \arg \max _{q\in {\mathcal {Q}}}\max \left\{\alpha :\ {r_{\rm {c}}}\leq \min _{u\in {\mathcal {U}}(\alpha ,{\tilde {u}})}R(q,u)\right\}=\arg \max _{q\in {\mathcal {Q}},\alpha \geq 0}\min _{u\in {\mathcal {U}}(\alpha ,{\tilde {u}})}f(q,\alpha ,u)$

In words, a decision $\ q$ is optimal wrt Info-Gap’s robustness model if and only if it is optimal wrt Sniedo’s Maximin model.

I cannot make this point more clear. Sniedo (talk) 01:39, 15 January 2008 (UTC)

As a matter of fact,

In his Counter-Proposal Sniedo suggests that the best way to resolve the "facts" issue and the dispute as a whole is to remove from the next version of the article any criticism of Info-Gap.

The next version of the paper should include only undisputed facts.

The following list consists of such facts and should, in any case, be included in the next version of the article. None is a criticism of Info-Gap.

Obviously, the list is not complete. There are of course many other facts about Info-Gap.

Fact 1:

In the last two Info-Gap books, Ben-Haim (2001, 2006) presents Info-Gap as a new theory that is radically different from all current theories of decision under uncertainty.

Fact 2:

Maximin is a major classical paradigm for decision under severe uncertainty and robust optimization.

Fact 3:

The three Info-Gap books, Ben-Haim(1996, 2006, 2006), do not mention Maximin, let alone discuss its relation to Info-Gap.

Fact 4:

Ben-Haim (2005) claims that Info-Gap's robustness model is similar to, but different from, Maximin.

Fact 5:

Sniedovich (2007) proves that Info-Gap's robustness model is a simple instance of Wald's Maximin model (Maximin Theorem).

Fact 6:

Sniedovich (2007) proves that Info-Gap's robustness model is invariant with the total region of uncertainty when the latter is larger than the region of uncertainty associated with the robustness of a decision (Invariance Theorem).

Fact 7:

Ben-Haim (2006) claims that usually the total region of uncertainty is unbounded. Hence, usually the safe region of uncertainty is miniscule in size in comparison to the total region of uncertainty.

Fact 8:

Info-Gap's robustness model has a No-Man's Land property (see article). In the usual (unbounded) case, the No-Man's Land region constitutes essentially the entire region of uncertainty.

Fact 9:

Ben-Haim (2006) asserts that in situations of severe uncertainty the estimate is a poor indication of the true value of the parameter of interest and is likely to be substantially wrong.

Fact 10:

Info-Gap's robustness analysis is local in nature and is conducted in the immediate neighborhood of an estimate that is likely to be substantially wrong.

Fact 11:

Info-Gap's robustness model has a Preference Reversal property (see article).

Fact 12:

A simple numerical example (see article) produces a situation where the total region of uncertainty is ${\mathfrak {U}}=(-\infty ,\infty )$ and ${\mathcal {U}}({\hat {\alpha }}({\hat {q}},r_{c}),{\tilde {u}})=(-2,2)$. The picture is this:

---

I repeat:

1. These are FACTS whose validity can be easily verified.
2. These FACTS do NOT criticize Info-Gap.

So let us leave aside the criticism and include in the new version of the article only FACTS, just simple old fashion FACTS.

Then we can gradually address the criticism, if any.

Remark:

I suggest that users/editors who cannot check on their own the validity of theorems such as the Maximin Theorem and the Invariance Theorem should refrain from expressing opinions about the technical aspects of Info-Gap. Sniedo (talk) 01:39, 15 January 2008 (UTC)

Let's make a deal!

The discussion is getting more and more interesting but we are going nowhere here and it is time to do something constructive about the article.

Sniedo posted a proposal and I suggest that all the contributors to this discussion should examine it carefully.

How can we go wrong by taking out all the criticism and retaining only FACTS that are agreed upon by this group? Sniedo (talk) 01:39, 15 January 2008 (UTC)

Response:

1. Sniedo's position is clear.

2. Some of the assertions which he makes are disputed by many people. These disputed assertions are points of view (POVs).

3. Wikipedia is not the proper forum for resolving those disputes.

4. Wikipedia should represent POVs as such, and in proportion to their support in the community. Dicklyon has suggested: "I agree that Sniedo's part of the article should be kept to a modest proportion." We all agree that Sniedo's contributions to the subject should be represented, but with due balance.

5. I will prepare a version of the article which presents info-gap theory, and Sniedo's POVs in appropriate proportion.

6. Since Sniedo repeatedly points out that I do not refer to maximin ideas in my books, I would like to mention that there is discussion of relations between info-gap robust-satisficing and worst-case analysis (another name for maximin) in a number of my other publications, including the following:

• Yakov Ben-Haim, 2005, Info-gap Decision Theory For Engineering Design. Or: Why `Good' is Preferable to `Best', appearing as chapter 11 in Engineering Design Reliability Handbook, Edited by Efstratios Nikolaidis, Dan M.Ghiocel and Surendra Singhal, CRC Press, Boca Raton.

• Yakov Ben-Haim, 2005, Value at risk with info-gap uncertainty, Journal of Risk Finance, vol. 6, #5, pp.388-403.

• Izuru Takewaki and Yakov Ben-Haim, 2005, Info-gap robust design with load and model uncertainties, Journal of Sound and Vibration, 288: 551-570. Ybenhaim (talk) 06:26, 15 January 2008 (UTC)

Sniedo's Response:

• I am very pleased that my position is clear.
• I am not aware of anyone disputing my assertions except the three other participants in the technical discussion, namely:
  • Yakov Ben-Haim (creator of Info-Gap)
  • Zvika (a student)
  • Lior Davidovitch (apparently a student)

all three apparently from the same academic institution. Note that according to Zvika, the validity of my theorems is not questioned. So is there really much substance to the majority vs minority issue?! Indeed who are the "many people" referred to by Ben-Haim and what exactly do they dispute? For the record, I know many people who agree with my views on Info-Gap.

• I agree that Wikipedia is not a proper forum for resolving disputes of this nature. This is precisely why I proposed that the new version of the article should be based only on facts. The next version of the article should be criticism-free.
• Many of Ben-Haim's statements in this article, and elsewhere, are his very own POVs. On the other hand, Sniedo spells out formal proofs demonstrating that some of these POVs are inaccurate, contradictory, fallacious. Wikipedia should not publish fallacious or inaccurate statements.
• No one can prevent Ben-Haim from preparing a new version of the article. But it will be wrong for Ben-Haim to write both his POV and the opposing POV. Needless to say, should my advice not to divide the article between Ben-Haim's point of view and Sniedo's point of view be ignored, I insist on writing my point of view myself. In any event, Ben-Haim should post his new version of the paper on this discussion page for comments/suggestions before changing the current article.
• Ben-Haim again does not explain why his three books on Info-Gap are Maximin-free. As for the 2005 papers, as I indicated on several occasions, I am thoroughly familiar with Ben-Haim's 2005 papers in which references are made to Worst Case analysis and/or Maximin. For the record, in these -- and other -- papers Ben-Haim contends that Info-Gap's robustness model is not a Maximin model. As I proved above, and elsewhere, this contention is erroneous. I have also explained, above and elsewhere, the flaw in Ben-Haim's argument. In any case, could Ben-Haim provide once and for all clear answers to the following questions:

Given the "close relationship" between Info-Gap and Maximin, how is it that none of the three books on Info-Gap mention Maximin, let alone discuss its relation to Info-Gap?

Given the "close relationship" between Info-Gap and Maximin, on what grounds does Ben-Haim (2001, 2006) claim that Info-Gap theory is radically different from all current theories for decision under uncertainty?

• It is also appropriate to ask Ben-Haim to clarify his position wrt Sniedo’s two theorems:

Does Ben-Haim, in contrast to Zvika, actually dispute the validity of the Maximin Theorem and the Invariance Theorem?

Action:

I shall be happy to prepare a criticism-free version of the article, based only on facts, and post it on this discussion page for comments/suggestions. Any comments on this idea? Sniedo (talk) 03:14, 17 January 2008 (UTC)

RfC again

Hi. I'm responding to the RfC on this article as well. For the record, I am a somewhat experienced Wikipedia editor, and I have a Ph.D. in mathematics, but I have little knowledge of decision theory and had never heard of Info-Gap before today.

I agree with a previous comment that this is a bit of a mess, and that I have no magic solution to suggest, when there is such obvious contention. So I will just focus on issues of Wikipedia policy and guidelines. Foremost is that Wikipedia runs on verifiability, not truth. That is a very difficult thing for many contributors to accept, and Sniedo's comments show clearly, I think, that he disagrees with this policy. Many of the long arguments and deductions made by Sniedo in this talk page are inappropriate, and amount to original research, since they are discussions about the subject of the article, not about the article itself. While it is quite likely that such a discussion needs to take place somewhere, the discussion on this talk page should simply focus on what the relevant literature says, and what weight various positions should be given, based solely on what already exists in reliable sources.

For example, if Sniedo produced a number of citations of papers (comparable to the number that are already cited), not primarily by himself, that voice exactly the criticisms that he wishes to include in the article, then it would make sense to give them more weight and more space in the article. I can't see that he has done that; please correct me if I am in error. But detailed proofs and expositions of theorems, even if technically correct, are simply not relevant, by the policies of Wikipedia. Again, that may seem strange, but that is how this enterprise works.

Sniedo has proposed that the article stick to "facts." It should indeed avoid opinion, POV-pushing, and interpretation. But it also should avoid anything that is not already published in a reliable source; and it should avoid giving undue weight to anything that is not a majority opinion. I'm sorry if anyone feels that this is not the correct way to write an encyclopedia; it is, however, the policy for Wikipedia.

I hope that is slightly helpful; responses and comments are welcome. -- Spireguy (talk) 17:31, 18 January 2008 (UTC)

I second that. But I also wonder if we should have an article here at all. What about notability? Where are the citations to multiple independent reliable sources about the topic? If the publications are all by the principles, who are editors there, then there's no independent evidence of notability. Deleting the article would be an easy way out of the mess. Or, cite the independent sources (find some here), and focus the content on what THEY say, not on the primary sources by Ben-Haim; published criticisms should be included, but should not be added to the article by the person who wrote them. If you guys will work on a realistic rewrite in terms of sources, without practicing WP:COI, I can help. If Sneido feels his published works are being misrepresented or underrepresented in the article, he can say so here, and I'll take a look at balancing it. But arguing about what's a "fact" is pointless. Dicklyon (talk) 20:35, 18 January 2008 (UTC)

I also agree with Spireguy. Thanks for a very lucid explanation, I may quote you sometime in some future argument :)

As for deletion: Given the mess the article is in right now, I have also thought of this option. However, I don't think notability of info-gap can seriously be questioned:

1. Google Scholar lists 264 papers with the word "info-gap".
2. Google Scholar lists 174 citations of the info-gap book.
3. The current version of the article contains references to several papers on info-gap which do not include Ben-Haim as the author. I count four such peer-reviewed articles with 10 different authors. Three other papers have Ben-Haim as one of several others authors.

I think this counts as multiple independent reliable sources. If the article is deleted, it is not because of lack of notability but because we have grown tired of arguing with a single, persistent user, and that would be a shame. --Zvika (talk) 06:58, 19 January 2008 (UTC)

I agree that the subject is notable, so there is no cause for deletion. But focusing on independent sources is crucial. -- Spireguy (talk) 14:12, 19 January 2008 (UTC)

So, Zvika, you seem to support the spread of the view that Info-Gap is a new theory that is radically different from all current theories for decision under uncertainty! And you are also happy to support the spread of the obviously wrong view that Info-Gap's robustness model is not a simple Maximin model! And you also do not mind the spread of the view that Info-Gap actually deals with severe uncertainty even though the Invariance Theorem tells us that this is not so!

What a shame!

Your recent statistics only prove my point: many people out there are wrong. I have seen it before and this is precisely why I participate in this discussion. Sniedo (talk) 05:28, 20 January 2008 (UTC)

I do not "support the spread" of any view. I am just trying to ascertain the current state of scientific consensus, which, as we are all trying to explain to you, is the single most important point to settle on before writing the article. --Zvika (talk) 09:33, 20 January 2008 (UTC)

Sniedo's Response to Spireguy:

1. Sniedo's long arguments are not Original Research a la Wikepedia. As Sniedo clearly indicates in the article and in this discussion, his arguments are not new: they appeared already in a peer reviewed article Sniedovich (2007). They were restated here for the convenience of the participants in this discussion.
2. Sniedo's comments are not just about the subject of the article, they are also very much about the article itself. Wikipedia's policy regarding correctness and accuracy is crystal clear, and the arguments are intended to improve the correctness and accuracy of the article. So for example, saying that Info-Gap robustness model is related to Maximin is unacceptable if the fact is that "Info-Gap robustness model is a simple instance of Wald's Maximin model". Sniedo's comments are mostly about inaccuracies in previous versions of the article.
3. Sniedo's arguments (including theorems and proofs) already exist in a reliable source (peer-reviewed article) so they definitely meet Wikipedia's requirements.

Which crystal clear policy are you referring to in 2 above? WP:V? Or another one? To me, it's not at all clear whether there's a policy in support of what you're trying to do here. Dicklyon (talk) 01:36, 20 January 2008 (UTC)

In short, Sniedo does not attempt to publish in this article Original Research findings. He prefers, in fact very much prefers, to publish his Original Research findings in books and peer-reviewed articles. He has been doing this for over 30 years now. His basic arguments, including the two theorems and their proofs, in the article and in this discussion, are all taken from a peer-reviewed article.

It is not clear who created the impression that this is not the case and why it is necessary to raise this none-issue. Sniedo (talk) 00:29, 20 January 2008 (UTC)

Sniedo's response to Zvika:

If you care to examine my publication record you'll notice that over the years I have published many articles showing how wrong experts can be and that even the best journals occasionally publish obviously "wrong" articles.

I have served on the editorial boards of a number of international journals for many years and I am familiar with this difficulty.

In any case, I have done it many times before and I'll do it again with Info-Gap.

The reason: Info-Gap theory is fundamentally flawed on all fronts, namely conceptually, methodologically, technically, and theoretically.

Incidentally, you might be interested in the following fact.

After one of my recent lectures on Info-Gap, a prominent Info-Gap person, the author of many peer reviewed articles about Info-Gap declared in public that he agreed with my two main points, namely

1. Info-Gap’ robustness model is a simple Maximin model.
2. Info-Gap’s robustness model is not suitable for decision-making under ‘’’severe’’’ uncertainty.

On a related issue, I know a large number of authors of peer-reviewed Info-Gap articles. None is an expert on decision theory. So here you go.

Anyhow, I suggest that instead of criticising me, defenders of Info-Gap should look at the basic facts and try to cope with them.

Just for the record: Do you now question the validity of the Maximin Theorem and the Invariance Theorem? If so, say so. Sniedo (talk) 00:29, 20 January 2008 (UTC)

About … The Mess,

It is a bit depressing to hear from a number of Wikipedia editors that this article is in a mess.

I do not see where the mess is and I think that it would be very unfortunate if this article will be deleted.

All that is needed now to fix this article is for all participants to refrain from making unsubstantiated statements. This is not difficult at all because the topic under consideration is mathematical in nature and the mathematical sophistication required for a meaningful discussion is minimal.

Furthermore, there seems to be a general consensus that the validity of Sniedo's two theorems is not questioned.

So where exactly is the dispute?

The dispute is with regard to certain implications of these theorems for the role and place of Info-Gap in decision theory.

My suggestion is then that for the time being we ignore these certain implications and accept the theorems themselves, as they are, for what they are: mathematical facts about Info-Gap that have been published in a peer-reviewed article. The implications of these mathematical facts will be dealt with in subsequent revisions of the article, if ever.

This will completely resolve the current dispute.

There is, however, the practical question of who should write the next version of the article.

I suggest that this should be a collaborative teamwork. Since the topic is mathematical in nature, how about volunteering the trio

• Spireguy
• Zvika
• Sniedo

for this task, asking them to prepare, behind the scenes, a new article, say in a month or so?

I realize that Zvika is in a conflict of interest position, but I will not object at all to his participation in this teamwork. In fact, I would like to invite him personally to join the team.

I am confident that this team will be able to compose an article that will be informative, correct, accurate, useful to the public and non-controversial.

Although Sniedo is very busy now with an intensive summer course on ... The art and science of Decision- Making, he will be happy to contribute his time and expertise to a successful resolution of this dispute.

In any case, I vote for this suggestion! Sniedo (talk) 00:29, 20 January 2008 (UTC)

The mess is not the article, it's the editing situation around it. All the editors have clear POV and COI, and different interpretations of what is a fact. Lacking a better idea, I'd say go ahead and edit the article to make improvements. Don't do it off on the side for a month, just do it normally. When disagreements come up, ask for outside opinions to resolve them; some of us will be watching, so you won't have to ask. It will be easier to outsiders like me to make judgments on specific issues, when we see who is making or objecting to what changes, than to try to make a blanket judgment on the "mess". Dicklyon (talk) 01:34, 20 January 2008 (UTC)

Before we begin editing the article, I'd like to make sure that Sniedo understands and accepts Wikipedia's core policy of verifiability, as explained above by Spireguy. Specifically, as encyclopedists, we must not ask ourselves what is correct, only what has been published and to what extent it is accepted in the scientific community. In our case, there are several published results discussing a relation between info-gap and minimax, and one published result claiming that info-gap is a special case of minimax. As you said yourself, many experts think (in your opinion, wrongly) that info-gap is indeed novel, and one person (Sniedo) thinks that info-gap is not. These are the points which are relevant in terms of WP:V and WP:UNDUE. If Sniedo accepts these points as the basis for the article, then I think we've made progress.

Also, I don't see any reason to exclude any cooperative person from editing. Wiki is built for collaborative editing, there's no reason to work behind the scenes. --Zvika (talk) 09:31, 20 January 2008 (UTC)

The so called "dispute"

Where exactly is the dispute?

Sniedo does not see that there is a "dispute" here because he has not seen anyone claiming that his two theorems are invalid. The fact that many Info-Gap users believe that Info-Gap is novel does not refute the validity of Sniedo's theorems. Indeed, a quick glance at the two Info-Gap books (Ben-Haim 2001, 2006) reveals that in 2006 Ben-Haim beleived that Info-Gap was new and radically different from all current theories for decision under uncertainty. In 2008 we know better. In fact we know that this is not so: Info-Gap's robustness model is a simple instance of the most famous model in decision theory under severe uncertainty.

As Sniedo indicated repeatedly, the "dispute" is not about the validity of his two theorems. The dispute is about some of their implications.

As suggested by Sniedo, all we have to do to move forward is to ignore the implications for the time being and focus on the validity of the theorems.

Why is it necessary to complicate things?

Since Zvika presents himself as an Info-Gap theorist, he is in a position to answer a simple question:

Are Sniedo's two theorems valid?

Once we know the answer to this question we can discuss the practical options available to us at this stage with regard to the next version of the article.

If Zvika claims that the theorems are invalid then we definitely have a dispute. If he acknowledges that they are valid, then we do not have a dispute at all.

Wikipedia's guidelines do not prohibit Zvika from answering this simple and obvious question. Sniedo (talk) 03:00, 22 January 2008 (UTC)

Your comment demonstrates very clearly that you have not accepted Wikipedia's WP:V policy. You seem to think that this is a place where academics can discuss the merits and faults of info-gap; this is entirely incorrect, as has been explained to you several times above.

I am not an "info-gap theorist". My field of research is signal processing and I once wrote a paper about an application of info-gap to signal processing. I have not read your paper, so I am in no position to judge the validity of its results, although they do not seem particularly surprising given that previous authors (myself included) have pointed out similar results (with a very different interpretation). The point is that whether I personally accept your results or not is irrelevant; the question is what the general consensus in the relevant community is. As you have said yourself, the consensus is that most people think info-gap is novel and useful. So indeed there is no reason for a dispute; there is only a refusal on your part to accept the role of Wikipedia as portraying current scientific consensus. In fact, I suggest that someone edit the article accordingly, since it seems that all other editors (including two outside opinions) agree that the current emphasis on criticism is exaggerated. --Zvika (talk) 06:29, 22 January 2008 (UTC)

Response to Zvika

1. You are wrong Zvika. I do accept Wikipedia's WP:V policy, and for that matter all other policies. The issue here is not the guidelines. Guidelines are just guidelines.

2. The discussion page of this article is designed for a discussion on matters related to the article and this is exactly what we do here.

3. I am not suggesting that you must answer the questions I raised. In fact, most of my questions are rhetorical. It is up to you to decide to what extent you should be engaged in a cooperative effort to resolve technical issues regarding Info-Gap. As you know, Wikipedia encourages cooperation.

4. You did refer to your 2005 paper as an example of what Info-Gap theorists did before I came along.

5. Whether you personally accept my results or not is very relevant to the discussion here. At this stage the Majority in this discussion consists of two persons, you and Ben-Haim. If you accept the validity of my results then we will be the majority in this discussion.

6. Your reference to the silent majority out there is ironic. Here we are in 2008, in Wikipedia, counting how many people accepted Info-Gap as a novel methodology before new results were published in 2007. My estimate is that it will take the silent majority about 5-6 years to change its mind. There are already major success stories on this front.

7. Wikipedia guidelines do not prohibit you and Ben-Haim from stating the following in this discussion:

We checked Sniedo's theorems. They are correct, hence accept them as an integral part of the state of the art in Info-Gap in 2008 and make them accessible to the public in this article.

8. This is how scientists work in academia. They check new results and embrace them if they are correct. They do not wait 4-5 years for the silent majority to decide on this matter.

9. You and Ben-Haim have chosen another option. Relying on Wikipedia's Majority/Minority guidelines, you deny the public access to new scientific results. This is bad for science, bad for Wikipedia and in the long run bad for Info-Gap.

10. To repeat, Wikipedia's guidelines do not prohibit you and Ben-Haim from embracing Sniedo's new results and incorporating them in this article for what they are, new results. Instead, it seems that you and Ben-Haim have chosen to deploy Wikipedia's guidelines as an administrative excuse to shield Info-Gap from valid criticism.

11. I am not trying here to change your and Ben-Haim's positions on this issue. I am merely stating the obvious: Wikipedia's guidelines do not prohibit you and Ben-Haim from incorporating in the article new verifiable results. It is up to you to decide and your decision is clear. Sniedo (talk) 03:25, 24 January 2008 (UTC)

Suggestion of onlooker

The intro to this article is phrased in terms understandable to a layman, as strikes me as entirely worthwhile and appropriate. However, introduction over, the article immediately plunges into an extremely formal mathematical discussion, pretty much unaccessible to the uninitiated. Reading this far I ask "Is there any reason to bring my skills up to speed to understand this formal argument?" My answer is "no" based upon there being absolutely no statement of achievements of this theory and no simple (or not so simple) examples of the utility it brings to the topic introduced at the beginning. My reaction to this is that possibly this entire discussion in fact is just a game for the initiated, leading ultimately to no practical results whatever, beyond the entertainment of the authors.

Couldn't a prologue be written to encourage one to enter into reading the remainder of the article, providing some understandable instances and examples where utility may be found, and a guide be given to preparatory material that could assist a novice in getting up to speed to do this?? Brews ohare (talk) 05:59, 21 January 2008 (UTC)

Thanks for the feedback -- as you can see above, we are planning some major changes in the article, and we'll certainly take your comments into account. --Zvika (talk) 07:04, 21 January 2008 (UTC)

I completely agree with your suggestion. If what you are looking for is a non-technical discussion of the issues involved, you can find a number of math-light articles on the subjects on my my website. Look for Info-Gap, Maximin, and Voodoo Decision Making. Sniedo (talk) 01:07, 22 January 2008 (UTC)

New Version

I have edited the article on info-gap decision theory. I believe this version conforms to Wikipedia policies, and I'm willing to discuss further issues if editors think it to be necessary.

I have taken care to observe Wikipedia's policies. In particular (quotes are from the WP policy pages):

1. VERIFIABILITY "in this context means that readers should be able to check that material added to Wikipedia has already been published by a reliable source."

The material which is presented is carefully referenced to reliable and independent sources. There are 48 citations to distinct sources -- books or journal articles published by reputable and well known publishers -- supporting the "standard interpretation" of info-gap theory and its application. These citations include 59 different authors. 22 of these publications do not include me (Yakov Ben-Haim) as a co-author.

2. NEUTRAL POINT OF VIEW. "NPOV says that the article should fairly represent all significant viewpoints that have been published by a reliable source, and should do so in proportion to the prominence of each. Now an important qualification: Articles that compare views should not give minority views as much or as detailed a description as more popular views, and may not include tiny-minority views at all."

The paper by Sniedovich is cited 3 times in the article (no article is cited more times and only one other article is cited 3 times), and the position is succinctly stated. This is certainly consistent with the "proportion to the prominence" clause, and is generous is not treating the article as a "tiny-minority" view. This judgement is independent of the fact that Sniedovich's article is in fact not yet available to the public. The article appears in the first volume of a journal whose publisher (a university in Krakow, Poland) does not have on-line access and does not list subscription information on its website. In a strict reading of the WP policy one might wish to exclude the citation to Sniedovich until the article is actually available to the public. I have not done so.

3. NO ORIGINAL RESEARCH. "Wikipedia does not publish original research or original thought. This includes unpublished facts, arguments, speculation, and ideas; and any unpublished analysis or synthesis of published material that serves to advance a position. This means that Wikipedia is not the place to publish your opinions, experiences, or arguments."

All the sections present material which is based on cited sources. The article is not polemical or speculative, nor does it engage in current scientific discussion, as required by the NOR policy.

Ybenhaim (talk) 13:23, 22 January 2008 (UTC)

Response to Ben-Haim

Given the history of this discussion, it is important to note not only what Wikipedia's policies and guidelines say, but also what they do not say.

In particular, these guidelines and policies do not prohibit the creator of Info-Gap from incorporating in the article new verifiable results whose validity is not questioned. It is up to him to decide what to do and he decided to deploy these guidelines as an administrative excuse whose aim is to shield Info-Gap from valid criticism.

I am not trying to changes Ben-Haim's position on this matter. This will not be possible. All I am saying is that

• • This attitude is in sharp contrast to the way scientists treat new, valid, verifiable, results.
  • Wikipedia's guidelines do not prohibit Ben-Haim from incorporating new, valid, verifiable results in the new version of the article.

Regarding the specific issues:

1. VERIFIABILITY. No one questions the verifiability of the publications cited by Ben-Haim . But none of these publications disputes the validity of Sniedo's new results. So there is no conflict here between two facts of life

• • Many people published papers where Info-Gap is portrayed in a positive way, and
  • New valid, verifiable, results depict Info-Gap in a completely different way.

I estimate that it will take about 4-5 years for the authors of these papers to realize that there are serious problems with Info-Gap. There are already major success stories on this front.

2. NEUTRAL POINT OF VIEW. This is a non-issue here. The key words are significant and prominence. One publication can be more significant than 345 others put together. The fact is, and it is a fact, that Info-Gap robustness model is a simple maximin midel is significant, in fact extremely significant. In fact, I am not surprised at all that Ben-Haim is so reluctant to incorporaqte it in the article. This will cause a major embarrassment.

The issue is whether the intention is to provide the public with the most recent results about Info-Gap and its role and place in decision theory or to deploy Wikipedia's guidelines as an excuse for excluding from the article valid, verifiable results.

The situation here is clear: A minority/majority issue was created by the majority. This is not dictated by Wikipedia's guidelines, it was Ben-Haim’s deliberate subjective decision.

The reference to the accessibility of Sniedo's (2007) paper to the public is out of place here. There is a website for the journal where one can easily find contact information. If Ben-Haim has suggestions regarding improvements to the publisher's website and customer service, he can direct them to the publisher. To raise this issue here under the header NEUTRAL POINT OF VIEW is a sort of a mystery.

3. NO ORIGINAL RESEARCH. The new version of the article excludes many sections of the old version that do not violate this policy. Furthermore, Ben-Haim is very selective in this matter.

4. CONFLICT OF INTERST. As was indicated already in this discussion by a Wikepedia editor, the conflict of interest issue is relevant: "one should not drive decisions in areas in which they have a conflict". Well, suffice it to say that Ben-Haim is the creator of Info-Gap and as such he has an obvious vested interest in presenting Info-Gap in the most positive way. The new version represents Ben-Haim's point of view.

What's next?

I plan to modify the new version of the article, taking into consideration Wikipedia's policies and guidelines. I am now teaching an intensive summer course ( The Art and Science of Decision-Making), so this will take some time.

My basic position remains:

1. Info-Gap's robustness model is a simple instance of Wald's maximin model.
2. Info-Gap's uncertainty model does not deal with severe uncertainty: it ignores it.
3. Info-Gap as a whole is fundamentally flawed: conceptually, methodologically, theoretically and technically.

These views are supported by valid, verifiable theorems and illustrative examples. Sniedo (talk) 03:38, 24 January 2008 (UTC)

Onlooker again

Thanks for citing the examples. It would be even more useful if an example could be presented in simple terms, rather than involving pursuit of arcane skills. This whole topic including the citation of opposing views clearly is a borderline case in conflicting with Wikipedia is not the place to publish your opinions, experiences, or arguments. It makes Wikipedia interesting to host some work in progress like this, but it detracts from this interest when understanding the controversy requires a PhD in set theory. Brews ohare (talk) 16:10, 22 January 2008 (UTC) The examples cited are not linked to available sources on the web, unless you subscribe to a service for technical journals - not true in my case. So I am still unhappy with the example situation. 19:06, 22 January 2008 (UTC) —Preceding unsigned comment added by Brews ohare (talk • contribs)

Many ideas in science and engineering require some level of mathematical effort to penetrate. In this case, I don't think that anything beyond an undergraduate math course is required. If you disagree, please be more specific and let us know what part you think is overly complex, and how you think it can be simplified -- or just be bold and improve it yourself.

Concerning the availability of online sources, Wikipedia policies require references to reliable sources; this generally means peer-reviewed journals, which are unfortunately not usually available for free download. However, the external links do contain some further essays with specific examples: see, for example, this essay which is taken from Yakov Ben-Haim's website. --Zvika (talk) 19:58, 22 January 2008 (UTC)

Many problems require sophisticated solutions that can be mathematically deep. For example, prediction of an eclipse of the moon. Not everyone can solve a three-body problem. However, anybody can understand what an eclipse is.

Many articles are cited. Presumably, some of these solved problems can be stated clearly in simple English, and so can the solutions. We don't need math for that. For example, designing a building for wind load (Y. Kanno Refs. 6 & 8) is a well known problem. What did info-gap bring to this design problem? What is the list of decisions it ranked for robustness??

Can you see any "prototypical" info-gap problems that might clarify what are the issues info-gap can deal with, and why it is more powerful than other methods??Brews ohare (talk) 01:13, 23 January 2008 (UTC)

A Math-Free example: The Treasure Hunt

There was a request for a math-light description of Info-Gap. Here is a variation of the one I use in my lectures.

The following tale describes the conceptual framework underling Info-Gap's approach to robust decision-making under severe uncertainty.

Chapter 1. You are in charge of a treasure hunt. All you know is that the treasure is hidden somewhere on a very large island in the Asia/Pacific region. You inquire about the true location of the treasure on the island and, you are advised that the true location is subject to severe uncertainty. There are some rumors about its location. Still, you havn't the faintest idea where the treasure is located.

Chapter 2. You have a catalogue outlining treasure hunt strategies, and you want to determine the best strategy for this particular expedition. You are adviced on a strategy called Info-Gap and you adopt its prescription.

Chapter 3. Following the Info-Gap prescription, first you somehow come up with a wild guess, or estimate. All you know is that this estimate is a poor indication of the true location of the treasure and that it is likely to be substantially wrong.

File:Australia 2.png

Chapter 4. You conduct a worst-case analysis in the immediate neighborhood of the estimate to determine how far you can deviate from the poor estimate without violating some given performance requirements.

Chapter 5. The maximum "safe" deviation from the poor estimate is the robustness you assign to the strategy you evaluate. You select the most robust strategy, namely the strategy whose robustness in the neighborhood of the substantially wrong estimate is the largest.

Chapter 6. As a reminder that you are dealing here with severe uncertainty, it is good practice to draw on the map a point representing the true location. Of course you do not know the true location. But since the estimate you use is poor and likely to be substantially wrong, it only makes sense to place the true location of the treasure at some distance from the poor estimate.

Chapter 7. Just in case you have not figured this out on your own, the Invariance Theorem reminds you that that this approach is local in nature and in effect it does not deal with severe uncertainty: it simply ignores it. To wit: you conduct the robustness analysis exclusively in the immediate neighborhood of the poor estimate. And so, hunting for the treasure, you may end conducting your robustness analysis in downtown Melbourne, whereas for all you know the treasure may be hidden in one of the sandy beaches near Perth. Or perhaps in the beautiful Barrier Reef. Perhaps.

Epilogue.

1. Would you be able to convince other expedition members to use this strategy? Indeed, can you seriously argue that this approach to severe uncertainty indeed yields robust decisions? The Info-Gap literature (Ben-Haim, 1996, 2001, 2006) does not address this issue. The Invariance Theorem suggests that this approach is fundamentally flawed.
2. If you are familiar with the distinction between local and global optimum you'll no doubt notice the analogy. Info-Gap is conducting a local analysis yet claims to yield global robustness.
3. If you are a statistician you'll no doubt notice that what Info-Gap is doing is analogous to risk analysis based on a sample of size 1.
4. If you read the Info-Gap literature you'll find out that Info-Gap is not aware of the fact that its robust model is a simple Maximin model. —Preceding unsigned comment added by Sniedo (talk • contribs) 02:48, 23 January 2008 (UTC)

Question

As posed, the treasure hunt seems to rule out info-gap as making any contribution. The question is: Could some modification of the rules of the treasure hunt make info-gap useful?

For example, advice often given to a writer, or to a circuit designer, is start with something, no matter what, and then revise it as you find the shortcomings of what amounts to a substantially wrong estimate. The idea is that correcting the wrong guess in itself educates the writer (designer) as to a better second guess. Is this process an intuitive form of info-gap, and if not, why not??

Brews ohare (talk) 18:34, 23 January 2008 (UTC)

Sneido's edit that I reverted

Sneido, if you claim to understand wikipedia guidelines, why don't you try applying them in your edits? Adding a statement to the article that refers to a discussion on the talk page is definitely not within guidelines, which is why I took it out. Try again, simply summarizing the points made in the Sneido papers, with attribution. Dicklyon (talk) 03:58, 23 January 2008 (UTC)

Hi Dicklyon

Ooops! I may need help in this department, as I am not aware of any such guidlelines. Can you please provide a link so that I can read the relevant guidelines?

In any case, I would greatly appreciate it if you could restore the section after deleting the link to the discussion page. Sniedo (talk) 02:16, 24 January 2008 (UTC)

See WP:SELF. Self-references, like putting an allusion to a talk-page discussion into an article, is out. If you put in a section on your criticism, straight, we could talk about it. Dicklyon (talk) 06:13, 24 January 2008 (UTC)

For Onlooker

Thanks for your comments. I think I've gotten your point. I want to keep the article brief, but I've added several sentences of further explanation of the engineering examples. I'd be glad to know if you think this is an improvement. Ybenhaim (talk) 05:33, 23 January 2008 (UTC)

If I got the changes right, you added a reference to a recent book. That book may have the answer to my problems, but why can't a simple example be provided in the Wiki article? Whatever may be said about the fairness and accuracy of Sniedo's appraisal of info-gap, it certainly is clear and to the point. Can't you find a counter-example to his treasure hunt, equally simple and clear, that would make it apparent that his view of the situation is perhaps one-sided, to say the least??

Surely among all the solved problems and citations it is possible to pick one that illustrates that info-gap provides useful guidance in a specific case, and spells out what specifically makes its success possible in that example, and what is the nature of its contribution???

Brews ohare (talk) 15:43, 23 January 2008 (UTC)

Perhaps the matter can be approached by viewing info-gap as guidance through a decision tree: at each decision point info-gap might weight the choices (by an evaluation procedure peculiar to info-gap that I don't understand) and thereby guide one (though perhaps not by the most direct path) to a favorable (though perhaps not the very best) outcome? Is there an example out there like this?? How about playing chess?? Just a thought.

Brews ohare (talk) 18:45, 23 January 2008 (UTC)

Advice to Sniedo

Sniedo, enough talk. The action you care about is the article, not the talk page. So make some constructive edits, to improve what's been said about your position. Play it straight, and I can help; go overboard, and I'll revert it. Dicklyon (talk) 06:30, 24 January 2008 (UTC)

Reply to Dicklyon

I am impressed -- but not intimidated -- by your rudeness (see relevant Wikipedia guidelines).

If you want to play it straight then the first thing you should do is deal with the serious conflict of interest that we have here.

You let the creator of Info-Gap, Ben-Haim, write an article about his theory where he shields his theory from valid criticism while his son Zvika is playing the role of a neutral Wikipedia mediator/observer.

Then, after you resolve this issue, we can come back to what we are supposed to do here: inform the public about the art and science of decision-making under severe uncertainty.

How should we go about correcting/updating the current version of the article? How do we fix obvious inconsistencies between what Ben-Haim writes in this article and what he writes elsewhere in the Info-Gap literature.

And how about omissions of crucial details about the theory? How should we go about including these details in the article.

And how about examples? As you can clearly see, Ben-Haim did not include in his update the examples that I developed in the previous version of the paper. What is wrong with simple illustrative examples?

The article requires a major revision and I really do not want to start this project before I know how this should be carried out in accordance with Wikipedia’s guidelines.

I do not want to waste my time and yours.

Your advice/suggestions on relevant Wikipedia guidelines will be greatly appreciated. Sniedo (talk) 05:08, 25 January 2008 (UTC)

Apparently that's not the case. I tried to help by telling you to make constructive edits, but you prefer to vent on the talk page; so there's not much more I can say; even being blunt didn't help. Dicklyon (talk) 05:32, 25 January 2008 (UTC)

For Onlooker

Many thanks for your persistent questions. I'm not sure that even now I've got your drift, but following is an example which you may find enlightening, and I'm considering putting it in the article. By the way, your mention of chess is interesting, since I had a student some years ago who designed a strategy for the board game "reversi" (something like "Go") based on an info-gap robust-satisficing strategy. His algorithm generally beat commercial programs at fairly high levels of competence (as measured by the number of forward-looking moves). However, I prefer the following example, which is more related to our troubled world.

EXAMPLE: MANAGING AN EPIDEMIC

The impact of an epidemic is evaluated with data and models from epidemiology and other fields. These models predict morbidity and mortality, and underlie strategies for prevention and response. The spread of disease can be managed through prophylactic or remedial treatment, quarantine, public information, and other means. Severe uncertainties accompany these models, and information is often too sparse to represent these uncertainties probabilistically, and even worst-case scenarios are hard to identify reliably.

Consider an example in which public officials must choose whether to quarantine the effected population, and if so, what population size to include. Also, planners must determine how quickly medical treatment will be dispensed upon detecting an emerging epidemic. Thousands or millions of individuals cannot be treated immediately, and plans must allow time for implementing large scale treatment.

The rate of infection is central in determining the spread of the epidemic, but it is hard to predict. Population studies of infection rates in normal circumstances may be of limited value when applied to stressful situations. Also, the disease may be poorly understood, as in SARS or avian flu. Population-mixing behavior, which influences the infection rate, can be influenced by public health announcements, but this is also hard to predict. Other properties are important, for instance, the number of initial infections and the identity of the disease, both of which may be hard to know.

We will consider three different quarantine options: no quarantine in which case the vulnerable population is one million; moderate quarantine which limits the vulnerable population to fifty thousand; and strict quarantine which limits the vulnerables to one thousand. In each case we will use an epidemiological model to predict the morbidity as a function of the time required to deploy and dispense medical treatment. One finds that stricter quarantine allows slower medical deployment without increasing morbidity, or conversely, lower morbidity at the same deployment rate. For instance, one might find that the morbidity reached in a population of one million, is reached in a quarantined sub-population of 50 thousand after a duration approximately 20 times longer. If the disease can be contained within a population of 1000, then the deployment-duration is extended by a further factor of 50 without increasing morbidity.

Clearly, quarantine is valuable, but how robust are these conclusions to modelling error? These conclusions depend on models and data which entail many info-gaps. Even small errors can result in performance which is substantially worse than predicted. We seek a strategy for which we are confident that the outcomes are acceptable. For any given choice of quarantine size and deployment duration, we must ask: by how much can the models err, and an acceptable outcome is still guaranteed? The answer to this question is expressed by the robustness function. In comparing two options, we will prefer the one with greater robustness. Incidentally, this preference-ranking of the options is independent of whether or not we judge the robustness of either option to be large enough.

Two important features are expressed by the robustness function. First, it quantifies the trade-off between robustness and morbidity: the robustness is greater for larger morbidity. Large robustness means that the corresponding morbidity is obtained for a larger range of contingencies. This suggests that one is less confident in obtaining low morbidity than high morbidity, with any given plan, because the robustness to uncertainty is lower for low morbidity. The planner who uses uncertain models to choose a plan for achieving low morbidity, must also accept low robustness. This is useful in identifying feasible values of morbidity: those values for which the robustness is very low are clearly unfeasible, large robustness suggests greater feasibility, etc. Second, when choosing between several plans, which plan is most robust depends on the acceptable level of morbidity. The preference-ranking of the plans can change as the planner considers different levels of morbidity. In other words, there need not be a unique robust-optimal plan, but instead the most robust plan may depend on the planner's (or the society's) preferences on the outcome (morbidity in this example). The robustness analysis thus supports debate and decision about resource allocation, by identifying feasible goals and plans which can reliably achieve them. In short, the info-gap analysis of robustness assists strategic planners to weigh the pros and cons of available options.

Finally, this example illustrates the relation between minimax and info-gap robust-satisficing. Both strategies - minimax and robust-satisficing - can be used to deal with uncertainty. The difference is that in minimax one assumes that the level of uncertainty is known, and one chooses a plan to minimize the maximum morbidity. In robust-satisficing one assumes that the acceptable morbidity level is known, and one chooses a maximally robust plan for that morbidity level. Either approach is acceptable, depending on what is known and what is unknown. Thus, they are two different (and complementary) techniques which may or may not lead to the same decision.

Ybenhaim (talk) 09:35, 24 January 2008 (UTC)

Response to epidemic example

I've tried adding notes to your example to indicate how I understand the relation of the example to info-gap itself. My comments are in italics, interspersed in your text.

Annotated version

The impact of an epidemic is evaluated with data and models from epidemiology and other fields. These models predict morbidity and mortality, and underlie strategies for prevention and response. The spread of disease can be managed through prophylactic or remedial treatment, quarantine, public information, and other means. Severe uncertainties accompany these models, and information is often too sparse to represent these uncertainties probabilistically, and even worst-case scenarios are hard to identify reliably.

The point here is to show that the situation is rather undefined, which means standard approaches based upon probabilities won't work

Consider an example in which public officials must choose whether to quarantine the effected population, and if so, what population size to include. Also, planners must determine how quickly medical treatment will be dispensed upon detecting an emerging epidemic. Thousands or millions of individuals cannot be treated immediately, and plans must allow time for implementing large scale treatment.

The rate of infection is central in determining the spread of the epidemic, but it is hard to predict. Population studies of infection rates in normal circumstances may be of limited value when applied to stressful situations. Also, the disease may be poorly understood, as in SARS or avian flu. Population-mixing behavior, which influences the infection rate, can be influenced by public health announcements, but this is also hard to predict. Other properties are important, for instance, the number of initial infections and the identity of the disease, both of which may be hard to know.

The point here is that the models aren't good and the input data to the models isn't solid; sounds like a re-emphasis of first paragraph

We will consider three different quarantine options: no quarantine in which case the vulnerable population is one million; moderate quarantine which limits the vulnerable population to fifty thousand; and strict quarantine which limits the vulnerables to one thousand.

Good, a clear statement of what the choices are

In each case we will use an epidemiological model to predict the morbidity as a function of the time required to deploy and dispense medical treatment.

Seems contradictory to earlier remarks about unreliability of models

One finds that stricter quarantine allows {slower medical deployment} medical assistance to be deployed more slowly without increasing morbidity, or conversely, lower morbidity at the same deployment rate. For instance, one might find that the morbidity reached in a population of one million, is reached in a quarantined sub-population of 50 thousand after a duration approximately 20 times longer longer than what?. If the disease can be contained within a population of 1000, then the deployment-duration is extended by a further factor of 50 without increasing morbidity.

Some rephrasing of these remarks would clarify matters a lot

Clearly, quarantine is valuable, but how robust are these conclusions to modelling error? These conclusions depend on models and data which entail many info-gaps. Even small errors can result in performance which is substantially worse than predicted. We seek a strategy for which we are confident that the outcomes are acceptable. For any given choice of quarantine size and deployment duration, we must ask: by how much can the models err, and an acceptable outcome is still guaranteed?

This appears to be a different question than choosing the correct strategy, the problem initially proposed. Maybe the point is that choice of which action to take is to be based upon the criterion of "robustness"?

The answer to this question is expressed by the robustness function. In comparing two options, we will prefer the one with greater robustness. Incidentally, this preference-ranking of the options is independent of whether or not we judge the robustness of either option to be large enough.

Seems to say that we prefer a fairly solid approach to a more speculative one, even if the more solid approach predicts a worse outcome. Maybe that could be stated?

Two important features are expressed by the robustness function. First, it quantifies the trade-off between robustness and morbidity: the robustness is greater for larger morbidity.

There seems to be an unstated assumption here: less speculative models predict higher morbidity. I doubt that this assumption always is valid, though it could turn out like that.

Large robustness means that the corresponding morbidity is obtained for a larger range of contingencies.

This statement is more an assumption than a logical conclusion; I'd guess that there are different models for different situations, and some models may be more accurate than others, regardless of morbidity? As a possible factor, models based on large populations are likely to more accurate for large populations than for small ones. Hence, model robustness increases with population size, not with morbidity.

This suggests that one is less confident in obtaining low morbidity than high morbidity, with any given plan, because the robustness to uncertainty is lower for low morbidity. The planner who uses uncertain models to choose a plan for achieving low morbidity, must also accept low robustness. This is useful in identifying feasible values of morbidity: those values for which the robustness is very low are clearly unfeasible, large robustness suggests greater feasibility, etc.

This argument is a bit shaky, I think; can it be improved?

Second, when choosing between several plans, which plan is most robust depends on the acceptable level of morbidity. The preference-ranking of the plans can change as the planner considers different levels of morbidity. In other words, there need not be a unique robust-optimal plan, but instead the most robust plan may depend on the planner's (or the society's) preferences on the outcome (morbidity in this example).

The robustness analysis thus supports debate and decision about resource allocation, by identifying feasible goals and plans which can reliably achieve them. In short, the info-gap analysis of robustness assists strategic planners to weigh the pros and cons of available options.

I understand this objective as a goal, but I don't understand how info-gap approaches the problem

Finally, this example illustrates the relation between minimax and info-gap robust-satisficing. Both strategies - minimax and robust-satisficing - can be used to deal with uncertainty. The difference is that in minimax one assumes that the level of uncertainty is known, and one chooses a plan to minimize the maximum morbidity. In robust-satisficing one assumes that the acceptable morbidity level is known, and one chooses a maximally robust plan for that morbidity level. Either approach is acceptable, depending on what is known and what is unknown. Thus, they are two different (and complementary) techniques which may or may not lead to the same decision.

This paragraph went off the deep end: insufficient development of terminology

Brews ohare (talk) 17:48, 24 January 2008 (UTC)

G'day:

In response to your earlier query whether one can "fix" Info-Gap's obvious flaws.

The short answer is No.

The flaws are fundamental. Info-Gap's robustness model is akin to risk analysis that is based of a sample of size 1. That is, the robustness is measured in the neighborhood of one wild guess of the true value of the parameter of interest. This analysis typically ignores what goes on in most of the total region of uncertainty.

According to the Universal Wrong-In Wrong-Out Axiom, given that the estimate we use is poor and can be substantially wrong, we have to assume (by default) that the results are poor and likely to be substantially wrong.

An attempt to fix this flaw will produce a robustness model of the type that has been used in the area Robust Optimization for more than 37 years. So what is the point of fixing Info-Gap? In any case, if we fix it we are going to end up with a Maximin model anyhow. So why should we re-invent the wheel?

A number of articles on my website deal with these aspects of Info-Gap. Sniedo (talk) 23:26, 24 January 2008 (UTC)

For Onlooker

Thanks once again for your comments and suggestions.

• I've tried to improve the piece based on your comments.

• I've not followed your suggestion about "speculative" vs. "solid" models or approaches. That's not the root of robustness. The robustness of a plan comes from how, and how much, information is exploited, and how uncertain that information is as expressed by an info-gap model of uncertainty.

• I've removed the final paragraph, under the COW (Can Of Worms) principle.

Here it is:

EXAMPLE: MANAGING AN EPIDEMIC

The impact of an epidemic is evaluated with data and models from epidemiology and other fields. These models predict morbidity and mortality, and underlie strategies for prevention and response. Severe uncertainties accompany these models, and information is often too sparse to represent these uncertainties probabilistically, and even worst-case scenarios are hard to identify reliably. The rate of infection is central in determining the spread of the epidemic, but it is hard to predict. Population studies of infection rates in normal circumstances may be of limited value when applied to stressful situations. Also, the disease may be poorly understood, as in SARS or avian flu. Population-mixing behavior, which influences the infection rate, can be influenced by public health announcements, but this is also hard to predict. Other properties are important, for instance, the number of initial infections and the identity of the disease, both of which may be hard to know.

The spread of disease can be managed through prophylactic or remedial treatment, quarantine, public information, and other means. Consider an example in which public officials must choose whether to quarantine the effected population, and if so, what population size to include. Also, planners must determine how quickly medical treatment will be dispensed upon detecting an emerging epidemic. Thousands or millions of individuals cannot be treated immediately, and plans must allow time for implementing large scale treatment.

We will consider three different quarantine options: no quarantine in which case the vulnerable population is one million; moderate quarantine which limits the vulnerable population to fifty thousand; and strict quarantine which limits the vulnerables to one thousand. We wish to analyze each option and then pick one, together with a rate of deployment of medical assistance. Our models are incomplete and uncertain, but they nonetheless represent the best available understanding of the processes involved. We will use the models as the starting point in the policy-selection process, followed by an analysis of the robustness to model-uncertainty and its implication for selecting a plan. We will illustrate the info-gap robust-satisficing strategy for selecting a plan.

Specifically, for each quarantine scenario, we will use an epidemiological model to predict the morbidity as a function of the time required to deploy and dispense medical treatment. From such an analysis one finds that stricter quarantine allows medical assistance to be deployed more slowly without increasing morbidity. Conversely, stricter quarantine results in lower morbidity at the same deployment rate. For instance, one might find that the morbidity reached in the no-quarantine case, is reached in a quarantined sub-population of 50 thousand after a deployment approximately 20 times slower than in the no-quarantine case. If the disease can be contained within a population of 1000, then the deployment-duration is extended by a further factor of 50 without increasing morbidity.

Clearly, quarantine is valuable, but how robust are these conclusions to modelling error? These conclusions depend on models and data which entail many info-gaps. Even small errors can result in performance which is substantially worse than predicted. We seek a strategy for which we are confident that the outcomes are acceptable. For any given choice of quarantine size and deployment duration, we must ask: by how much can the models err, and an acceptable outcome is still guaranteed? The answer to this question is expressed by the robustness function. In comparing two options, we will prefer the one with greater robustness; we will prefer the option which guarantees a specified level of morbidity for the widest range of contingencies. Incidentally, this preference-ranking of the options is independent of whether or not we judge the robustness of either option to be large enough.

Before discussing how the robustness function is used to select a plan, let's recall that large robustness means that the corresponding morbidity is obtained for a large range of contingencies. The robustness of a plan is a result of how, and how much, information is exploited, and how uncertain that information is as expressed by an info-gap model of uncertainty. Further understanding of the roots of robustness can be obtained by mathematical analysis.

Two attributes of any option are expressed by the robustness function. (The theorems which underlie these statements depend on the nesting axiom of info-gap models of uncertainty, discussed earlier.) First, the robustness function quantifies the irrevocable trade-off between robustness and morbidity: for any plan, lower morbidity entails lower robustness; higher morbidity, higher robustness. This suggests that one is less confident in obtaining low morbidity than high morbidity, with any given plan, because the robustness to uncertainty is lower for low morbidity. The planner who uses uncertain models to choose a plan for achieving low morbidity, must also accept low robustness. This is useful in identifying feasible values of morbidity: those values for which the robustness is very low are clearly unfeasible, large robustness suggests greater feasibility, etc. Second, when choosing between several plans, which plan is most robust depends on the acceptable level of morbidity. The preference-ranking of the plans (based on robustness) can change as the planner considers different levels of morbidity. In other words, there need not be a unique robust-optimal plan, but instead the most robust plan may depend on the planner's (or the society's) preferences on the outcome (morbidity in this example). By identifying feasible goals, and plans which can reliably achieve them, the robustness analysis supports debate and decision about resource allocation. In short, the info-gap analysis of robustness assists strategic planners to weigh the pros and cons of available options.

Ybenhaim (talk) 09:12, 25 January 2008 (UTC)

Quote

• I've not followed your suggestion about "speculative" vs. "solid" models or approaches. That's not the root of robustness. The robustness of a plan comes from how, and how much, information is exploited, and how uncertain that information is as expressed by an info-gap model of uncertainty.

You have raised the issue of model accuracy previously. Does this remark suggest that info-gap assumes all models are accurate, only the data put into the model is uncertain or limited? If so, that point could be clarified in the article.

That assumption seems to skirt the issue of choice of appropriate model. For example, if a bacteria is suspected when a virus is the cause, all bets are off.

This example seems to cry out for a decision tree approach, rather than a "model" approach. Some of the decisions involve selection of appropriate models. Brews ohare (talk) 03:56, 26 January 2008 (UTC)

Brews ohare (talk) 01:55, 26 January 2008 (UTC)

More suggestions from Onlooker First, I suggest weeding out some of the verbiage and a bit of reformatting; Here is an example of same.

EXAMPLE: MANAGING AN EPIDEMIC

Consider an example in which public officials must choose whether to quarantine an infected population, and if so, what population size to include. Also, planners must determine how quickly medical treatment can be dispensed upon detecting an emerging epidemic. Thousands or millions of individuals cannot be treated immediately, and plans must allow time for implementing large scale treatment.

We consider three different quarantine options:

1. No quarantine in which case the vulnerable population is one million;
2. Moderate quarantine which limits the vulnerable population to fifty thousand; and
3. Strict quarantine which limits the vulnerables to one thousand.

We wish to pick one, together with a rate of deployment of medical assistance.

Specifically, for each quarantine scenario, we use a model relating morbidity to the time required to deploy medical treatment. Stricter quarantine allows a slower deployment of medical assistance, or lower morbidity at the same rate.

Clearly, quarantine is valuable, but these conclusions depend on data that entail many info-gaps. We seek a strategy for which outcomes are acceptable. For each choice of quarantine size and deployment duration, we ask: by how much can the models err, and an acceptable outcome is still guaranteed? (Note that this is different from asking: 'how wrong are the models', or 'what is the worst case'?)

The answer is expressed by the robustness function. In comparing two options, we prefer the option which guarantees a specified level of morbidity for the widest range of contingencies.

The robustness function makes these assumptions:

1. Large robustness implies that target morbidity is obtained for a large range of contingencies.
2. Robustness depends upon how much information is used, and
3. Robustness depends upon uncertainty of information as found using an info-gap model of uncertainty.

Two attributes are expressed by the robustness function. (The theorems which underlie these statements depend on the nesting axiom of info-gap models of uncertainty, discussed earlier.)

First, the robustness function quantifies the trade-off between robustness and morbidity.

One is less confident in obtaining low morbidity than high morbidity, because robustness is lower for low morbidity. The planner who chooses a plan aimed at low morbidity must accept low robustness. This trade off helps to identify feasible values of morbidity: those values for which the robustness is very low are clearly unfeasible, large robustness suggests greater feasibility, etc.

Second, robustness of a plan can depend on the acceptable morbidity (in a way which is revealed by the mathematical representation of robustness).

The preference-ranking of the plans (based on robustness) can change as the planner considers different levels of morbidity. In other words, there need not be a unique robust-optimal plan, but instead the most robust plan may depend on the planner's (or the society's) preferences on the outcome (morbidity in this example). By identifying feasible goals, and plans that can reliably achieve them, robustness analysis supports debate and decision about resource allocation. In short, the info-gap analysis of robustness assists strategic planners to weigh the pros and cons of available options.

More, the example stops short of actually describing the result of the theory, or providing any specific instances of the various steps. For some scenario, what is the ranking of the the three posed options, and why is that ranking supported? Unfortunately, the description does very little for me beyond the simple unsupported statement that info-gap theory is useful in this context.

Brews ohare (talk) 15:40, 28 January 2008 (UTC)

Onlooker: If you want to see actual results of the theory, including specific instances of the various steps, you will have to deal with mathematical symbols, equations, numbers and graphs. Ybenhaim (talk) 18:55, 28 January 2008 (UTC)

That is an unfortunate conclusion. What it means is that the doctors involved in control of the epidemic will simply be told to implement a strategy without any explanation of why, other than the info-gap people said so. Of course, the info-gap people will not mind being treated like gods, but the doctors may not go for it. Brews ohare (talk) 21:06, 28 January 2008 (UTC)

Updates to the new version

Math-free description of Info-Gap's robustness model

As indicated by Brews ohare, there is a need for a math-free description of Info-Gap's robustness model.

I added a new section entitled Beyond/Behind the Math. It explains clearly the robustness model and the complexities of decision-making under severe uncertainty.

I'll be happy to modify/update it as per comments/suggestions.

It is criticism-free. Sniedo (talk) 02:00, 27 January 2008 (UTC)

I wouldn't call it criticism free, just because you posed the criticism as a rhetorical question. But criticism would be fine, as long as it was sourced. If this example is in one of your publications, describe it more briefly, summarize the point, and cite the source. Dicklyon (talk) 05:47, 27 January 2008 (UTC)

Thanks for the feedback, Dicklyon.

I'll shorten the description and provide a source. I hope that you appreciate the fact that there is a need for a math-free description of Info-Gap's robustness model. Sniedo (talk) 00:16, 28 January 2008 (UTC)

I'd like to reinforce the request for a math-free description. It is not useful to be told that the requisite info is in an archival journal. Even basic terminology has not been defined and there are no examples, however simplistic, to show what it means. No conclusions from application of the theory are presented. Are there any?? The result is a vague feeling that the author is too caught up in formalism to be concerned about explanation. Brews ohare (talk) 16:22, 28 January 2008 (UTC)

G'day Brews:

Later today I'll incorporate in the article a math-Free description of Info-Gap's robustness model. It is based on my earlier version of a new section entitled "Beyond/Behind The Math" and on Dicklyon's suggestions/comments. Sniedo (talk) 01:18, 29 January 2008 (UTC)

I'm not going to revert it this time, but it would be nice if you want observe standard heading case and avoid saying things like "it is important..."; that's just an opinion. Also, get rid of the red, and avoid html markup in favor of wiki markup. Dicklyon (talk) 01:59, 29 January 2008 (UTC)

Thanks for the comments/suggestions, Dicklyon. I do not like the red either, and I shall definitely change it to something more civilized. Getting rid of HTML will be a bit difficult for me because I am still in the process of learning the wiki markup language. I hope that this will be an exception. Sniedo (talk) 05:48, 29 January 2008 (UTC)

Hi Sniedo: It seems to me that in many cases as a matter of practice, one must start with a bad estimate and improve it. Even so, the obstacle of starting from a bad beginning is overcome. However, as you point out, it is not possible to do that based on some local max or min. It strikes me that info-gap could avoid this locality drawback by using a decision tree. Any hope for info gap in this direction? Brews ohare (talk) 04:59, 29 January 2008 (UTC)

Hi Brews: Yes, very often we start with a bad estimate. But the problem with Info-Gap is not that the estimate is bad: the flaw is in the local nature of the analysis.

I am not an Info-Gap user and I do not know in what direction it will go. The Decision-Tree option will be relevant if the problem as a whole can be decomposed into "stages". Sniedo (talk) 05:48, 29 January 2008 (UTC)

Brews: Two points.

• First, a decision tree is a "model" just as much as a differential equation. As such, it is subject to uncertainty, which can be modelled and managed by info-gap theory, or maximin, or probability, or fuzzy logic, depending on the nature of the uncertainty. For instance, the search for contraband in ship containers has an element of decision-tree structure, which has been studied from an info-gap perspective (Moffitt et al mentioned in the article, which is available for inspection on line from BE Press, if I'm not mistaken.) as well as many other perspectives.

• Second, in some situations of decision under uncertainty we conclude that the robustness of any available option is low. That would certainly be the case in the treasure hunt example, but it's not invariably the case. Low robustness (or low probability of success in a probabilistic analysis) is not a fault of the method, but a result of the prior information available to the analyst. Let's not shoot the messenger. Ybenhaim (talk) 07:19, 29 January 2008 (UTC)

The first comment does not address the locality issue - a decision tree can be a global (not local) approach. The decision among branches can be based upon understanding of the whole solution space, and is not restricted to the vicinity of the initial guess. The decision tree also provides the possibility of amassing new info peculiar to the branch taken, which allows for evolution of the solution procedure, and even back tracking to previous junctions. My point is to avoid the debacle so well described by the treasure hunt.

The last comment is cogent. Could it not be explored in the article?

Brews ohare (talk) 15:17, 29 January 2008 (UTC)

G'day Brews.

Concerning Ben-Haim's second point: don't shoot the messenger.

It is obvious that Ben-Haim underestimates the seriousness of the flaw in Info-Gap's robustness model.

The fact that according to Info-Gap the robustness of a given decision is small does not mean that this is indeed the case. A decision can be very fragile in the neighborhood of the estimate but very robust elsewhere in the total region of uncertainty.

Conversely, a decision can be very robust in the neighborhood of the estimate but very fragile elsewhere in the total region of uncertainty.

So the difficulty is not that the model cannot be blamed for reporting that a decision is not robust. The model is blamed for providing a local rather than global view of robustness.

The flaw is not with the messenger, the flaw is with the model.

The Treasure Hunt paradigm makes this point crystal clear. The local robustness provided by Info-Gap cannot be extrapolated.

This point is reinforced by the fact that many of the robust optimization methods are global in nature. Sniedo (talk) 02:56, 30 January 2008 (UTC)

Thank you for these remarks, which seem sensible to me Brews ohare (talk) 14:36, 30 January 2008 (UTC)

Regarding Onlooker's new paragraph

Brews:

• The paragraph which you added to the epidemic example would be more valuable if you would cite verifiable sources to support the view expressed that physicians (or whoever is responsible for implementation) would not be able to implement the policy. This is in accordance with WP policy of verifiability, which "in this context means that readers should be able to check that material added to Wikipedia has already been published by a reliable source." WP is not the place to express one's personal point of view. In fact, there is extensive verifiable evidence that info-gap policies are implementable by non-info-gap experts such as biological conservationists, to whose work there are many references in the article.

• Your comment about the "concrete nature of a robustness function" is surprising, since the robustness function is discussed in the section of the article just prior to the example, and is developed in technical detail in the two references which accompany the example. Consequently your comment seems out of place.

• Your paragraph is an editorial suggestion regarding the previous material, and thus not encyclopedic at all. It would belong in the talk section.

Ybenhaim (talk) 05:46, 2 February 2008 (UTC)

A new section: A Maximin perspective

From a classical decision theory perspective the most significant feature of Info-Gap theory is, by far, the similarity between Info-Gap's robustness model and Wald's famous Maximin model. Therefore, this detail should be flagged out in the Preview section and be discussed properly under a suitable heading. Note that in the current version of the article this fundamental issue is all but hidden in two sentences in the last paragraph of the section "Some applications".

Thus I added

• (a) two sentences about this point at the end of the Preview section of the article;
• (b) a short new section entitled "A Maximin perspective" that summarizes the state of the art on the Info-Gap/Maximin connection. This summary incorporates the relevant references provided by Ben-Haim in the last paragraph of the section "Some applications".

In view of this, Ben-Haim may wish to delete the two sentences in the last paragraph of the section "Some applications" that briefly mention this aspect of Info-Gap.

Any comments/suggestions? Sniedo (talk) 08:14, 2 February 2008 (UTC)

Is Sniedo's paper a reliable source?

Sniedo is persistently attempting to add more and more references to his paper containing criticism of info-gap. This single paper is already referred to in the article more times than any other reference, including the info-gap books and the basic info-gap papers, many of which are highly cited in academic journals. Also, Sniedo's paper underlies 3 of the 8 sections of the article (sections 4, 5 and 8). I'd like to point out that the reliability of this one source is questionable. Sniedo's paper appeared in the first issue (volume 1, number 1/2) of a journal called Decision-Making in Manufacturing and Services (DMMS), the only issue published so far. Here is some information about the journal:

• DMMS is published by the "AGH University of Science and Technology" in Poland, rather than by a reputable academic publisher or a large scientific organization, as is usually the case for academic journals.

• The journal is not indexed either by Web of Knowledge or by

[http://scholar.google.com/scholar?hl=en&lr=&q=%22Decision+Making+in+Manufacturing+and+Services%22&btnG=Search Google Scholar].

• It is not possible to download electronic copies of papers from the journal website (even for a cost), nor is there any information about how one may subscribe to the journal or order back copies. So there is no way for the public to obtain a copy of this paper, or even read its abstract.

• Moshe Sniedovich is on the editorial board of this journal.

It thus appears that Sniedo's "campaign" against info-gap (his word) is backed up by a single source, whose reliability and independence are questionable. Given the exceptional nature of his claims (as we all agree, his opinion goes against hundreds of publications on info-gap), I would think that reasonable reading of Wikipedia guidelines would classify his opinion as a "tiny minority."

In the interests of compromise, Zvika has previously proposed that the article contain a single, one-paragraph section describing Sniedo's critique. I agree with this proposal, which I think is more than fair. Unless Sniedo can provide further reliable, independent sources supporting his claims, I do not think it is appropriate to include additional detail, beyond a one-paragraph summary, about Sniedo's interpretation, as his recent edits are attempting to do. Ybenhaim (talk) 14:18, 2 February 2008 (UTC)

Actually it's easy to find and freely available here. The problem is more WP:COI than WP:RS. If we can get some neutral editors to agree to work on it, then we could get him and you both out of it and see where it settles. But I don't have the time to take it on. Dicklyon (talk) 17:49, 2 February 2008 (UTC)

I would support the idea of neutral editors supervising a balanced version. 132.68.249.199 (talk) 20:01, 2 February 2008 (UTC) Sorry, I was not logged in when I added this comment. Ybenhaim (talk) 20:02, 2 February 2008 (UTC)

G'day:

Sniedo's paper is a very reliable source. Ben-Haim does not like it because it exposes the flaws in Info-Gap. Instead of addressing the valid criticism Ben-Haim is diverting attention to non-issues. Sniedo (talk) 08:57, 3 February 2008 (UTC)

Comments on Sniedo's new section: A Maximin perspective

It is high time that the creator of Info-Gap Theory -- Yakov Ben-Haim -- inform the public, at the outset, that Info-Gap's robustness model is not new much less radically different from all current methodologies. Indeed, Ben-Haim should acknowledge that Info-Gap's robustness model is a special instance of Wald's famous Maximin Model.

Sneidovich's (2007) results were published only recently (December 2007). Hence, all the Info-Gap papers cited in the article predate the publication of these new results. The minority/majority question is therefore not an issue here and it cannot and should not be used as a means to shield a theory from valid criticism.

The so called "dispute" regarding the Info-Gap/Maximin connection can be resolved in one second. All that Ben-Haim needs to do is to answer the following simple question:

Does Ben-Haim dispute the validity of Sniedovich's (2007) Maximin Theorem?

If he does not dispute the validity of the theorem then there is no dispute. There is no minority/majority conflict and the creator of Info-Gap should embrace this new result and make sure that his readers are aware of it. This is how we do things in science and Wikipedia's rules and guidelines do not prohibit us from adhering here to this long tradition. It is our obligation to inform the public about new, relevant, results.

Remarks:

• Ben-Haim is aware of the fact that Sniedo's criticism is valid.
  • For example, Ben-Haim now concedes that Info-Gap's robustness analysis is local in nature. This is a new development! For until recently Ben-Haim insisted that this is not the case. In fact, in the FAQs paper (3.10.07 version) on Ben-Haim's website he still argues that Info-Gap's robustness analysis is not local and he explains why this is so!!!!
  • Similarly, Ben-Haim now understands that the majority's interpretation of Info-Gap's robustness is wrong. Indeed, in the Preview section of the article he describes it using the correct interpretation that Sniedo provided in an earlier version of the article.
  • In the article Ben-Haim acknowledges -- albeit in a roundabout way -- that Sniedovich's Maximin Theorem is valid. Compare it with Ben-Haim's (2005 ; FAQs paper 3.10.07) insistence that although Info-Gap's robustness model is similar to Maximin, it is not a Maximin model.
• So, as we can clearly see, Ben-Haim slowly but surely accepts Sniedo's valid criticism.
• To recap, as stated above, it is high time that Ben-Haim give here, in this discussion, a clear cut answer to the following question:

Does Ben-Haim dispute the validity of Sniedovich's (2007) Maximin Theorem?

This will completely resolve the current dispute.

Sniedo (talk) 08:57, 3 February 2008 (UTC)

Actually, that question, and his answer to it, if any, are not proper matter for wikipedia. The validity of info-gap is something to be worked out elsewhere. In the mean time, the article should just report what has been published about it, and not get into interpretations. Dicklyon (talk) 17:41, 3 February 2008 (UTC)

G'day Dicklyon:

I am fully aware of the fact that Ben-Haim does not have to answer such questions in the context of this discussion.

I raised that question as an attempt to resolve the current dispute triggered by Ben-Haim's objections to the incorporwation in the article of verifiable results the validity of which he does not question!

It looks like the dispute will last as long as Ben-Haim insists on the exclusion of verifiable results that he does not like.

For the record, although I disagree with many of Ben-Haim's statements in the article, I will not mind if this version will stay "as is".

Perhaps this could be a temporary "compromise". Sniedo (talk) 06:12, 4 February 2008 (UTC)

Revisions by Brews_ohare

I've tried to make clearer the original presentation by adding some topic sentences and subtitle heads. These are pretty accurately done, and break the discussion into manageable pieces. However, they do not enhance my view of the presentation because I'd like to know how info-gap works. When it comes to details, the presentation is pretty thin. A lot of what is said is simply "filler". Brews ohare (talk) 01:50, 5 February 2008 (UTC) I hope that any infelicities in translating the exposition are viewed as flags suggesting more clarity is needed, rather than as inflammatory intrusions. Brews ohare (talk) 19:50, 5 February 2008 (UTC)

More on revisions

I have made extensive reorganization and rewriting of some sections of this article. My aim has been (i)to eliminate long digressions that distract the reader by using footnotes (ii) to organize the text so that topics are discussed once and not revisited over again (iii) to make topic sentences, subtitles and introductory phrases that indicate what the point of various paragraphs are. Needless to say, these changes may reflect actual distortions of intent due to misunderstanding or impatience on my part. Therefore, the original authors should take a look at the article, and hopefully revise it in a short, illuminating way. Brews ohare (talk) 19:44, 11 February 2008 (UTC)

I have added a new section entitled "Robust Optimization" to the section "Alternatives to info-Gap". In view of this it might be appropriate to delete the last sentence of the preceeding paragraph. Sniedo (talk) 21:56, 11 February 2008 (UTC)

Revisions by Lior Davidovitch

I have rearranged the sections to get a coherent structure for the article. A reasonable structure would be:

1. Example - I think the example should be more graphic, and much simpler, at the expense of reality.
2. Info-gap theory
   1. Info-gap models
   2. Immunity functions
3. Applications of info-gap
4. Criticism - two or three consice criticisms (similarity / identity to Wald's Maximin, locality, etc). For instance, the treasure hunt is a little bit too "educational" and long. Each critisicm will be followed by a concise retort.
5. Alternatives to info-gap. At the moment, this section is not very informative: most of it just repeats Sniedo's criticism. I think it would be useful to note the advantages and disadvantages of different methods in different situations. Some examples:
   1. When there is absolutely no info, there is no benefit in squeezing a best estimate from the expert. In thins case a global (worst case?) analysis would probably be a better idea.
   2. When there is uncertainty, but an expert can give some sort of estimate, it is sometimes wasteful to ignore it. In this case perhaps a global analysis is an overkill.
   3. When there is a critical value, a global analysis may be insufficient. For instance, suppose Sniedo's treasure hunt is not a treasure hunt, but a water hunt. If you fail to find water within 3 days, you will die. A global analysis finds a search pattern that assures you will find water within at most 5 days. On the other hand, a robust satisficing analysis will look for a search pattern that is "more likely" to find water within relevant time. In this case you will probably choose the best estimate, flawed as it may be.

Lior Davidovitch (talk) 13:54, 12 February 2008 (UTC)

These suggestions sound good to me

How about taking a whack at it? Also, a large fraction of Ben-Haim's citations could be removed: it isn't necessary to have 500 examples of uncertainty and unending exhortation that even if info-gap is wrong, it's useful. So what if there are 10⁶ snake doctors? Put up some real content, not references to inaccessible (to the nonprofessional) literature. Provide an example where a selection of decisions has actually been sorted and say why the order is that way in simple language. Brews ohare (talk) 15:49, 12 February 2008 (UTC)

Back to square one

G'day:

(a) There is a confusion in the new version of the article between the simplicity of a model and the degree to which it might be easy/difficult to solve the problem represented by this model. The Maximin model for the prime numbers is very simple: the decision space is simple, the state space is simple and the objective function is simple. This, however, does not mean that the problem represented by this model is simple/easy to solve.

This is a well known phenomenon. Indeed, many of the models for NP-Hard problems are very simple (eg. models for the traveling salesman problem).

By the same token, Info-Gap's robustness model is very simple but this does not mean that the optimization problem it represents is simple/easy to solve.

In short, as shown in the article, the instance of Wald's Maximin model representing Info-Gap's robustness model is very simple: its decision space is simple, its state space is simple and its objective function is simple. The Theorem is not about how easy/difficult it is to solve Info-Gap problems. It is about the simple structure of the Maximin model that represents Info-Gap's robustness model.

(b). Why should the Maximin Theorem be understood and phrased in a weaker manner? The Maximin Theorem does not merely claim that Info-Gap's robustness model is an instance of Wald's Maximin model: it provides the specific instance representing Info-Gap's robustness model. There are many instances of Wald's Maximin model out there and Info-Gap's robustness model is not just one of them -- it is the very one formulated in the article.

(c). Thus, the entire discussion on the prime number model is a counter-productive diversion and should be deleted.

(d). Info-Gap theory is designed specifically for decision making under severe uncertainty, namely for situations where the estimate we have is a poor indication of the true value of the parameter of interest and is likely to be substantially wrong. In this framework one cannot justify a local analysis in the immediate neighborhood of the estimate. This, however, does not mean that we should ignore the estimate. It only means that it is imperative to consider -- in addition to the neighborhood of the estimate -- other neighborhoods of the total region of uncertainty. Otherwise the analysis will be exposed to the Wrong-in Wrong-out Axiom.

(e). It is unclear why the subsection "A Maximin Perspective" now appears under the header "Criticism". The proof that Info-Gap's robustness model is an instance of Wald's Maximin model is not criticism. It is a simple, valid mathematical statement. The fact that Info-Gap proponents do not like it does not make it a criticism.

(f). It is unclear why the discussion on the Treasure Hunt now appears under the header "Criticism." It does not criticize Info-Gap. It provides a clear math-free description of Info-Gap robustness model. Again, the fact that info-Gap proponents do not like it does not make it a criticism.

(g). The Water Hunt problem does not hold water. On what grounds is it claimed that a critical time constraint on the search cannot be incorporated in a global analysis? Does Info-Gap have a monopoly on the incorporation of critical performance constraints in robust optimization models? What exactly does "In this case you will probably choose the best estimate" mean? Why should we restrict the analysis to the immediate neighborhood of a poor estimate that is likely to be substantially wrong?

(h). It looks like we are opening a new round of the same, familiar, info-gap diversions. Sniedo (talk) 09:14, 13 February 2008 (UTC) Sniedo (talk) 09:36, 13 February 2008 (UTC)

Proposal to eliminate Managing an Epidemic

I believe the new Illustrative Example is much more helpful than the Epidemic example, which I frankly find meandering and unhelpful. I propose it be dropped. Brews ohare (talk) 21:32, 25 February 2008 (UTC)

Question on Wald's Minimax

Links are given to Wald and to Minimax, but neither helps to discover how Wald modified Minimax. Can some info be provided here or in the Minimax article about Wald's version? Brews ohare (talk) 22:11, 25 February 2008 (UTC)

Failings of this article

Due to its unfortunate history, this article is not user friendly. It lacks any real comparison to other methods, like Bayesian analysis for example, puts nothing in context. No links to other articles are provided that might guide the reader to some understanding of the issues. A huge number of totally useless references are provided that basically are a "snow job" Brews ohare (talk) 22:20, 3 March 2008 (UTC)

Response to Brews' Notes

1. Wald's Maximin model is an adaptation of von Neumann's conceptual model used in Game Theory. In Wald's model the second (inner) player represents uncertainty. As such this player ("Nature") does not have objectives/goals of its own. Its sole interest in the "game" is to hurt the other player (Decision Maker) as much as possible. So this player always selects the worst state of nature relative to the decision/alternative selected by the decision maker. According to this scheme, the decision-maker plays first and in response Nature selects the worst state relative to the decision/alternative selected by the decision-maker. This is the reason that in the framework of Wald's model, in contrast to the Game-Theory model, Equilibrium is not an issue.
2. Indeed, the current version of the article is not reader-friendly. In particular, the discussions on the relationship to the classical Maximin paradigm and robust optimization should be expanded.
3. I plan to revise the article soon and shall address these two issues in the revision. Sniedo (talk) 23:02, 4 March 2008 (UTC)

Next revision

As indicated by Brews, the current version of the article is not reader-friendly. I plan to revise it so that it will better explain the fundamental ideas underlying Info-Gap Theory and its role and place in decision theory.

But before I do that, it would be useful to fix the following two items:

Item 1. The Minimax representation of Info-Gap's opportuneness model.

This model, namely

$z=\min _{\alpha \geq 0}\max _{u\in {\mathcal {U}}(\alpha ,{\tilde {u}})}\varphi (q,\alpha ,u)$

where

$\varphi (q,\alpha ,u)=\left\{{\begin{matrix}\alpha &,&{r_{w}}\leq R(q,u)\\-\infty &,&{r_{w}}>R(q,u)\end{matrix}}\right.\ ,\ \alpha \geq 0,u\in {\mathcal {U}}(\alpha ,{\tilde {u}})$

seems to be wrong.

Observe that according to this model the Min player has no incentive to move away from $\ \ \displaystyle \alpha =0\ \$.

Thus, according to this model $\ \ \displaystyle \alpha =0\ \$ is always optimal. This result is correct if $\displaystyle R(q,{\tilde {u}})\geq r_{w}$, but is wrong otherwise.

For example, consider the simple instance where

$\displaystyle R(q,u)=|q+u|$

$\displaystyle {\mathcal {U}}(\alpha ,{\tilde {u}})=\{u\in \mathbb {R} :|u-{\tilde {u}}|\leq \alpha \}$

$\displaystyle r_{w}=5$

$\displaystyle q'=0$

$\displaystyle {\tilde {u}}=0$

In this case Info-Gap yields $\ {\hat {\alpha }}(q',r_{w})=5$, whereas the Minimax model yields $\ \displaystyle z=-\infty \$, and any $\ \ \displaystyle \alpha \ \$ such that $|\displaystyle \alpha |<5\$ is optimal.

So it seems that the proposed Minimax model yields the correct result only in the trivial case where $R(q,{\tilde {u}})\geq r_{w}$.

In contrast, Sniedo's old Minimin model, namely

$\min _{\alpha \geq 0}\min _{u\in {\mathcal {U}}(\alpha ,{\tilde {u}})}\varphi (q,\alpha ,u)$

where

$\varphi (q,\alpha ,u)=\left\{{\begin{matrix}\alpha &,&{r_{w}}\leq R(q,u)\\\infty &,&{r_{w}}>R(q,u)\end{matrix}}\right.\ ,\ \alpha \geq 0,u\in {\mathcal {U}}(\alpha ,{\tilde {u}})$

always yields the correct result.

Request 1: Whoever incorporated this model in the article, please either restore Sniedo's old Minimin model, or check this Minimax model and show that it is correct after all.

Item 2. The investment example.

This example does not address the key issue on the agenda: severe uncertainty.

Note that according to the example, Info-Gap simply conducts a Pareto trade-off (robustness vs performance) analysis in the immediate neighborhood of the given estimate. This raises a number of fundamental questions:

1. How does Info-Gap actually deal with severe uncertainty?
2. Where precisely in the analysis does Info-Gap deal with the severe nature of the uncertainty?
3. On what grounds are we to accept the results generated by Info-Gap as valid given that under severe uncertainty the estimate we use is a poor indication of the true value of the parameter of interest and is likely to be substantially wrong?

In short, the example is utterly oblivious to Info-Gap's stated mission: decision-making under severe uncertainty. Indeed, it does not illustrate at all the very feature that Info-Gap theory is supposed to offer, namely the ability to deal with severe uncertainty.

Request 2: Whoever incorporated this example in the article, please add to it an explanation outlining how Info-Gap tackles the severe nature of the uncertainty.

I can fix these two items myself but I would rather let the persons who authored the two items do it.

I'll wait a week or so for these two issues to be fixed before I go ahead with my plan to revise the article. Sniedo (talk) 02:05, 6 March 2008 (UTC)

Sneido, I object to your plan. If any major revision is needed, feel free to outline it here on the talk page. But you have too much conflict of interest in this topic to be making major rewrites of the article. If you have uncontroversial corrections to make, that's fine, too. But a major reorg to better reflect your attitude on the topic is not a good idea. Others can respond to your concern. Of course, if you see other editors with a bias on the other side making major changes in their favor, point that out and we'll correct it. —Preceding unsigned comment added by Dicklyon (talk • contribs) 05:26, 6 March 2008 (UTC)

G'day Dicklyon.

May thanks for the tips.

Given the history of this article I know that I should not overstate my position regarding the topic.

The difficulty is that the last two major revisions were made by Info-Gap proponents with obvious conflict of interest.

As I indicated above, we are back to square one.

One thing is clear, the article is not reader-friendly and something should be done about this.

I'll wait a week or so to see how things develop and how we should proceed from here. Sniedo (talk) 06:02, 6 March 2008 (UTC)

The only editor here who appears to be involved yet neutral is Brews ohare. It's not fair to expect him to do everything in arbitrating between you guys, but so far he seems to think it's not so bad, and until we get someone else to help, that's all we have to go on. Dicklyon (talk) 06:10, 6 March 2008 (UTC)

I have added a few links to Bayesian articles.

I am not sufficiently versed in this area to undertake a revision. I do believe that Sniedo can provide more balance to this article.

I also would argue that there is way too much fluff in the info-gap presentation, and way too little context and comparison Brews ohare (talk) 15:51, 8 March 2008 (UTC)

New introductory section

In view of Dicklyon's and Brews ohare's comments on my suggestion for a revision, I took a close look at the article to determine how it can be improved to be more reader-friendly.

My conclusion is that clearly missing here is an introductory section the aim of which is to put the entire discussion on info-gap in a proper context and to outline at the outset the key issues that must be dealt with in this context.

This section could serve as a guide for possible revisions of other sections of the article.

I thus added a new section entitled Background, working assumptions and a look ahead immediately following the Overview.

I propose that we now go through each of the existing sections to determine how they can be improved.

For example, as I indicated already, the discussion in the Investment Example is utterly oblivious to the fact that info-gap is designed specifically for decision under severe uncertainty. The discussion should therefore be revised to make this point clear and to show how info-gap's analysis deals with the severity of the uncertainty. -- Sniedo (talk) 23:37, 16 March 2008 (UTC)

New subsection to Illustrative Example

G'day:

1. I added a new subsection entitled Analysis   to the Illustrative Example. It deals with the severe nature of the uncertainty.
2. I support Brews ohare's suggestion to delete the Epidemic example. It severes no purpose and is not reader-friedly.
3. My next project is to revise the section on Maximin. -- Sniedo (talk) 23:32, 20 March 2008 (UTC)

Revision of the Maximin section

G'day:

I revised the discussion on the info-gap/Maximin/Minimin connection. For the reader's convenience I also appended notes on this topic.

It is now necessary to revise the Criticism section. --Sniedo (talk) 08:44, 24 March 2008 (UTC)

The weight of Maximin discussion within the article

It seems that the latter is somewhat over-represented within the article. I am not sure that the article on info-gap is the place for in-depth analysis of Wald's Maximin.

I think that most of the Maximin section belongs in a separate article, maybe along with the notes on the art as modeling problems as optimization problems. It is important as it is, and right now it is just an appendix to a related article (which is bad for both topics). Lior Davidovitch (talk) 11:02, 25 March 2008 (UTC)

G'day:

It seems that Lior Davidovitch got it all wrong, again.

1. Given that info-gap's robustness model is a simple instance of the generic Maximin model and its opportuneness model is a simple instance of the generic Minimin model, it makes sense to delete the info-gap article altogether and simply discuss info-gap theory in a section of the existing article on Minimax.
2. However, considering the three books on info-gap, 'the 264 papers with the word "info-gap" and 174 citations of the info-gap book listed in Google Scholars,' -- all of which are unaware of the extent of the info-gap/Maximin/Minimax connection -- it is necessary to keep the info-gap article as a separate entry in Wikipedia.
3. But ... enough is enough. The time has come to put an end to the spin and present info-gap to the public for what it is.
4. The discussion in the current version of the section on the Maximin/Minimax connection does exactly that. It is concise, constructive and informative.
5. In fact, this section does what the creator of info-gap should have done at the outset: relate info-gap theory to classical decision theory.
6. Needless to say, this section may be a major cause of embarrassment in some quarters, but this concern should not dictate the content of this article.
7. If Lior Davidovitz is so concerned about the quality of this article, then the first thing he should do is ... delete the epidemic example that he retained in his re-arrangement of the article on February 12, 2008. And he should also restore the valid criticism of info-gap that he deleted on that occasion. --Sniedo (talk) 19:32, 25 March 2008 (UTC)

TSP, chromatic number and Sudoku are all NP-hard / NP-complete problems. And yet, they are not all just briefly mentioned in one big NP article.

Even if info-gap is an instance of maximin, I think it is interesting enough to deserve its own article.

Also, I replaced the analysis at the end of the illustrative example with a comparison to both Bayesian analysis and Maximin. I hope this comparison better describes the differences, advantages, and weaknesses of info-gap, and that its less POVish...

Following the wills of the masses, I have removed the epidemic example. Lior Davidovitch (talk) 16:19, 30 March 2008 (UTC)

Comments on Lior Davidovitch's Revision of the illustrative example

G'day:

It was definitely a move in the right direction to delete the epidemic example.

Unfortunately, Lior Davidovitch got a number of things wrong.

1. First let us set the record straight. TSP, chromatic number and Sudoku do not claim to be radically different from all current NP-hard problems, nor is it claimed that they are not NP-hard problems. In sharp contrast Info-gap is claimed to be radically different...while in actual fact it is no more than a simple instance of the famous Maximin model.
2. So, given that it is an instance of the Maximin model the question is whether it deserves a separate article. At present this is an open question. Yet, for various reasons I vote for the continuing existence of a separate article.
3. The main thrust of the illustrative example should be to explain clearly and without obfuscation how info-gap deals with the severity of the uncertainty.
4. Unfortunately the latest revision does the precise opposite. It conceals this central issue by diverting attention to other, unrelated issues.
5. It does not make much sense to compare info-gap with other methods before one describes in full detail how Info-Gap works as a methodology for severe uncertainty with the emphasis being on its treatment of the severity in the uncertainty.
6. The Comparative Analysis subsection should be placed in the Critique section or in the Alternatives to Info-Gap section, or it should be a section on its own toward the end of the article.
7. On what grounds is it claimed that " ... Another characteristic of the Maximin analysis is its lack of use of estimates. ...". Maximin can easily incorporate estimates in the analysis (proof: (a) this is what info-gap does (b) info-gap is a special case of Maximin/Minimin).
8. This, however, is not the issue. The issue is whether it makes sense to confine the Maximin analysis to an immediate neighborhood of the estimate in situations where the estimate is a poor indication of the true value and is likely to be substantially wrong. The answer is obviously no! it is not! Which is precisely the reason why methodologies based on the Maximin paradigm that handle severe uncertainty properly do not even contemplate doing what Info-gap does.
9. It is interesting to note that info-gap's scholars are aware of the fact that under severe uncertainty it is wrong   to base the analysis on the given value of the estimate. For instance, in the context of an Epidemic example, where $\ \displaystyle {\overline {\beta }}\$ denotes a poor estimate of some function $\ \displaystyle \beta \$ that is subject to severe uncertainty, Yoffee and Ben-Haim (2006, p. 556) state the following obvious fact of life:

   Since the function $\ \displaystyle {\overline {\beta }}(t)\$ is most possibly wrong, the result in equation (6) is hardly reliable and therefore is not a good basis for choosing policy interventions which influence $\ \displaystyle {\overline {\beta }}(t)\$ or $\ \displaystyle N\$.

   Rephrasing this common-sensical conclusion in the context of our discussion we conclude that

   Since the estimate $\ \displaystyle {\tilde {u}}\$ is most possibly wrong, the results generated by the info-gap robustness/opportuneness models are hardly reliable and therefore are not a good basis for choosing decisions.

10. In any case, the comparison analysis should be scraped and rewritten from scratch as the current version is clearly biased in favor of info-gap. Furthermore, it should be written by someone who is well versed in both Maximin and Bayesian analysis.

Comments:

1. It is counter-productive for Info-Gap proponents to continue avoiding the central issue: severity of the uncertainty and the poor quality of the estimate.
2. I request again that a clear, unequivocal explanation be provided in the illustrative example outlining exactly how info-gap deals with the severity of the uncertainty.
3. Until this is done, Lior Davidovitch should undo his latest revision of the illustrative example.
4. In view of the repeated attempts to divert attention from this central issue, I restored Sniedo's Invariance Theorem as a reminder that info-gap does not deal with the severe uncertainty. It simply ignores it.
5. It should be stressed that the new section Invariance Property   is not a criticism of info-gap. It simply lays out mathematically, pictorially and discoursively an obvious idiosyncratic property of info-gap's robustness/opportuneness models for what it is. --Sniedo (talk) 05:53, 31 March 2008 (UTC)

I think critique is a legitimate and important part of any debate. It is not less important than the issue itself. However, a critique may also be based on mathematical truths. The invariance theorem is an example of a mathematical truth that is only interesting in the context of the criticism that robustness does not encompass the entire space of uncertainty. This criticism is true and important, but a) it does not mean that info-gap is useless - it just means that it is imperfect (much like any other decision theory), and b) it is still a criticism.

I think that the criticism section should contain more than subjective arguments: it should contain objective shortcommings of info-gap, perhaps even backed up with mathematical and pictorial illustrations. From this reason I think the maximin issue (that is, whether or not info-gap is radically different), the local vs. global robustness (from the background section), etc. (I remember something about reversal of preferences), should be in the criticism section. Yes, all of the above are (to some extent) mathematicl properties of info-gap theory, but they are only interesting in the context of criticizing this theory.

I prefer a consice article, followed by a lengthy mathematically backed criticism to the current state.

Lior Davidovitch (talk) 11:58, 31 March 2008 (UTC)

G'day:

I shall respond to Lior Davidovitch's specific comments later this week. At this stage I respond only to the general drift of his note.

• The comments reveal a serious misrepresentation of critique, criticism, and presentation of a subject.
• The fact that a substantiated argument brings to light a truth about a theory that subsequently happens to be unflattering cannot be regarded criticism. It is simply a fact that calls a spade a spade.
• So, before we go into the question of whether info-gap is rendered utterly useless or just partly useless or whatever, we must first be clear on the relevance of this truism for info-gap.
• An encyclopedia article outlining a theory must provide a faithful and correct description of the theory's theses, how it works, its scope of operation, its role and place and so on. This must apply to info-gap.
• So, before we proceed to discuss info-gap's failings -- and there is plenty to discuss here -- and how we should go about revising the article, we must have an informative, unequivocal explanation of how info-gap deals with the severity of the uncertainty.
• This is crucial for any meaningful discussion on info-gap. After all, this is what Info-Gap is all about as indicated by the subtitle of the two editions of the info-gap book: Decisions Under Severe Uncertainty.
• The onus is therefore on info-gap proponents to provide a full explanation here of this matter.
• I repeatedly requested such an explanation, but to no avail. All we get instead of an exposition of this central issue is repeated diversions into secondary issues and endless spin.
• Should it prove impossible to obtain such an explanation, we shall have to reject outright the contention that info-gap is a methodology for decisions under severe uncertainty.

Until we get such an explanation, Lior Davidovitch should undo his latest revision of the illustrative example. --Sniedo (talk) 08:25, 1 April 2008 (UTC)

G'day:

Some comments on Lior Davidovitch's recent thoughts about a revision of the article.

The idea that one has to separate the "bad" from the "good" in the exposition of a theory and to put the "bad" in the attic is amusing.

Following this idea, when discussing the properties of a function we shall indicate in the early "good" part of the discussion that the function is say differentiable, but shall hide to the bitter end the fact that the function is say not convex. And when discussing an optimization method, we shall indicate early on, in the "good" part of the discussion, that the method does not require the function being minimized to be convex, but shall hide to the bitter end the fact that the method can only guarantee a local minimum. And when discussing an algorithm, we shall announce at the outset that the algorithm can solve any nonlinear optimization problem, and then in the last page we shall indicate in a footnote that, computationally, the algorithm can only handle one decision variable and only one constraint which, by the way, must be a box constraint.

Come to think about it, why don't we apply this paradigm to movies, news broadcasts, poetry, music, manuals, dinners, the lot? This maxim will make it easy to focus exclusively on the good things in life.

Now back to info-gap.

1. Ideally, the article should be written so that there will be no need for a Critique section. In fact, I seem to recall that Wikipedia's guidelines recommend this option.
2. This can be done by incorporating in the exposition of the theory, in a smooth and reader-friendly manner, both its "good" and "bad" features.
3. It was impossible to do this here because info-gap proponents were reluctant to incorporate in the article new results. They insisted on hiding from the public, as long as possible, results that reflect badly on info-gap.
4. The Maximin Theorem per se is not criticism of info-gap. Most of the robust optimization methodologies are presented to the public as Maximin paradigms.
5. The Maximin Theorem becomes a major embarrassment to info-gap scholars when it is contrasted with info-gap's portrayal in the info-gap literature as a novel methodology that is radically different from all current theories of decision under uncertainty. The discussion of the details of this emabarrasing fact can be deferred to a Discussion section at the end of the article.
6. This factor should not be used as an execuse to place the Maximin Theorem in a Critique section. Readers should be advised at the outset that info-gap's robustness/opportuneness models are instances of classical decision theoretic models. What is wrong with that?
7. The Invariance Theorem per se is not a criticism of info-gap. Many methodologies are presented as "local" and there is nothing wrong with such a portrayal.
8. Of course, the Invariance Theorem becomes a major embarrassment to info-gap scholars when it is used as an argument that completely demolishes the contention that info-gap is a methodology for decision making under severe uncertainty. The discussion of this emabarrasing fact can be deferred to a Discussion section at the end of the article.
9. This factor should not be used as an execuse to place the theorem in a Critique section. Readers should be advised at the outset that info-gap's robustness/opportuneness models are inherently local and are therefore insensitive to the severity of the uncertainty. What is wrong with that?
10. Info-gap scholars should be welcome to discuss (in a Discussion section at the end of the article) whatever is relevant to the article, including the exact degree of uselessness of info-gap theory. Needless to say, critics of info-gap should also be welcome to contriute to that section.
11. This Discussion section could include subsections dealing with limitations, advantages, comparisons with other methods etc. and could be as long as one wishes.
12. Given the history of this article, it is essential now to add a section entitled History where the history of info-gap can be documented and discussed.
13. The article itself, however, should portray info-gap as we understand and view it today within the frameworks of decision theory and robust optimization.

I estimate that we can cut by more than 1/2 the length of the article simply by presenting the material in the usual academic style. It should take no more than two A4 pages to explain clearly and concisely what info-gap is all about. But to do this we need the cooperation of contributors such as Lior Davidovitch. Otherwise, will shall continue going around in circles forever.

I modified the article as follows:

1. Restored the discussion on the severity of the uncertainty in the Investment Example.
2. Added a quote in the Maximin/Minimin section to motivate the discussion on the Maximin/Info-gap connection.
3. Modified the layout of the Treasure Hunt storyboard.

We now have to clean up the Comparative Analysis subsection of the Investment Example and revise the Criticism section.

--Sniedo (talk) 08:48, 5 April 2008 (UTC)

G'day:

I revised the article as suggested above:

• Moved some text from the "Illustrative Example" and "Criticism" sections to a new section entitled "Discussion".
• Revised the "Comparative Analysis" subsection.
• Revised the "Criticism" section.
• Fixed a number of small things (eg references, links)

The long history of the article produced a comprehensive and technically sound thesis on info-gap that is ... completely incoherent as far as the "average" reader is concerned. Now that we have reached a consensus on the technical details, it is time to condense the article into a short, (no more than two or three A4 pages long) coherent description of Info-Gap decision theory. But, as I indicated above, to do this we need the cooperation of contributors such as Lior Davidovitch. Otherwise, will shall continue going around in circles forever.

-- Sniedo (talk) 02:27, 1 May 2008 (UTC)

Unfortunately, technical details were never the (main) disputed issue. The discussion has always revolved around interpretation, connotation, nuances. And here a consensus is yet to be reached. The problem will only be aggravated when the article will be condensed.

I think that the next stage should be to 'discuss' the future structure of the article: what sections, what is in (and where), and what is not. I expect it will be difficult to reach an accepted version, but that should be our aim - not condensing the current disputed one.

Lior Davidovitch (talk) 20:28, 14 May 2008 (UTC)

G'day:

After a long and tedious process the article is now almost spin-free. The role and place of Info-Gap in decision theory is now unequivocally spelled out by two theorems. Given that these theorems make unambiguous technical statements, they require no interpretation, much less a nuance analysis. The force of these theorems is self-evident. So, no more than 2-3 pages will be required to describe the local Maximin robustness method entitled Info-Gap and to explain why it is incapable of dealing with severe uncertainty:

1. The Maximin Theorem states in no uncertain terms that Info-Gap's robustness model is an instance of Wald's Maximin model. This means that whatever Info-Gap's robustness model can do, Wald's Maximin model can do -- and much more. This undercuts the contention that Info-Gap is a new methodology that is radically different from all current theories of decision under uncertainty. But what is more, given that the generic Maximin model is by far more powerful, what need is there for Info-Gap in the first place? The technical, spin-free answer is: none.
2. The Invariance Theorem shows Info-Gap's robustness model for what it is: a local Maximin robustness model that does not handle the severe uncertainty -- instead it simply ignores it. This, of course, is due to the analysis focusing solely on the immediate neighborhood of a poor estimate of the parameter of interest. So, given that global robustness models suitable for severe uncertainty are available aplenty in the literature, what is the rationale for using a local robustness model? The technical, spin-free answer is: none.

In short, this portrayal of Info-Gap, substantiated as it is by technical proof, leaves no room for discussion, interpretation or nuance as to what Info-Gap really is. It is a simple Maximin model that operates in the neighborhood of a poor (most likely substantially wrong) estimate of the parameter of interest. Hence it is -- in principle -- incapable of handling severe uncertainty, thus thoroughly unsuitable for decision-making under severe uncertainty.

Still, it is too soon to call it a day.

Before we can proceed to shorten the article, the subsection "Satisficing and bounded rationality" should in the very least be revised as in its present form it is pure spin.

To begin with, the opening statement of this subsection is not only misleading but downright incorrect. It reads as follows:

It is correct that the info-gap robustness function is local, and has restricted quantitative value in some cases.

Of course the phrase in some cases is out and out wrong!

Indeed, the opposite is the case!

It should read as follows:

As indicated by the Invariance Theorem and amplified by the Treasure Hunt in the Criticism section, Info-Gap's robustness analysis is local. What is more, under conditions of severe uncertainty it is conducted in the immediate neighborhood of a poor estimate that is likely to be substantially wrong. Thus, there is no other way but to assume that -- as a matter of principle -- the results yielded by Info-Gap's robustness/opportuneness model are poor and likely to be substantially wrong.

In other words, there are no two ways about it: in the framework of decision-making under severe uncertainty the Info-Gap analysis cannot be counted on -- methodologically speaking -- to generate sound/meaningful/valuable results.

As for the remainder of this paragraph, one wonders what is the meaning of:

However, a major purpose of decision analysis is to provide focus for subjective judgments. That is, regardless of the formal analysis, a framework for discussion is provided. Without entering into any particular framework, or characteristics of frameworks in general, discussion follows about proposals for such frameworks.

In any event, in my opinion the subsection "Satisficing and bounded rationality" should be deleted altogether.

-- Sniedo (talk) 03:30, 21 May 2008 (UTC)

It seems that the promised land of a stable and agreed article is still far away. In this case, I don't think there's any point in condensing the article.

Lior Davidovitch (talk) 07:26, 21 May 2008 (UTC)

The Info-Gap/Maximin connection revisited!

G'day.

The latest news!

Lior Davidovitch and Yakov Ben-Haim are at it again!

In a recent (June 5, 2008) working paper entitled "Profiling for crime reduction under severely uncertain elasticities", Lior Davidovitch and Yakov Ben-Haim (2008) revisit the Info-Gap/Maximin issue.

They circulate yet again Ben-Haim's old, flawed, ill-conceived Maximin/Minimax model, and ignore, again, the existence of correct Maximin models that are described in detail in, among other easily accessible sources, ... our WIKIPEDIA article!

I do not have the full bibliographical details of Davidovitch and Ben-Haim (2008), so at this stage I am not going to discuss it in the article itself. I shall do it once the working paper is published and these details become available.

Given the long discussions we had on this issue here, it is important to bring this new development to the attention of participants in this discussion.

The story is as follows (using the notation we adopted in this discussion and the WIKIPEDIA article):

${\begin{array}{c}\\{\it {\textrm {\it {Info-Gap's\ Robustness\ Model}}}}\\\displaystyle \max _{q\in {\mathcal {Q}}}\max \ \{\alpha \geq 0:r_{c}\leq R(q,u),\forall u\in {\mathcal {U}}(\alpha ,{\tilde {u}})\}\\\\\end{array}}$

 

Failed to parse (unknown function "\begin{array}"): {\displaystyle \begin{array}{c||c} \hline \it \textrm{\it Correct\ Maximin\ Model} &\it \textrm{\it Misguided\ Maximin\ Model} \\ \hline & \\ \displaystyle \max_{q\in \mathcal{Q}\,,\, \alpha \ge 0}\ \, \min_{u\in \mathcal{U}(\alpha,\tilde{u})} \alpha \cdot \left(r_{c}\preceq R(q,u)\right) & \displaystyle \max_{q\in \mathcal{Q}}\ \min_{u\in \mathcal{U}(\alpha_{m},\tilde{u})} R(q,u)\\ \displaystyle a \preceq b := \begin{cases} 1 &, \ a \le b \\ 0 &, \ a > b\end{cases}& \alpha_{m} = {\it some\ fixed\ value} \\[0.3in] \hline & \\ \it \textrm{\it a\ la\ Sniedovich\, (2007)} & \it \textrm{\it a\ la\ Davidovitch\ and\ Ben-Haim\, (2008)} \end{array} }

Note that I refer to Davidovitch and Ben-Haim's (2008) model as "Misguided" rather than "wrong". The reason is the explanation -- or rather lack of it -- that Davidovitch and Ben-Haim (2008) provide for fixing the value of the parameter $\ \alpha \$ in their wrong ad hoc model, and ... the lack of any reference to the existence of "correct" Maximin models that Davidovitch and Ben-Haim (2008) no doubt are familiar with, eg. those set out in the WIKIPEDIA article.

The excuse, this time, for the modeling blunder is as follows: for some inexplicable reason Davidovitch and Ben-Haim (2008) state that in the framework of a Maximin/Minimax model they have to assume that the object $\ \alpha \$ must be treated as a parameter whose value is fixed in advance.

Why should the value of $\ \alpha \$ be fixed in advance in the context of a Maximin/Minimax model while in the framework of Info-Gap's robustness model the very same mathematical object is "allowed" to vary and is assigned the role of a decision variable?

The fact is, and it is a fact, that there are no such modeling rules and regulations with regard to of Maximin/Minimax.

In short, it looks like Davidovitch and Ben-Haim (2008) are determined to show, by hook or by crook, the impossible: that Info-gap's robustness model is not a Maximin model.

And all this, mind you, when the obvious -- The Maximin Theorem -- is starring us, including Davidovitch and Ben-Haim, in the face, in among other sources, the WIKIPEDIA article itself:

Maximin Theorem

As shown in Sniedovich (2007), Info-gap's robustness model is a simple instance of Wald's Maximin model. Specifically,

${\hat {\alpha }}(q,{r_{c}})=\max \left\{\alpha :\ {r_{\rm {c}}}\leq \min _{u\in {\mathcal {U}}(\alpha ,{\tilde {u}})}R(q,u)\right\}=\max _{\alpha \geq 0}\min _{u\in {\mathcal {U}}(\alpha ,{\tilde {u}})}\varphi (q,\alpha ,u)$

recalling that

$\varphi (q,\alpha ,u):={\begin{cases}\quad \alpha &,\ \ r_{c}\leq R(q,u)\\-\infty &,\ \ r_{c}>R(q,u)\end{cases}}\ ,\ q\in {\mathcal {Q}},\alpha \geq 0,u\in {\mathcal {U}}(\alpha ,{\tilde {u}})$

What then is the logic behind yet another futile attempt to justify an obviously erroneous explanation of the Info-Gap Maximin connection?

More on the issue of the InfoGap/Maximin connection can be found in the working paper "Anatomy of a misguided Minimax Model"  that is available on my website (info-gap.moshe-online.com).

Note: The model that Davidovitch and Ben-Haim (2008) actually formulate is a Minimax model. Here I translated it into the equivalent Maximin model by multiplying the performance constraint by -1 and reversing the "sign" of the constraint. This is done so as to comply with the format of the model formulated in the WIKIPEDIA article.

Sniedo (talk) 05:40, 15 July 2008 (UTC)