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Reviews of publications on Info-Gap decision theory

Review # 14 (Posted: July 22, 2010; last update: September 12, 2010)

Reference: Ben-Haim, Y.
Info-Gap Economics: An Operational Introduction
Palgrave, 2010
Product Description

After every crisis economists and policy analysts ask: can better models help prevent or ameliorate such situations? This book provides an answer. Yes, quantitative models can help if we remember that they are rough approximations to a vastly more complex reality. Models can help if we include realistic but simple representations of uncertainty among our models, and if we retain the pre-eminence of human judgment over the churning of our computers.

Info-gap theory is a new method for modeling and managing severe uncertainty. The core of the book presents detailed examples of info-gap analysis of decisions in monetary policy, financial economics, environmental economics for pollution control and climate change, estimation and forecasting. This book is essential reading for economic policy analysts and researchers.

Provisional Scores TUIGF:100%
SNHNSNDN:1299%
GIGO:100%

Review

Debunking info-gap decision theory
Reviews of info-gap publications
Voodoo decision-making
Second Opinion
Guided Tour
Myths and Facts
FAQS
Mobile Maximin Theorem
Mobile Radius of Stability Theorem
This book is the latest addition to the author's series of books on info-gap decision theory. It is devoted to the application of info-gap decision theory in economics.

As in the case of the previous books on info-gap decision theory, this book as well constitutes a major indictment of the state of the art in decision-making under severe uncertainty. Because, if the book's central thesis holds, namely if info-gap decision theory does indeed do what the author claims it capable of doing, then the following conclusion is immediate:

For at least fifty years now, the radius of stability model has been used by countless scholars in areas ranging from numerical analysis, applied mathematics, control theory, optimization theory, to economics, etc., to model and analyze the robustness of systems against small perturbations in the nominal value of a parameter of interest.

Yet, all these years, all these scholars had no clue that precisely the same model, using exactly the same analysis, can deal reliably with severe uncertainty, namely with cases where the perturbations of interest are extremely large, even unbounded!

The question is then, how could this possibly happen?!

How could all these scholars fail to see the enormous potential latent in the old warhorse, the radius of stability model? How could they fail to see that this simple intuitive model is capable of handling rare events, surprises, shocks, catastrophes --- perhaps even Naseem Taleb's Black Swans?

There is, of course, another possibility!

The other possibility is that the thesis advanced in the books on info-gap decision theory is fundamentally flawed, indeed downright erroneous, and that all those countless scholars who all these years proceeded on the assumption that the radius of stability model is unsuitable for modeling/analyzing very large perturbations, were right.

As it turns out, this is indeed the case!

It turns out that info-gap decision theory amounts to a gross misapplication of a model that is in fact, a reinvented, simple, radius of stability model.

Thus, what this book demonstrates is a total lack of appreciation of the difference between local and global robustness and a lack of familiarity with Hansen and Sargent's extensive work on robust decision-making under uncertainty in economics, notably their 2007 book entitled Robustness.

It is hard to imagine how a book on robust decision-making under uncertainty in economics, published in 2010, can fail to cite, let alone discuss, Hansen and Sargent's extensive work in the area.

I shall not be surprised, therefore, if economists who are familiar with robust decision-making under uncertainty may also find this surprising.

My objective, of course, is not to second guess other scholars, but to express my own views on the book.

I should point out, at the outset, that the harshness of my criticism of info-gap decision theory, here and elsewhere, is a reflection of the seriousness of the flaws in the methodology proposed in the books on this theory and the author's total oblivion to the state of the art in robust decision-making under severe uncertainty.


My Review

To put it mildly, it is naive in the extreme to propose that a local analysis in the neighborhood of a poor estimate, a wild guess, constitutes a suitable approach to the modeling and analysis of economic systems that are subject to severe uncertainty of the type postulated by info-gap decision theory (vast uncertainty space, likelihood-free uncertainty model). For one thing, such an approach clearly violates universally accepted norms of scientific reasoning, such as

So clearly, the onus is on the author to show that an economic analysis based on this proposition can be justified. But, there is nothing in the new book to support info-gap decision theory's local approach to severe uncertainty.

In greater detail, the author must explain how an analysis (which is in fact a radius of stability analysis) in the neighborhood of a poor estimate (guess) of the true value of a parameter can possibly furnish a reliable means for determining the robustness of decisions against severe uncertainty in the true value of the parameter. He must explain how such an analysis can reliably handle rare events, surprises, shocks, catastrophes, etc.

In fact, prior to this the author must explain on what grounds does he claim that his proposed method is "new". Because, given that -- as indicated above -- the model used in the Info-gap robustness analysis is in fact a "radius of stability" model, the author should have in the very least compared the two models. However, not only is such a comparison absent from the book, the term ``radius of stability'' is not even mentioned in it. Is it because the author is unaware that his robustness model is a radius of stability model? Or is it because the author holds that his robustness model is not a radius of stability model? If so, what exactly is the difference?

The same applies to the Maximin connection, especially because Ben-Haim (2010) goes out of his way to stress that info-gap's robustness model is different from Maximin models:

Info-gap theory is not a worst-case analysis. While there may be a worst case, one cannot know what it is and one should not base one's policy upon guesses of what it might be. Info-gap theory is related to robust-control and min-max methods, but nonetheless different from them. The strategy advocated here is not the amelioration of purportedly worst cases.

Ben-Haim (2010, p. 9)

The difference from min-max approaches is that we are able to select a policy without ever specifying how wrong the model actually is. Min-max and info-gap robust-satisficing strategies will sometime agree and sometime differ.

Ben-Haim (2010, p. 10)

So let us examine more closely the relationship between info-gap's robustness model and these two other models.

The Wald's Maximin connection

As I discuss in detail the whole question of the info-gap/Maximin connection on other pages on this site (see for instance FAQs about info-gap decision theory), all I need to do here is remind the readers of the following.

A formal rigorous proof demonstrating that info-gap's robustness model is a simple instance of Maximin model has been available to the public since the end of 2006, and in peer reviewed publications since 2007.

Yet , Ben-Haim continues to obfuscate on this point, vacillating between admission that the proof is mathematically correct to claims in a recent publication maintaining that info-gap's robustness model is not a Maximin model.

I have no explanation for this.

All I can do is again, give the reader easy access to the theorem and its proof. And all you have to do is click on the show/hide for the theorem and its proof.

Regarding Ben-Haim's (2010, p. 10) reference to worst-case analysis.

It should be stressed that since info-gap's robustness model is a local robustness model, the worst-case analysis that it conducts is a local one. The picture is this:

Info-gap's robustness model
max {α ≥ 0: r* ≤ r(q,p),∀p∈B(α,p*)}
The rectangle represents the parameter space, P. The shaded area represents the values of the parameter p for which the system satisfies a given performance requirement, namely r* ≤ r(q,p). The center of the circles, p*, represents a give estimate of the parameter p. B(α,p*) denotes a ball of radius α around p*.

In other words, info-gap's robustness model does not search for the worst p in P. Rather, for each value of α, it searches for the worst p in B(α,p*). The robustness of a decision/system is then equal to the largest value of α for which the worst value of p in B(α,p*) satisfies the performance requirement.

This is a typical worst-case analysis a la Maximin.

The Radius of Stability connection

The reference to robust-control in Ben-Haim's (2010, p. 9) new book prompted me to remind the Father of info-gap decision theory and his followers that the most popular model of local robustness in control theory is the Radius of Stability model (circa 1960).

Recall that

The Radius of Stability of a system is the radius of the largest ball around a given nominal value of the parameter of interest all of whose elements satisfy pre-determined stability requirements.

The info-gap robustness of a system is the size of the largest ball around a given estimate of the parameter of interest all of whose elements satisfy a single pre-determined performance requirement of the "≤" or "≥" type.

Obviously, info-gap's robustness model is a very simple instance of the Radius of stability model, namely that instance where the stability requirement is specified by a single "≤" or "≥" performance constraint. The picture is this:

Find the differences
Radius of Stability (circa 1960) Info-gap decision theory (circa 2000)
max {α ≥ 0: p∈P(q),∀p∈B(α,p*)} max {α ≥ 0: r* ≤ r(q,p),∀p∈B(α,p*)}
The rectangle represents the parameter space, P. The shaded area represents the set P(q) that consists of the values of the parameter p for which the system satisfies given stability requirements. The center of the circles, p*, represents a given nominal value of the parameter p. B(α,p*) denotes a ball of radius α around p* The rectangle represents the parameter space, P. The shaded area represents the values of the parameter p for which the system satisfies given a given performance requirement, namely r* ≤ r(q,p). The center of the circles, p*, represents a give estimate of the parameter p. B(α,p*) denotes a ball of radius α around p*.
So clearly:
Theorem
Info-gap's robustness model is a simple instance of the radius of stability model, that is the instance specified by P(q) = {p∈P: r* ≤ r(q,p)}.

Proof.
Substituting P(q) = {p∈P: r* ≤ r(q,p)} in the expression defining the radius of stability model, we obtain info-gap's robustness model.

It is as simple as that.

For the record, a trivial formal proof is provided in my recent paper entitled "A bird's view of info-gap decision theory" (Journal of Risk Finance, 11(3), 263-268, 2010).

And to see how elementary the formal proof is, simply click here to hide/show it.

For the benefit of readers who encounter this theorem for the first time I want to reiterate its implications for info-gap decision theory.

  • The Radius of stability model is a model of local robustness. This means that it functions as a tool for the modeling/analysis/determination of small perturbations in a given nominal value of the parameter of interest.

  • The implication is that using the Radius of stability as a robustness model for the treatment of severe uncertainty of the type considered by info-gap decision theory -- where the estimate is poor, the uncertainty space is vast and the uncertainty model is likelihood free -- amounts to a misapplication of this model.

  • This misapplication renders info-gap decision theory a voodoo decision theory par excellence.

Official Mobile Debunker of info-gap decision theory

The above analysis, which shows how easy it is to debunk info-gap decision theory, does the same to Info-Gap Economics.

Hence, the more concerted the effort to salvage this theory, the easier it is to demonstrate how flawed it is. That is, the more vehement the claims (Ben-Haim 2010) that info-gap’s robustness model is different from robustness models used in robust-control and from the Maximin/Minimax model, the easier it is to show how groundless they are. And all this, needless to say, undercuts the claim that info-gap decision theory offers a response to the challenge posed by surprises associated with the "economic problem".

DEBUNKED!

The reader may want to read my Official Mobile Debunker of info-gap decision theory.

Summary

A short summary of my position on the book is as follows:

DEBUNKED!

Some readers may be interested in my preliminary review of the book.


Preliminary Review
(July 22, 2010)

I ought to make it clear that at this point I have not read the entire text. All I have read so far are the pages that are available online by Amazon. These include the preface, table of contents, first chapter (where Info-Gap decision theory is described), subject and author indices, and the cover matter. I have also used the online facility to search the entire book by means of relevant key words. Using this facility I managed to conduct an extensive search of the book which enabled me to read the material associated with these key words.

So, although I cannot, at this stage, provide a full assessment of the book, based on what I have read I can decidedly conclude the following:

The extremely high provisional SNHNSNDN (see nothing, hear nothing, say nothing, do nothing) score that I have given this publication reflects the author's apparent reluctance to deal seriously with the fundamental flaws afflicting Info-gap decision theory. These are described in detail in publications that are easily accessible to the public. The author's disregard of a damming critique of his theory is of a piece with his total disregard of the state-of-the-art in decision-making under severe uncertainty in general, and robust decision-making in particular. The author does not even bother to refer to publications that are milestones in the area of decision-making (especially, under sesver uncertainty) or to more recent publications in the area of Robust Optimization that bear immediately on his theory.

The upshot of this is that the author continues to hold that Info-Gap's robustness model is not a Maximin model and he remains oblivious to the fact that the local nature of Info-Gap's robustness model renders this theory a voodoo decision theory par excellence.

I should also add that there is equally no reference in this book to the fact that Info-Gap's robustness model is a Radius of Stability model (circa 1960).

In view of all of this, my first impression is that this new book does not meet even minimum universally accepted academic standards regarding literature surveys aimed at providing the basis for an objective assessment of theories proposed in academic publications. There are therefore no grounds whatsoever to argue that this book offers a new method for economic analysis and decision-making because there are no grounds whatsoever to the claim that "... Info-gap theory is a new method for modeling and managing severe uncertainty ...". Much less are there any grounds to contend that the book offers a sound/reliable/effective method for this purpose.

Because, to repeat:

The point that economic policy analysts and researchers should take note of is that Info-Gap Economic's thesis is that a local analysis of the Radius of Stability type is a suitable tool for the treatment of severe uncertainty.

The picture is this:

To give you a Bird's View of this thesis, imagine that the uncertainty space W is represented by the island, and the sample space w by the area surrounding Elliot Price Conservation Park (The small whitish area is Lake Eyre). The picture is a NASA satellite image of Australia. See WIKIPIDIA at http://en.wikipedia.org/wiki/File:Australia_satellite_plane.jpg.

Thus, Info-Gap Economics' central proposition is the absurd idea that an economic decision that is found to be robust (fragile) for a small sample (the small area in the middle of the island), is also robust (fragile) for a whole system (the entire island). Hence, no robustness analysis is required for the system (island) as a whole: The local robustness of a decision over the small square w is a good indication of its robustness over the entire island W.

This prescription for the modeling and management of severe uncertainty is hailed by the author as "realistic but simple"!

State of the art in economics

To corroborate my contention that the author's claim that Info-Gap Economics offers a new method for economic analysis is groundless, observe that this claim is made in a vacuum, without any reference to the robustness models that have been used in economics for many years.

Consider for example the abstract of the entry Robust Control by Noah Williams in the New Palgrave Dictionary of Economics, Second Edition, 2008:

Robust control is an approach for confronting model uncertainty in decision making, aiming at finding decision rules which perform well across a range of alternative models. This typically leads to a minimax approach, where the robust decision rule minimizes the worst-case outcome from the possible set. This article discusses the rationale for robust decisions, the background literature in control theory, and different approaches which have been used in economics, including the most prominent approach due to Hansen and Sargent.

It is particularly striking that Info-Gap Economics takes no notice whatsoever of the numerous publications on this topic by Hansen and Sargent, e.g. their book Robustness (2007), whose Product Description reads as follows:

.

The standard theory of decision making under uncertainty advises the decision maker to form a statistical model linking outcomes to decisions and then to choose the optimal distribution of outcomes. This assumes that the decision maker trusts the model completely. But what should a decision maker do if the model cannot be trusted?

Lars Hansen and Thomas Sargent, two leading macroeconomists, push the field forward as they set about answering this question. They adapt robust control techniques and apply them to economics. By using this theory to let decision makers acknowledge misspecification in economic modeling, the authors develop applications to a variety of problems in dynamic macroeconomics.

Technical, rigorous, and self-contained, this book will be useful for macroeconomists who seek to improve the robustness of decision-making processes.

Lars Peter Hansen, and Thomas J. Sargent
Robustness
Princeton University Press, 2007.

The only conclusion that can be drawn from the bibliography list in Info-Gap Economics, is that the author is not at home with the state-of-the-art in robust decision making in economics.

I shall extend this review once I have read the book in full.


Other Reviews

  1. Ben-Haim (2001, 2006): Info-Gap Decision Theory: decisions under severe uncertainty.

  2. Regan et al (2005): Robust decision-making under severe uncertainty for conservation management.

  3. Moilanen et al (2006): Planning for robust reserve networks using uncertainty analysis.

  4. Burgman (2008): Shakespeare, Wald and decision making under severe uncertainty.

  5. Ben-Haim and Demertzis (2008): Confidence in monetary policy.

  6. Hall and Harvey (2009): Decision making under severe uncertainty for flood risk management: a case study of info-gap robustness analysis.

  7. Ben-Haim (2009): Info-gap forecasting and the advantage of sub-optimal models.

  8. Yokomizo et al (2009): Managing the impact of invasive species: the value of knowing the density-impact curve.

  9. Davidovitch et al (2009): Info-gap theory and robust design of surveillance for invasive species: The case study of Barrow Island.

  10. Ben-Haim et al (2009): Do we know how to set decision thresholds for diabetes?

  11. Beresford and Thompson (2009): An info-gap approach to managing portfolios of assets with uncertain returns

  12. Ben-Haim, Dacso, Carrasco, and Rajan (2009): Heterogeneous uncertainties in cholesterol management

  13. Rout, Thompson, and McCarthy (2009): Robust decisions for declaring eradication of invasive species

  14. Ben-Haim (2010): Info-Gap Economics: An Operational Introduction

  15. Hine and Hall (2010): Information gap analysis of flood model uncertainties and regional frequency analysis

  16. Ben-Haim (2010): Interpreting Null Results from Measurements with Uncertain Correlations: An Info-Gap Approach

  17. Wintle et al. (2010): Allocating monitoring effort in the face of unknown unknowns

  18. Moffitt et al. (2010): Securing the Border from Invasives: Robust Inspections under Severe Uncertainty

  19. Yemshanov et al. (2010): Robustness of Risk Maps and Survey Networks to Knowledge Gaps About a New Invasive Pest

  20. Davidovitch and Ben-Haim (2010): Robust satisficing voting: why are uncertain voters biased towards sincerity?

  21. Schwartz et al. (2010): What Makes a Good Decision? Robust Satisficing as a Normative Standard of Rational Decision Making

  22. Arkadeb Ghosal et al. (2010): Computing Robustness of FlexRay Schedules to Uncertainties in Design Parameters

  23. Hemez et al. (2002): Info-gap robustness for the correlation of tests and simulations of a non-linear transient

  24. Hemez et al. (2003): Applying information-gap reasoning to the predictive accuracy assessment of transient dynamics simulations

  25. Hemez, F.M. and Ben-Haim, Y. (2004): Info-gap robustness for the correlation of tests and simulations of a non-linear transient

  26. Ben-Haim, Y. (2007): Frequently asked questions about info-gap decision theory

  27. Sprenger, J. (2011): The Precautionary Approach and the Role of Scientists in Environmental Decision-Making

  28. Sprenger, J. (2011): Precaution with the Precautionary Principle: How does it help in making decisions

  29. Hall et al. (2011): Robust climate policies under uncertainty: A comparison of Info-­-Gap and RDM methods

  30. Ben-Haim and Cogan (2011) : Linear bounds on an uncertain non-linear oscillator: an info-gap approach

  31. Van der Burg and Tyre (2011) : Integrating info-gap decision theory with robust population management: a case study using the Mountain Plover

  32. Hildebrandt and Knoke (2011) : Investment decisions under uncertainty --- A methodological review on forest science studies.

  33. Wintle et al. (2011) : Ecological-economic optimization of biodiversity conservation under climate change.

  34. Ranger et al. (2011) : Adaptation in the UK: a decision-making process.


Recent Articles, Working Papers, Notes

Also, see my complete list of articles
    Moshe's new book!
  • Sniedovich, M. (2012) Fooled by local robustness, Risk Analysis, in press.

  • Sniedovich, M. (2012) Black swans, new Nostradamuses, voodoo decision theories and the science of decision-making in the face of severe uncertainty, International Transactions in Operational Research, in press.

  • Sniedovich, M. (2011) A classic decision theoretic perspective on worst-case analysis, Applications of Mathematics, 56(5), 499-509.

  • Sniedovich, M. (2011) Dynamic programming: introductory concepts, in Wiley Encyclopedia of Operations Research and Management Science (EORMS), Wiley.

  • Caserta, M., Voss, S., Sniedovich, M. (2011) Applying the corridor method to a blocks relocation problem, OR Spectrum, 33(4), 815-929, 2011.

  • Sniedovich, M. (2011) Dynamic Programming: Foundations and Principles, Second Edition, Taylor & Francis.

  • Sniedovich, M. (2010) A bird's view of Info-Gap decision theory, Journal of Risk Finance, 11(3), 268-283.

  • Sniedovich M. (2009) Modeling of robustness against severe uncertainty, pp. 33- 42, Proceedings of the 10th International Symposium on Operational Research, SOR'09, Nova Gorica, Slovenia, September 23-25, 2009.

  • Sniedovich M. (2009) A Critique of Info-Gap Robustness Model. In: Martorell et al. (eds), Safety, Reliability and Risk Analysis: Theory, Methods and Applications, pp. 2071-2079, Taylor and Francis Group, London.
  • .
  • Sniedovich M. (2009) A Classical Decision Theoretic Perspective on Worst-Case Analysis, Working Paper No. MS-03-09, Department of Mathematics and Statistics, The University of Melbourne.(PDF File)

  • Caserta, M., Voss, S., Sniedovich, M. (2008) The corridor method - A general solution concept with application to the blocks relocation problem. In: A. Bruzzone, F. Longo, Y. Merkuriev, G. Mirabelli and M.A. Piera (eds.), 11th International Workshop on Harbour, Maritime and Multimodal Logistics Modeling and Simulation, DIPTEM, Genova, 89-94.

  • Sniedovich, M. (2008) FAQS about Info-Gap Decision Theory, Working Paper No. MS-12-08, Department of Mathematics and Statistics, The University of Melbourne, (PDF File)

  • Sniedovich, M. (2008) A Call for the Reassessment of the Use and Promotion of Info-Gap Decision Theory in Australia (PDF File)

  • Sniedovich, M. (2008) Info-Gap decision theory and the small applied world of environmental decision-making, Working Paper No. MS-11-08
    This is a response to comments made by Mark Burgman on my criticism of Info-Gap (PDF file )

  • Sniedovich, M. (2008) A call for the reassessment of Info-Gap decision theory, Decision Point, 24, 10.

  • Sniedovich, M. (2008) From Shakespeare to Wald: modeling wors-case analysis in the face of severe uncertainty, Decision Point, 22, 8-9.

  • Sniedovich, M. (2008) Wald's Maximin model: a treasure in disguise!, Journal of Risk Finance, 9(3), 287-291.

  • Sniedovich, M. (2008) Anatomy of a Misguided Maximin formulation of Info-Gap's Robustness Model (PDF File)
    In this paper I explain, again, the misconceptions that Info-Gap proponents seem to have regarding the relationship between Info-Gap's robustness model and Wald's Maximin model.

  • Sniedovich. M. (2008) The Mighty Maximin! (PDF File)
    This paper is dedicated to the modeling aspects of Maximin and robust optimization.

  • Sniedovich, M. (2007) The art and science of modeling decision-making under severe uncertainty, Decision Making in Manufacturing and Services, 1-2, 111-136. (PDF File) .

  • Sniedovich, M. (2007) Crystal-Clear Answers to Two FAQs about Info-Gap (PDF File)
    In this paper I examine the two fundamental flaws in Info-Gap decision theory, and the flawed attempts to shrug off my criticism of Info-Gap decision theory.

  • My reply (PDF File) to Ben-Haim's response to one of my papers. (April 22, 2007)

    This is an exciting development!

    • Ben-Haim's response confirms my assessment of Info-Gap. It is clear that Info-Gap is fundamentally flawed and therefore unsuitable for decision-making under severe uncertainty.

    • Ben-Haim is not familiar with the fundamental concept point estimate. He does not realize that a function can be a point estimate of another function.

      So when you read my papers make sure that you do not misinterpret the notion point estimate. The phrase "A is a point estimate of B" simply means that A is an element of the same topological space that B belongs to. Thus, if B is say a probability density function and A is a point estimate of B, then A is a probability density function belonging to the same (assumed) set (family) of probability density functions.

      Ben-Haim mistakenly assumes that a point estimate is a point in a Euclidean space and therefore a point estimate cannot be say a function. This is incredible!


  • A formal proof that Info-Gap is Wald's Maximin Principle in disguise. (December 31, 2006)
    This is a very short article entitled Eureka! Info-Gap is Worst Case (maximin) in Disguise! (PDF File)
    It shows that Info-Gap is not a new theory but rather a simple instance of Wald's famous Maximin Principle dating back to 1945, which in turn goes back to von Neumann's work on Maximin problems in the context of Game Theory (1928).

  • A proof that Info-Gap's uncertainty model is fundamentally flawed. (December 31, 2006)
    This is a very short article entitled The Fundamental Flaw in Info-Gap's Uncertainty Model (PDF File) .
    It shows that because Info-Gap deploys a single point estimate under severe uncertainty, there is no reason to believe that the solutions it generates are likely to be robust.

  • A math-free explanation of the flaw in Info-Gap. ( December 31, 2006)
    This is a very short article entitled The GAP in Info-Gap (PDF File) .
    It is a math-free version of the paper above. Read it if you are allergic to math.

  • A long essay entitled What's Wrong with Info-Gap? An Operations Research Perspective (PDF File) (December 31, 2006).
    This is a paper that I presented at the ASOR Recent Advances in Operations Research (PDF File) mini-conference (December 1, 2006, Melbourne, Australia).

Recent Lectures, Seminars, Presentations

If your organization is promoting Info-Gap, I suggest that you invite me for a seminar at your place. I promise to deliver a lively, informative, entertaining and convincing presentation explaining why it is not a good idea to use — let alone promote — Info-Gap as a decision-making tool.

Here is a list of relevant lectures/seminars on this topic that I gave in the last two years.


Disclaimer: This page, its contents and style, are the responsibility of the author (Moshe Sniedovich) and do not represent the views, policies or opinions of the organizations he is associated/affiliated with.


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