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Decision-Making Under Severe Uncertainty  
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Reviews of publications on Info-Gap decision theory

Review # 1 (Posted: April 5, 2009; Last update: April 10, 2009)

Reference: Ben-Haim, Y.
Info-Gap Decision Theory: decisions under severe uncertainty
Academic Press, 2006
Information-Gap Decision Theory: decisions under severe uncertainty
Academic Press, 2001
Scores TUIGF:100%
SNHNSNDN:200%
GIGO:100%


Overview

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
These are the two editions of the Info-Gap book. I shall refer to the second edition.

A number of my colleagues who are also critical of Info-Gap decision theory have long suggested that I review this book. However, at present I do not plan to do this. The reason is simple: the book abounds with so much empty rhetoric and spin that an "official" review will require concentrating on the rhetoric to the detriment of a detailed treatment of the more urgent failings of this theory. At this stage, therefore, I prefer to focus only on the theoretical, methodological and technical aspects of Info-Gap decision theory.

Readers who are interested to see how spin and hollow rhetoric play out in this literature can visit other pages on my site where some references are made to this aspect of the Info-Gap enterprise:

The comprehensive compilation FAQs about Info-Gap can be viewed as a review of the scientific aspects of Info-Gap decision theory. Please note that a PDF file of this compilation is available. This compilation will serve as core material for my planned book "A Critique of Info-Gap Decision Theory". The spin and rhetoric aspects of Info-Gap will be discussed in the planned manuscript "The Rise and Rise of Voodoo Decision-Making".

So, stay tuned ...

Note:
The super-high SNHNSNDN scored by the book is due to the erroneous analysis of the relationship between Info-Gap and Maximin, and the claim that Info-Gap's robustness analysis is not a Maximin analysis (page 93).

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 claim that info-gap's robustness analysis is not a worst-case analysis.

It should be pponted out 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 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*.

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 local 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 the 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

Based on the above analysis, it is clear that it is very easy to debunk info-gap decision theory.

In fact, the more Ben-Haim attempts to salvage his theory, the easier it is to demonstrate how wrong he is. In his new book Ben-Haim (2010) claims that his robustness model is different from robustness models used in robust-control and the Maximin/Minimax model. Furthermore, he presents info-gap decision theory as a theory that is a response to the challenge posed by surprises associated with the "economic problem".

DEBUNKED!
Obviously, Ben-Haim (2001, 2006, 2010) is very wrong on all fronts.

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

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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