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Debunking Info-Gap decision theory

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Some of my colleagues are more than a bit mystified that it should take so long to stop info-gap decision theory in its tracks -- at least in Australia.

The point, of course, is that the flaws in this theory are so obvious, that one would have expected that a presentation of no more than 15-20 minutes should have sufficed to convince any info-gap enthusiast that the theory is indeed fundamentally flawed.

So the question is: why should it take so long to accomplish what can be done in 15-20 minutes?

That this is a valid question is of course obvious, still I shall not pursue it here. But, I'll be more than happy to discuss it with you over a cup of coffee (skinny latte, no sugar, please!)

For the moment, I suggest that you draw on your own experience to work out your own answer to this question

All I can say is this:

Debunking info-gap decision theory is a simple, straightforward exercise. But, containing its spread is a different matter altogether. Because, this involves dissuading people who are already committed to it. And this, as you can no doubt imagine, is a far more difficult and complicated task.

So, the objective of this short discussion is to provide the interested reader with easy and immediate access to what I shall refer to here as the Official Mobile Debunker of the theory. The point of this device is to make vivid to the reader that the length of this campaign does not in any way reflect on the ease with which info-gap decision theory can be debunked.

And before I proceed to do this, I want to point out that the debunker that I am going to nominate here as the Official Mobile Debunker is not my favorite choice for the job. Suffice it to say that the Official Debunker is based on the Radius of Stability model and that I prefer a slightly different version thereof, namely that which is based on Info-Gap robustness model's connection to Wald's Maximin model. The reason that I nominate the first as the Official Debunker is that my experience has shown that it is easier to put this idea across with the aid of the Radius of Stability model, especially to persons who are not familiar with Wald's maximin model.

But first, let us remind ourselves of what is being debunked here.

The Debunkee

In a nutshell, info-gap decision theory's principal propositions (Ben-Haim 2001, 2006) are that:

So, to debunk the info-gap decision theory, it is sufficient to show that:

As we shall see, the Official Debunker does much more than this.

With this in mind, let us meet the real McCoy.

The official Mobile Debunker of Info-Gap Decision Theory

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 associated with the system. Symbolically, the radius of stability of system q at p* is defined as follows:

max {α ≥ 0: p∈P(q),∀p∈B(α,p*)}

The info-gap robustness of a system/decision 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 imposed on the system. In symbols, the robustness of system/decision q at p* is defined as follows:

max {α ≥ 0: r* ≤ r(q,p),∀p∈B(α,p*)}

It is immediately clear that info-gap's robustness model is a very simple instance (special case) of the Radius of stability model. Namely, it is that instance (special case) 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:

Radius of Stability Theorem
Info-gap's robustness model is a simple instance of the radius of stability model, namely 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.

A more formal, all the same trivial proof, is provided in my recent article: "A bird's view of info-gap decision theory" (Journal of Risk Finance, 11(3), 263-268, 2010).

And to see for yourself 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.

A prescription for Voodoo decision-making

The Radius of Stability model is a model of local robustness. This means that it functions as a tool for the modeling/analysis/management of small perturbations in a given nominal value of the parameter of interest. Indeed, it has been performing this function faithfully for many years now -- officially, at least since the early 1960s.

But the whole point is that Info-Gap decision theory prescribes an application of the Radius of Stability to model/analyze/manage the robustness of situations that are subject to conditions of severe uncertainty, namely situations where

To give you a vivid illustration of the absurd latent in info-gap decision theory's treatment of severe uncertainty of this type consider the following picture:

No Man's LandûNo Man's Land
-∞ <-------------- Complete region of uncertainty under consideration --------------> ∞

where

 û   denotes the estimate of the parameter of interest.
    denotes the complete region of uncertainty under consideration.
    represents the region of uncertainty that actually affects the results
  generated by info-gap's robustness analysis.
No Man's Land   represents the vast part of the complete region of uncertainty that has no
  impact whatsoever on the results generated by info-gap's robustness model.

What this picture makes vivid is that Info-gap decision theory's central proposition to use the radius of stability model to model/analyze/manage the robustness of situations that are subject to severe uncertainty effectively means that it prescribes the following:

This approach, as I have been arguing, amounts to a prescription for: voodoo decision-making.

The Maximin Debunker

Although the Radius of Stability based mobile debunker does its job perfectly well, as indicated above, I prefer the debunker based on the Wald's Maximin model.

There are a number of reasons for this, but I shall mention only the following:

That said, the Maximin debunker asserts the following:

Maximin Theorem
Info-gap's robustness model is a simple instance of Wald's famous Maximin model (circa (1940), the foremost model for the treatment of severe uncertainty in classical decision theory.

A formal, still elementary, proof is outlined in my recent article: "A bird's view of info-gap decision theory" (Journal of Risk Finance, 11(3), 263-268, 2010) as well as in an older article: "The art and science of modeling decision-making under severe uncertainty" (Decision Making in Manufacturing and Services, 1-2, 111-136, 2007).

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

Response to my critique of Info-Gap decision theory

People often ask me: what is the response in the Info-gap literature to your critique of Info-Gap decision theory?

To the best of my knowledge, there is no explicit reference in Ben-Haim's publications to the specifics of my criticism of Info-Gap decision theory. Indeed, there is no explicit reference in them to my work on info-gap decision theory, period.

What is more, in his latest book, Info-Gap Economics, Ben-Haim (2010) continues to maintain that Info-Gap decision theory is a new theory and that info-gap's robustness model is different from Wald's Maximin model and from robustness models used in robust-control.

On the other hand, there has been some (direct and indirect) reference to my work in other Info-gap publications. For example, in (Beresford-Smith and Thompson 2009) there is an explicit acknowledgment (albeit incorrectly phrased) of my proofs showing that info-gap robustness model is a Maximin model.

Also, some Info-Gap scholars now begin to respond to my arguments which highlight the absurd in Info-Gap decision theory's prescription for the treatment of severe uncertainty.

Thus, to presumably justify Info-Gap's local robustness analysis (which as demonstrated above renders it a voodoo decision theory par excellence) Hall and Harvey (2009) and Hine and Hall (2010) supplement info-gap decision theory with additional explicit assumptions which effectively ascribe a likelihood structure to Info-Gap's (likelihood-free) uncertainty model.

Similarly Rout et al (2009) now propose that for Info-Gap decision theory's prescription for severe uncertainty to make sense, the uncertainty cannot be severe , more specifically, the estimate must be "reasonable", whatever this means.

More on this can be found in my reviews of the following Info-Gap publications: Hall and Harvey (2009), Beresford-Smith and Thompson (2009), Rout et al (2009), Hine and Hall (2010).

Conclusions

The Official Mobile Debunker of info-gap decision theory performs these two tasks:

DEBUNKED! √
Hence, the Official Mobile Debunker performs the task assigned to it.

And yet, for all that, my campaign continues. Why?

I shall be delighted to discuss this fascinating topic with you over a cup of coffee. Until then, I suggest that you read my short discussion on fog, spin and rhetoric.

What Next?

It will be interesting to see how long will info-gap scholars continue to cling to their unsupported positions on info-gap decision theory, and how long will they continue to advance them in publications.

And it will be even more interesting to see how long will peer-reviewed journals continue to publish articles promulgating these positions on info-gap decision theory.

This, no doubt, will have an immediate impact on the duration of my campaign.

As we say here, No Worries, Mate!!

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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