| 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 | ||
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:
- http://voodoo.moshe-online.com: A general discussion on voodoo decision theories
- http://robust.moshe-online.com: A general discussion on robust decision-making
- http://www.moshe-online.com/satisficing: A discussion on the "optimize vs satisfice" debate
- http://www.moshe-online.com/responsible: A general discussion on responsible decision-making
- http://www.moshe-online.com/severe_uncertainty: A general discussion on decision-making under severe uncertainty
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*. |
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! √ |
The reader may wish to read my Official Mobile Debunker of info-gap decision theory.
