Reviews of publications on Info-Gap decision theory

Review # 22(Posted: October 11, 2010)

Reference: Arkadeb Ghosal, Haibo Zeng, Marco Di Natale, Yakov Ben-Haim

Computing Robustness of FlexRay Schedules to Uncertainties in Design Parameters

Proceedings ofDesign, Automation and Test in Europe Conference and Exhibition,March 8-12, 2010, Dresden, Germany.Abstract In the current environment of rapidly changing invehicle requirements and ever-increasing functional content for automotive EE systems, there are several sources of uncertainties in the definition of EE architecture design. This is also true for communication schedule synthesis where key decisions are taken early because of interactions with the suppliers. The possibility of change necessitates a design process that can analyze schedules for robustness to uncertainties, e.g., changes in estimated task durations or communication load. A robust design would be able to accommodate these changes incrementally without changes in the system scheduling, thus reducing validation times and increasing reusability. This paper introduces a novel approach based on the info-gap decision theory that provides a systematic scheme for analyzing robustness of schedules by computing the greatest horizon of uncertainty that still satisfies the performance requirements. The paper formulates info-gap models for potential uncertainties in schedule synthesis for a distributed automotive system communicating over a FlexRay network, and shows their application to a case study. Scores TUIGF:100%

SNHNSNDN:2321%

GIGO:100%

## Overview

The reason that this paper holds a special interest for me is that it contains a paragraph that apparently seeks to explain the difference between info-gap's robustness model and Wald's famous Maximin model. This attempted explanation is presumably intended to rebut my claim that info-gap's robustness model is an instance of Wald's Maximin model (see formal proof).

So, although over the past four years I published a number of proofs demonstrating that info-gap's robustness model

is a simple instance(special case) of Wald's famous Maximin model, it looks like I need to do it all over again.But, as we say here: No Worries, Mate!!

## The Maximin connection

To begin with, I need to point out,

again, that it is elementary to show that info-gap's robustness model is a simple instance of Wald's Maximin model, and that a formal proof of the theorem asserting this fact has been in the public domain since the end of 2006 (see formal proof). So, before I go into the specifics of the argument, I want to explain in general terms what needs to be done to this end.Wald's Maximin model is a general, hence all-embracing, modeling paradigm. The austere simplicity of its formulations entails that it is extremely pliable, hence capable of yielding countless instances. One of these instances is info-gap's robustness model. Thus, to show that info-gap's robustness model is one of the many instances that are subsumed by this stalwart of decision theory, all it takes is to phrase Wald's Maximin model's constituent components in such a way that the product will be a model representing info-gap's robustness model.I need hardly point out that performing this elementary mathematical exercise will yield countless other models. And to be sure, in addition to yielding models such as info-gap's robustness model, Wald's Maximin model encompasses many other models that have no connection to info-gap's robustness model.

The point here is that when you perform this formulation properly, the resulting instance of Wald's Maximin model that you obtain is

equivalentto info-gap's robustness model. This instance therefore generatesexactly the same resultsas those that are generated by info-gap's robustness model. In short, this specific instance of Wald's Maximin model iscompletely equivalentto info-gap's robustness model.With this in mind, let us examine the claim made on page 2:

Relation to the Min-Max Strategy.The min-max strategy selects the design that minimizes the maximal loss. The infogap robustness function has a formal relation to the min-max strategy. However, there are two important differences. First, implementation of a min-max strategy requires knowledge of a worst case. In contrast, an info-gap model of uncertainty is explicitly designed to represent situations in which we do not know how wrong the best estimate can be. Second, even if we reliably know the worst that can occur, we may not want to design for that contingency. The clearest case is when the outcome anticipated from the min-max design is unacceptable because it violates the performance requirements.Because the authors do not stipulate what

specificmin-max strategy they have in mind, namely to whatspecificmin-max strategy they are comparing the "info-gap model of uncertainty", it is difficult to pinpoint the specific technical errors in their arguments/logic. However, the following should be noted.First, recall that according to info-gap decision theory, the robustness of decision q is defined as follows:

Generic Info-Gap Robustness model:max {α≥0: r* ≤ r(q,u),∀u∈U(α,û)}where û denotes the estimate of the true value of the parameter of interest, r* ≤ r(q,u) is a pre-specified performance requirement and U(α,û) denotes a ball of radius α centered at û.

In words, the robustness of decision q is the radius (α) of the largest ball U(α,û) centered at û all of whose elements (u) satisfy the constraint r* ≤ r(q,u). That is, it is the radius of the largest ball U(α,û) centered at û whose

worstelement satisfies the performance constraint associated with q.Now, consider one of the most well-known min-max models in this Universe, namely:

min max {x ^{2}+ 2xy − y^{2}}x∈R y∈R where R denotes the real line. The optimal solution is the saddle point (x,y) = (0,0).

Is there any doubt that this is

notan info-gap's robustness model?So what?

The fact that this particular min-max model is not an info-gap robustness model does not prove that info-gap's robustness model is not a min-max or max-min model. All that this fact proves is that

this particular instanceof the generic min-man model is not an info-gap robustness model.But this is not the question on the agenda. The question on the agenda is this:

Is there an instance of the generic Maximin or Minimax model that is equivalent to info-gap's robustness model?By

equivalentwe mean of course a model that is constructed from the same ingredients as those constituting info-gap's robustness model such that italwaysgenerates the same results as those generated by info-gap's robustness model.So, the point to note about the statements quoted above is that they miss their mark because they are oblivious to the fact that this is the question that must be answered first and foremost. Once this question is answered, only then is one in a position to assess info-gap decision theory's role and place in decision theory and robust optimization.

To set the scene, observe that info-gap's robustness model is an instance of the following simple Maximin model:

Generic Maximin model:max min f(x,s) x∈X s∈S(x)

Hint:The correspondence between the two models is as follows:

- x in the Maximin model corresponds to α in info-gap's robustness model.

- s in the Maximin model corresponds to u in info-gap's robustness model.

- S(x) in the Maximin corresponds to U(α,û) in info-gap's robustness model.

- f(x,s) in the Maximin model corresponds to ????? info-gap's robustness model.
Try to figure out on your own what ????? is. The full correspondence is given below.

Note that this model represents a situation where the decision maker seeks to maximize the value of the objective function, whereupon Nature, namely Uncertainty, seeks to minimize the value of the objective function.

In situations depicted by the generic Minimax model the objectives are reversed:

Generic Minimax model:min max f(x,s) x∈X s∈S(x) In other words, the generic Minimax model gives expression to a situation where the decision maker wants to minimize the value of the objective function where in response Nature seeks to maximize the value of this objective function.

So, your immediate conclusion would no doubt be that, because in the case of info-gap's robustness model the decision maker wants to

maximizethe radius (α) of the ball centered at the estimate û, it follows that the model that info-gap's robustness model should in fact be compared to is aMaximinmodel andnot a Minimaxmodel.That said, before I show formally how erroneous the above statements are, I shall comment briefly on specific assertions in the quoted paragraph.

Authors' assertion My comments Relation to the Min-Max Strategy. Wrong approach. As explained above, info-gap's robustness model should be compared to a Maximin strategy. The min-max strategy selects the design that minimizes the maximal loss. As explained above, info-gap's robustness model maximizesthe objective function, so aMaximinrather than a Minimax model should be considered.The infogap robustness function has a formal relation to the min-max strategy. Why is this formal relation not specified in the article? Namely, what exactly is this 'formal' relation? Why is it not indicated that this formal relation is in fact given by theorems proving that info-gap's robustness model is a specific case of Wald's Maximin model? Why are there no references to these theorems in the paper? However, there are two important differences. How can you identify any differences between the two models without stipulating exactly to what specific min-max model you are comparing info-gap's robustness model? First, implementation of a min-max strategy requires knowledge of a worst case. This statement is and will remain meaninglessunless it is corroborated with regard to a specific case. That is, unless it is shown in the context of a specific case that contrary to info-gap's model the implementation the specific min-max strategy in question requires knowledge of a worst case this statementis without any merit.

But what is more, the info-gap's robustness model that is yielded by a proper Maximin formulation will require the same (local) "worst case" information that is required by info-gap's robustness model. Because this is precisely what info-gap's robustness modeldoes in the first place, for each value of α it seeks to identify theworstelement of U(α,û).In contrast, an info-gap model of uncertainty is explicitly designed to represent situations in which we do not know how wrong the best estimate can be. That specific case which is obtained from a properly defined Maximin formulation and which is equivalent to info-gap's robustness model will exhibit the same characteristic as info-gap's robustness model. Second, even if we reliably know the worst that can occur, we may not want to design for that contingency. Whether you want it or not, info-gap's robustness model always generates a (local) "worst case". Because, by design, this is precisely the business of info-gap's robustness model: for each value of α it seeks to identify theworstelement of U(α,û).

Hence, that instance yielded by a properly formulated Maximin model which is the equivalent of info-gap's robustness model will always yield the same (local) "worst case" that is generated by info-gap's robustness model.The clearest case is when the outcome anticipated from the min-max design is unacceptable because it violates the performance requirements. A properly formulated Maximin representation of info-gap's robustness model will yield the same results as those generated by info-gap's robustness model. So a proper Maximin representation will yield an unacceptable design iff info-gap's robustness model itself will yield the very same unacceptable design. In short, the point is this:

We can easily construct aMaximinmodel that iscompletely equivalentto info-gap's robustness model. Therefore, this Maximin model willalwaysyield exactly the same results generated by info-gap's robustness model. Meaning that, this model willnotgenerate an unacceptable design -- unless info-gap's robustness model itself generates thesamedesign.The fact that info-gap's robustness model is different from some Minimax model, presumably contemplated by the authors, does not prove that info-gap's robustness model is not a Maximin model.

This only proves that in view of it being

a general all-embracing prototype,Wald's Maximin model encompasses -- in addition to info-gap's robustness model -- many other models that are different from info-gap's robustness model. Hence, the differences between info-gap's robustness and other minimax or maximin models are differences between specific cases that are subsumed by the prototype: Wald's Maximin model.I use a rather large font here in the hope that this will make it easier to put my point across ... . My previous attempts, using regular font, were not entirely successful ... The use of color did not do the job either ....

It is instructive to explain the flawed logic underlying the argument of the above quoted statement by means of a simple example.

## A magic proof that q(x) = x

^{2}- x + 2 is not a polynomial

- Step 1: Clearly, p(x) = x
^{2}+ x - 3 is a polynomial.

- Step 2: Clearly, p(x) is different from q(x) for some x.

- Step 3: Since p(x) = x
^{2}+ x - 3 is a polynomial and it is different from q(x) = x^{2}- x + 2, it follows that q(x) = x^{2}- x + 2 is not a polynomial.QEDThe following proof is perhaps more appropriate.

## A magic proof that Jack the Kangaroo is not a marsupial

- Step 1: Clearly, Sam the Koala is a marsupial.

- Step 2: Clearly, Sam the Koala is decidedly different from Jack the Kangaroo.

- Step 3: Since Sam the Koala is a marsupial and he is decidedly different from Jack the Kangaroo, it follows that Jack the Kangaroo is not a marsupial.
QEDTo reiterate then, it is a fact that among the countless Maximin (and minimax) models there are those that are different from info-gap's robustness model. So what? This does not prove that info-gap's robustness model is not a Maximin (Minimax) model. All this proves is that as a prototype, Wald's Maximin model is incomparably more general and powerful than info-gap's robustness model, hence, some of its instances are equivalent to info-gap's robustness model and others are not.

The proof of the Maximin Theorem is not only straightforward, it is also instructive. To wit: the Maximin Theorem makes the task of constructing an instance of the Maximin model that is equivalent to info-gap's robustness model an easy task.

As a matter of fact, not only is the task of constructing an instance of Wald's Maximin model that is the equivalent of info-gap's robustness model an easy one, it is equally easy to construct a number of such instances. The one below is used in the proof of the Maximin Theorem.

## The Maximin Theorem

As there is nothing in this paper to apprise the readers of the proofs showing that info-gap's robustness model is a simple instance of Wald's Maximin model, I call attention to the fact that these have been made public at the end of 2006 and since then have appeared in a number of articles (e.g. Sniedovich (2007, 2008, 2009, 2010).

The following formal analysis provides a simple proof that info-gap's robustness model is a simple instance of Wald's Maximin model, and a complete, detailed formulation of this instance.

So what is the moral of the story?

The instance of Wald's Maximin model formulated in the proof of the theorem is equivalent to info-gap's robustness model. It follows therefore that this instance always generates the same results as those generated by info-gap's robustness model.Hence, the characterization of the relation between info-gap's robustness model and the so called "minimax strategy" read "Wald's Maximin model", in this article is erroneous.

## The Radius of Stability Theorem

But there is more.

Info-gap's robustness model is not only a simple instance of the Maximin model. It is that simple instance of Wald's Maximin model that is known universally as Radius of Stability model, a staple model of

localrobustness/stability in numerical analysis, control theory etc.More specifically, Info-gap's robustness model 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.

## What is at stake here?

In case you are wandering what the fuss is all about, take note that info-gap decision theory was launched (in 2001) as a new theory that is radically different from all current theories for decision under uncertainty.

But the Maximin Theorem and the Radius of Stability Theorem have proved that this claim is without any foundation, hence misleading.

In an attempt to meet the criticism (formal proofs) showing that Info-gap's robustness model is a simple instance of Wald's maximin model, (hardly) half truths that end being untruths are being advanced to meet this criticism. This is how statements such as this: "The infogap robustness function has a formal relation to the min-max strategy. However, there are two important differences." should be read.

It is important therefore to appreciate what is at stake here.

- Take note then that from a purely scholarly point of view, the claims that info-gap's robustness function (model) is "new" or "different" or "behaves differently" or "does different things from Minimax (namely Wald's maximin model) are erroneous, hence misleading.

- The immediate implication of info-gap's robustness function (model) being a simple instance of Wald's Maximin model is of course that any problem that can be formulated as an info-gap robustness problem can be formulated by an equivalent Maximin model, and also by an equivalent Radius of Stability model. But, as a simple instance of the Maximin model, info-gap robustness function (model)'s scope and capabilities are incomparably more limited than those of Wald's maximin.

- Thus, unlike Wald's maximin model, which can be used to assess/determine
localas well asglobalrobustness, because info-gap robustness function (model) has an inherentlylocalorientation, it can be used only to assess/determinelocalrobustness. And thislocalorientation renders it utterly unsuitable for the management ofsevereuncertainty which it expressly aims to manage.In short, what is at stake here is not "just a scholarly academic quibble". We are talking here about claims asserting that info-gap decision theory provides a "new/different"

sound/reliablemethod for dealing with practical decision problems that are subject tosevereuncertainty. These claims must be debunked, and are debunked by my critique of info-gap decision theory.## So what's next?

You would think that having shown, (yet again), that info-gap's robustness model is a simple instance of Wald's famous Maximin model, I can now move on to other, more challenging, tasks ....

However:

Given my experience over the past seven years, I imagine that I shall have to repeat this exercise again, and ... again.

As you can clearly see, the reasons for my having to repeat this exercise are not due to the proof being difficult to comprehend ....

To see for yourself, read my Official Mobile Debunker of info-gap decision theory.

I shall repeat this exercise as many times as it takes and ... I shall increase the size of the fonts accordingly ....

But as we say here, No Worries, Mate!!

Appendix: the Wide World of Local Worst Cases

The info-gap literature is spotted with numerous claims asserting that info-gap's robustness analysis is not a worst-case analysis. These claims are

groundless. Because, ... info-gap's robustness analysis is a worst-case analysispar excellence.More precisely, info-gap's robustness analysis is based on a

localworst-case analysis, wherelocalmeans "within the region of uncertainty U(α,p*)" associated with the stipulated value of α, where p* denotes the estimate of the parameter of interest, p.That is, the admissibility of a given value of α is determined by the performance of the worst p in U(α,p*), where "worst" refers to the performance constraint r* ≤ r(q,p).

There are two cases:

- If there is a p∈U(α,p*) that
violatesthe constraint r* ≤ r(q,p), then all such values of p are "worst cases" and all values of p∈U(α,p*) thatsatisficethe constraint r* ≤ r(q,p) are "best cases". In this case α isadmissible.

- If there is
nop∈U(α,p*) thatviolatesthe constraint r* ≤ r(q,p), then all values of p∈U(α,p*) are both "worst cases" and "best cases". In this case α isinadmissible, namely its value is too large.The picture is this:

Info-gap's Robustness modelmax {α ≥ 0: r* ≤ r(d,p),∀p∈U(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 for decision d, namely r* ≤ r(d,p). The center of the circles, p*, represents a give estimate of the parameter p. U(α,p*) denotes a circle of radius α around p*. Note that the performance requirement r* ≤ r(d,p) is satisficed by every point in any circle whose radius is equal to or smaller than the radius of the blue circle. Hence, in all these circles, all the points are both "worst cases" and "best cases".

In contrast, consider the large dashed circle. Some of its points reside in the shaded area and some reside in the white area. All the points in this circle that reside in the shaded area are "best cases" and all the points that reside in the white area are "worst cases".

It follows then that the robustness of decision d is equal to the radius of the largest circle all of whose points are both "worst cases" and "best cases". Any element of a larger circle is either a "worst case" or a "best case", but not both.

The instance of the Maximin model that represents info-gap's robustness model conducts an identical local worst-case analysis and therefore yields the same results.

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

- 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-GapisWald's Maximin Principlein disguise. (December 31, 2006)

This is a very short article entitled Eureka! Info-Gap is Worst Case (maximin) in Disguise! (PDF File)

It shows thatInfo-Gapis not a new theory but rather a simple instance ofWald's famous Maximin Principledating back to 1945, which in turn goes back to von Neumann's work on Maximin problems in the context ofGame 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 becauseInfo-Gapdeploys 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 theASOR 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.

- ASOR Recent Advances, 2011, Melbourne, Australia, November 16 2011. Presentation: The Power of the (peer-reviewed) Word. (PDF file).

- Alex Rubinov Memorial Lecture The Art, Science, and Joy of (mathematical) Decision-Making, November 7, 2011, The University of Ballarat. (PDF file).

- Black Swans, Modern Nostradamuses, Voodoo Decision Theories, and the Science of Decision-Making in the Face of Severe Uncertainty (PDF File) .

(Invited tutorial, ALIO/INFORMS Conference, Buenos Aires, Argentina, July 6-9, 2010).

- A Critique of Info-Gap Decision theory: From Voodoo Decision-Making to Voodoo Economics(PDF File) .

(Recent Advances in OR, RMIT, Melbourne, Australia, November 25, 2009)

- Robust decision-making in the face of severe uncertainty(PDF File) .

(GRIPS, Tokyo, Japan, October 16, 2009)

- Decision-making in the face of severe uncertainty(PDF File) .

(KORDS'09 Conference, Vilnius, Lithuania, September 30 -- OCtober 3, 2009)

- Modeling robustness against severe uncertainty (PDF File) .

(SOR'09 Conference, Nova Gorica, Slovenia, September 23-25, 2009)

- How do you recognize a Voodoo decision theory?(PDF File) .

(School of Mathematical and Geospatial Sciences, RMIT, June 26, 2009).

- Black Swans, Modern Nostradamuses, Voodoo Decision Theories, Info-Gaps, and the Science of Decision-Making in the Face of Severe Uncertainty (PDF File) .

(Department of Econometrics and Business Statistics, Monash University, May 8, 2009).

- The Rise and Rise of Voodoo Decision Theory.

ASOR Recent Advances, Deakin University, November 26, 2008. This presentation was based on the pages on my website (voodoo.moshe-online.com).

- Responsible Decision-Making in the face of Severe Uncertainty (PDF File) .

(Singapore Management University, Singapore, September 29, 2008)

- A Critique of Info-Gap's Robustness Model (PDF File) .

(ESREL/SRA 2008 Conference, Valencia, Spain, September 22-25, 2008)

- Robust Decision-Making in the Face of Severe Uncertainty (PDF File) .

(Technion, Haifa, Israel, September 15, 2008)

- The Art and Science of Robust Decision-Making (PDF File) .

(AIRO 2008 Conference, Ischia, Italy, September 8-11, 2008 )

- The Fundamental Flaws in Info-Gap Decision Theory (PDF File) .

(CSIRO, Canberra, July 9, 2008 )

- Responsible Decision-Making in the Face of Severe Uncertainty (PDF File) .

(OR Conference, ADFA, Canberra, July 7-8, 2008 )

- Responsible Decision-Making in the Face of Severe Uncertainty (PDF File) .

(University of Sydney Seminar, May 16, 2008 )

- Decision-Making Under Severe Uncertainty: An Australian, Operational Research Perspective (PDF File) .

(ASOR National Conference, Melbourne, December 3-5, 2007 )

- A Critique of Info-Gap (PDF File) .

(SRA 2007 Conference, Hobart, August 20, 2007)

- What exactly is wrong with Info-Gap? A Decision Theoretic Perspective (PDF File) .

(MS Colloquium, University of Melbourne, August 1, 2007)

- A Formal Look at Info-Gap Theory (PDF File) .

(ORSUM Seminar , University of Melbourne, May 21, 2007)

The Art and Science of Decision-Making Under Severe Uncertainty(PDF File) .

(ACERA seminar, University of Melbourne, May 4, 2007)

- What exactly is Info-Gap? An OR perspective. (PDF File)

ASOR Recent Advances in Operations Researchmini-conference (December 1, 2006, Melbourne, Australia).

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