At the end of 2006 I posted on my website a short article entitled Eureka! Info-Gap is Worst Case Analysis (Maximin) in Disguise! where I set out a formal, rigorous proof that info-gap's robust-satisficing decision model is a (Wald) maximin model 1. Since then I outlined similar formal proofs in other articles, including peer-reviewed articles, and I posted on my website a wealth of material supplementing this fact 2. Over the years I repeatedly called the attention of many info-gap scholars, including Prof. Yakov Ben-Haim, the Father of info-gap decision theory, to the misleading rhetoric in the info-gap literature concerning the maximin connection. Regrettably, the misconceptions about this connection continue to be promulgated in the professional literature, including peer-reviewed journals such as Risk Analysis, whose referees should know better. They should know better because this matter is as good as self-evident. Namely, it can be settled by inspection. For the question is this: is the model on the right hand-side an instance of the model on the left hand-side? Prototype Maximin model Info-gap's robust-satisficing decision model max y∈Y min s∈S(y) {f (y, s) : con(y, s), ∀s ∈ S(y)} max q∈Q,α≥0 {α : r c ≤ r(q, u), ∀u ∈ U (α, ˜ u)} (1) where con(y, s) denotes a list of constraints on the (y, s) pairs. The rhetoric in the info-gap literature on this issue has it that the two models " are different ". For, consider this: These two concepts of robustness—min-max and info-gap—are different, motivated by different information available to the analyst. The min-max concept responds to severe * This article was written for the Risk Analysis 101 Project to provide a Second Opinion on pronouncements on the relationship between Wald's maximin paradigm and info-gap's robust-satisficing approach to decision making under severe uncertainty, published recently in Risk Analysis. See Risk-Analysis-101.moshe-online.com. 1 uncertainty that nonetheless can be bounded. The info-gap concept responds to severe uncertainty that is unbounded or whose bound is unknown. It is not surprising that min-max and info-gap robustness analyses sometimes agree on their policy recommendations, and sometimes disagree, as has been discussed elsewhere. (40) Ben-Haim (2012, p. 7) where reference [40] is Ben-Haim et al. (2009). The implication therefore must be that, Risk Analysis referees are apparently of the opinion that the following model, where R denotes the real line, namely R := (−∞, ∞), is not a minimax model: z * := min x∈R max y∈R {x 2 + 2xy − y 2 }. (2) Or, could it be that these referees hold that, insofar as Risk Analysis is concerned, the interval (−∞, ∞) is bounded !! One wonders. .. The incontestable fact obviously is that the above model is a perfectly kosher minimax model and the real line R remains unbounded. The conclusion therefore must be that Risk Analysis referees are unaware of the fact that info-gap's robustness model and info-gap's robust-satisficing decision model are both maximin models. Specifically, they are unaware that these models are rather simple instances of the following prototype maximin model 3 : z • := max y∈Y min s∈S(y) {f (y, s) : con(y, s), ∀s ∈ S(y)}. (3) Or, if you will, these models are simple instances of the following " textbook " maximin model: z := max y∈Y min s∈S(y) g(y, s). (4) This being so, the implication therefore is that Risk Analysis referees second the absurd proposition that a simple instance of a prototype model is capable of representing situations that the prototype itself cannot represent. Namely, Risk Analysis referees accept the astounding proposition that while maximin models cannot handle unbounded uncertainty spaces, info-gap's robustness model indeed can! Again, one wonders. .. It is important to take note that claims that info-gap's robust-satisficing decision model is not a maximin model are based on a comparison of these two models: Maximin model Info-gap's robust-satisficing decision model max q∈Q min u∈U (α ,˜ u) r(q, u) max q∈Q,α≥0 {α : r c ≤ r(q, u), ∀u ∈ U (α, ˜ u)} (5) where α is a given value of α. But the point to note here is that this is a non sequitur par excellence. That is, the fact that the model on the left hand-side of (5) is dissimilar from the model on the right hand-side of (5) does not imply that the latter is not a maximin model. Indeed, it is elementary to show that info-gap's robust-satisficing decision model is a max-imin model. It is therefore mind boggling that info-gap scholars who base their claims on the comparison shown in (5), do not bother to consider the following comparison: Maximin model Robust-satisficing decision model max q∈Q,α≥0 min u∈U (α,˜ u) {h(q, α, u) : r c ≤ r(q, u), ∀u ∈ U (α, ˜ u)} max q∈Q,α≥0 {α : r c ≤ r(q, u), ∀u ∈ U (α, ˜ u)} (6) 3 Here con(y, s) denotes a list of constraints on the (y, s) pairs. 2 Because, the fact that info-gap's robust-satisficing decision model is an instance of the maximin model shown in (6) simply stares one in the face! So, again, one wonders. .. This state of affairs raises a number of questions. For instance, consider these two: · Considering how easy it is to show/prove/verify that info-gap's robustness model and info-gap's robust-satisficing decision model are both maximin models, on what grounds do info-gap scholars claim, and Risk Analysis referees apparently concur, that these models are not maximin models? · Why is it important to be clear on the fact that info-gap's robustness model and info-gap's robust-satisficing decision model are simple maximin models? I take up the first question in the sequel. At this stage I address only the second question whose answer is in four parts: · Info-gap decision theory is being proclaimed a new theory that is radically different from all current theories on decision under uncertainty. So, showing that its two core models are in fact simple instances of the most famous non-probabilistic robustness model used is the broad area of decision making, risk analysis etc., demonstrates how groundless this claim is. But more importantly, this fact raises serious questions about the narrative in the info-gap literature on Wald's maximin model, worst-case analysis, control theory, and so on. In short, this fact calls into question statements made in the info-gap decision theory about classic decision theory (Luce and · The info-gap literature is saturated with misleading pronouncements on Wald's maximin paradigm and its many variant models: on its capabilities and limitations and its relation to info-gap's robustness model and info-gap's robust-satisficing decision model. It is regrettable that such pronouncements have found their way into peer-reviewed journals, such as Risk Analysis. It is important therefore to dispense with the fallacies about Wald's maximin paradigm that continue to be disseminated by peer-reviewed journals such as Risk Analysis. · It is important that readers take special note of the following facts. Articles, such as Ben-Haim (2012), denying that info-gap's robust-satisficing decision model is a maximin model, and articles such as Schwartz et al. (2010), seeking to promote info-gap's robust-satisficing approach as a new normative standard of rational decision making, are engaged in a blatant misrepresentation of the state of the art in the broad area of decision making especially of the field of robust optimization. · Indeed, in spite of the fact that both info-gap's robust-satisficing decision model and info-gap's robustness model are simple robust optimization models, not a single reference can be found to robust optimization in these two articles, nor in the three books on info-gap decision theory (Ben-Haim 2001, 2006, 2010). In fact, it would seem that every effort is made to avoid any discussion on robust optimization, and this in spite of the fact that the robust-satisficing approach advocated by info-gap decision theory is a simplistic, indeed, naive robust optimization approach. It is important that referees of journals such as Risk Analysis be aware of these facts and their implications. 3 A close examination of info-gap's misleading rhetoric on the maximin connection reveals that info-gap scholars, and by implication Risk Analysis referees, have serious misconceptions about the following: · The difference between local and global worst-case analysis. · The difference between local and global robustness. · The difference between robustness with respects to payoffs and robustness with respect to constraints. · The relation between a prototype model and its instances. These misconceptions are merely touched on in this article, for its main objective is to introduce referees of journals, such as Risk Analysis, to the rhetoric in the info-gap literature on the relationship between this theory and Wald's maximin paradigm. The rhetoric in the info-gap literature surrounding the profound incongruity between the severity of the uncertainty postulated by info-gap decision theory, and the model of local ro-bustness that the theory deploys for the management of this uncertainty, will be discussed in a separate article entitled Rhetoric in risk analysis, Part II: Anatomy of a Peer-reviewed Voodoo Decision Theory.