The Info - Gap / Maximin Saga Continues

On numerous occasions and in many articles I have formally shown (proved) that Info-Gap’s robustness model (Ben-Haim 1999, 2001, 2006) is a Maximin model (Wald 1945, 1950) par excellence and that it is fundamentally flawed in the way it handles severe uncertainty. Furthermore, I have shown that the Info-Gap/Maximin connection is not strictly mathematical in nature. Indeed, the conceptual framework of Info-Gap’s robustness model is the same as that of the instance of the Maximin model representing it, namely it is grounded in a typical “worst-case analysis” approach to uncertainty. The difference is in the terminology and jargon. I was therefore surprised to learn that in a recent article Los and Tungsong (2008) raise some doubts regarding the validity of my criticism in Sniedovich (2007) of Info-Gap decision theory. The good news is that Los and Tungsong’s (2008) off-the-cuff commentary on my views on the Info-Gap/Maximin connection and the local nature of Info-Gap’s robustness model is . . . totally wrong. The bad news is that what we have here is a completely uncalled for academic style “comedy of errors”, one that I take seriously, hence this paper. I do hope that, as in the case of the original (Shakespeare 1594) play, there will be a happy-end here as well! In any case, Los and Tungsong (2008) use the term “information gap” very, very loosely and with no apparent reason they assume that my criticism of BenHaim’s (2001, 2006) Info-Gap decision theory also applies to information gap models/theories that are not compliant with the structure of the model specified in . . . Ben-Haim (2001, 2006). In other words, I criticize a very specific information gap model, namely BenHaim’s (2001, 2006) model, whereas Los and Tungsong (2008) misconstrue this criticism by assuming that it applies to all information gap models in this Universe. I have no idea what prompted Los and Tungsong (2008) to commit this blatant, uncalled for error, but they did. The objective of this paper is to fix the blunder on the part of Los and Tungsong (2008), and to explain, once more, the Info-Gap/Maximin connection. It turns out, however, that this “comedy of errors” does have some positive contribution to the state of the art in decision theory: it confirms the validity of my harsh criticism of Ben-Haim’s (2001, 2006) Info-Gap decision theory. This entire episode, therefore, reminds me of Samson’s very famous riddle: Out of the eater came something to eat and out of the strong came something sweet. Judges 14:14