# Info-gap decision theory: Reality Check

December 29, 2011 Leave a comment

Info-gap decision theory’s primary texts, namely the three books by Ben-Haim (2001, 2006, 2010), present the theory as though it constitutes a major breakthrough in the quantification of uncertainty and in decision-making under severe uncertainty.

Not only that these claims are not corroborated, the fact of the matter is that the central model deployed by info-gap decision theory, namely its robustness model, is a reinvention of a staple model of robustness — known universally as radius of stability (circa 1960).

But more than this, from the standpoint of decision theory, this model is a very simple instance of Wald’s famous maximin model (circa 1940), the foremost model for dealing with a non-probabilistic uncertainty used in decision theory, robust optimization, robust control, robust statistics, etc.

Adherents of info-gap decision theory would therefore be well advised to take a hard critical look at the following statements, which they apparently take seriously:

Info-gap decision theory is radically different from all current theories of decision under uncertainty. The difference originates in the modeling of uncertainty as an information gap rather than as a probability. The need for info-gap modeling and management of uncertainty arises in dealing with severe lack of information and highly unstructured uncertainty.

Ben-Haim (2001, 2006, p. xii)

In this book we concentrate on the fairly new concept of information-gap uncertainty, whose differences from more classical approaches to uncertainty are real and deep. Despite the power of classical decision theories, in many areas such as engineering, economics, management, medicine and public policy, a need has arisen for a different format for decisions based on severely uncertain evidence.

Ben-Haim (2001, 2006, p. 11)

Probability and info-gap modelling each emerged as a struggle between rival intellectual schools. Some philosophers of science tended to evaluate the info-gap approach in terms of how it would serve physical science in place of probability. This is like asking how probability would have served scholastic demonstrative reasoning in the place of Aristotelian logic; the answer: not at all. But then, probability arose from challenges different from those faced the scholastics, just as the info-gap decision theory which we will develop in this book aims to meet new challenges.

Ben-Haim (2001 and 2006, p. 12)

The emergence of info-gap decision theory as a viable alternative to probabilistic methods helps to reconcile Knight’s dichotomy between risk and uncertainty. But more than that, while info-gap models of severe lack of information serve to quantify Knight’s ‘unmeasurable uncertainty’, they also provide new insight into risk, gambling, and the entire pantheon of classical probabilistic explanations. We realize the full potential of the new theory when we see that it provides new ways of thinking about old problems.

Ben-Haim (2001 p. 304; 2006, p. 342)

Info-gap decision theory clearly presents a ‘replacement theory’ with which we can more fully understand the relation between classical theories of uncertainty and uncertain phenomena themselves.

Ben-Haim (2001 p. 305; 2006, p. 343)

The management of surprises is central to the “economic problem”, and info-gap theory is a response to this challenge. This book is about how to formulate and evaluate economic decisions under severe uncertainty. The book demonstrates, through numerous examples, the info-gap methodology for reliably managing uncertainty in economics policy analysis and decision making.

Ben-Haim (2010, p. x)

Info-gap scholars would also do well to consider the following two very simple questions:

- Given that info-gap’s robustness model and info-gap’s decision model for robustness are simple
robust optimizationmodels, how is it that not a single reference can be found in Ben-Haim (2001, 2006, 2010) to the vast literature on robust optimization?- How is it that there is not a single reference in:
Info-gap Economics: An Operational Introduction(Ben-Haim 2010) to Hansen and Sargent’s extensive work (e.g. their 2008 book Robustness) on the use of robustness models in economics?For the benefit of info-gap scholars, here is the publisher’s description of the book:

The standard theory of decision making under uncertainty advises the decision maker to form a statistical model linking outcomes to decisions and then to choose the optimal distribution of outcomes. This assumes that the decision maker trusts the model completely. But what should a decision maker do if the model cannot be trusted?

Lars Hansen and Thomas Sargent, two leading macroeconomists, push the field forward as they set about answering this question. They adapt robust control techniques and apply them to economics. By using this theory to let decision makers acknowledge misspecification in economic modeling, the authors develop applications to a variety of problems in dynamic macroeconomics.

Technical, rigorous, and self-contained, this book will be useful for macroeconomists who seek to improve the robustness of decision-making processes.

In short, info-gap decision theory is in dire need of a serious reality check.

### PostScript:

All that is “new” and “revolutionary” in info-gap decision theory is the proposition to use a model of local robustness (radius of stability) to manage a severe uncertainty expressed in terms of a vast (e.g. unbounded) uncertainty space. It is precisely this proposition that makes info-gap decision theory a voodoo decision theory par excellence.

**Viva la Voodoo!**