Information Gap Decision Theory: Decisions under Severe Uncertainty

This (hardback) book presents a new theory of decision-making under severe uncertainty. The author argues that using information gap theory allows the decision maker to deal with situations where there is a disparity between what is known and what needs to be known in order to make a well-founded decision. Although information gap theory deals with various problems of classical decision analysis such as risk assessment, gambling and value of information, the character of information gap uncertainty gives new insights into the situations that are analysed. The book considers several applications such as medical decisions, strategic planning and environmental management, and it is in these applications that the book's strength lies. Although it is not an easy book to understand, it is well worth the effort that is required to understand how to apply information gap theory to decision-making under severe uncertainty. I would certainly recommend this book for practising decision analysts or for use in a post-graduate course on decision theory. The book is divided into 12 chapters. Chapters One and Ten give an overview of what information gap theory can do, without any details about how to do it. Chapter One gives a basic overview whereas Chapter Ten is entitled a ‘Retrospective essay: risk assessment in project management’ and considers value judgments, robustness and quantitative decision support systems. Chapter Two introduces some of the information gap models and gives four axioms of information gap uncertainty. Chapter Three covers robustness and opportunity, and gives three components of information gap models, namely the system model, performance requirements and the uncertainty model. This is followed by eight examples including engineering design and project management. Chapter Four considers value judgments whereas Chapter Five looks at antagonistic and sympathetic immunities. Basically, if the opportunity function increases with robustness against failure, then the two immunities are said to be sympathetic. If, however, an increase in one causes a decrease in the other, then the two immunities are said to be antagonistic. Chapter Six covers gambling and risk sensitivity, whereas Chapter Seven covers value of infor- mation. Both chapters give examples in project management. In particular, Chapter Seven considers the Allais and the Ellsberg paradoxes. Chapter Eight considers information gap supervision of a classifier where a decision problem exists for selecting one from a number of classes by use of a quantitative measured vector. As the author states, ‘While strategic structural modification of the decision process may entail revision of the classes themselves, the operative decision algorithm assumes that any measured vector arises from one and only one class’. Coherent uncertainties and consensus are thetopics that are covered in Chapter Nine, with hybrid uncertainties in Chapter Eleven. Finally, the book concludes with a chapter on the implications of information gap uncertainty. As stated earlier in this review, the book's strength lies in the number and diversity of applications that it covers within the chapters. They assist the reader in understanding and applying the theory as do the problems given at the end of each chapter for the reader to work on. It would, however, be helpful if the solutions to the problems were given in an appendix rather than giving problems with no solutions available. However, I would still recommend this book for people who are currently working in the field of decision analysis or risk analysis, or those with a particular interest in this area. I would not recommend it for anyone who does not have a good grounding in mathematics and a reasonable understanding of decision analysis.