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Decision-Making Under Severe Uncertainty  
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Reviews of publications on Info-Gap decision theory

Review # 33 (Posted: November 19, 2011)

Reference: Brendan A. Wintle, Sarah A. Bekessy, David A. Keith, Brian W. van Wilgen, Mar Cabeza, Boris Schroder, Silvia B. Carvalho, Alessandra Falcucci, Luigi Maiorano, Tracey J. Regan, Carlo Rondinini, Luigi Boitani and Hugh P. Possingham
Ecological–economic optimization of biodiversity conservation under climate change
Nature Climate Change, Volume 1, October 2011, 355-359. (DOI: 10.1038/NCLIMATE1227)
Abstract Substantial investment in climate change research has led to dire predictions of the impacts and risks to biodiversity. The Intergovernmental Panel on Climate Change fourth assessment report 1 cites 28,586 studies demonstrating significant biological changes in terrestrial systems 2. Already high extinction rates, driven primarily by habitat loss, are predicted to increase under climate change 3–6. Yet there is little specific advice or precedent in the literature to guide climate adaptation investment for conserving biodiversity within realistic economic constraints 7. Here we present a systematic ecological and economic analysis of a climate adaptation problem in one of the world’s most species-rich and threatened ecosystems: the South African fynbos. We discover a counterintuitive optimal investment strategy that switches twice between options as the available adaptation budget increases. We demonstrate that optimal investment is nonlinearly dependent on available resources, making the choice of how much to invest as important as determining where to invest and what actions to take. Our study emphasizes the importance of a sound analytical framework for prioritizing adaptation investments 4. Integrating ecological predictions in an economic decision framework will help support complex choices between adaptation options under severe uncertainty. Our prioritization method can be applied at any scale to minimize species loss and to evaluate the robustness of decisions to uncertainty about key assumptions.

Acknowledgment This work was funded by the Commonwealth Environment Research Facility; Applied Environmental Decision Analysis and by the Australian Research Council (LP0989537, FF0668778). M.C. was supported by the EU project RESPONSES. We thank M. Bode and W. Morris for assistance in modelling the fire management efficiency curves, G. Forsyth for evaluation of the fire, habitat and weed management cost estimates, and L. Rumpff for help with Fig. 1.
Author contribution B.A.W., S.A.B., D.A.K., and H.P.P. designed the research. B.A.W., D.A.K., and B.W.v.W. performed the analysis. B.A.W., S.A.B, M.C., B.S., S.B.C., L.B., A.F., L.M., C.R., T.J.R., and H.P.P. wrote the paper. All authors discussed the results and edited the manuscript.
Scores TUIGF: 100%
GIGO: 200%

I discovered a reference to this article in the November 2011 issue of Decision Point. Recall that Decision Point is the monthly magazine of the Center of Excellence for Environmental Decisions (CEED), presenting articles, views and ideas on environmental decision making, biodiversity, conservation planning and monitoring. Note that four of the co-authors are affiliated with CEED.

Just as Wintle et al. (2010) heralded a major breakthrough in decision theory by proposing the use of info-gap decision theory to tackle Black Swans and Unknown Unknowns, Wintle et al. (2011) report on a remarkable advance in decision theory (emphasis added):

Info-gap generalizes the maximin strategy by identifying worst-case outcomes at increasing levels (horizons) of uncertainty. This permits the construction of `robustness curves' that describe the decay in guaranteed minimum performance (or worst-case outcome) as uncertainty increases.
Wintle et al. (2011, p. 357)

To appreciate the full significance of this statement, keep in mind that Wald's Maximin model has, for at least five decades, figured as the foremost tool for the treatment of severe uncertainty in areas such as decision theory, robust optimization, and others. The implication clearly is then that a generalization of this tool that enables the generation of `robustness curves' would most certainly be greeted as a major contribution to the state of the art in decision theory.

But the fact of the matter is, given the state of the art, that I need not even work out a detailed argument to show how absurd the claim that "Info-gap generalizes the maximin strategy" actually is. The reader is simply reminded that if A is an instance of B then A cannot possibly generalize B. Still, it is important to call the reader's attention to the fact that claims of this nature attest to a profound misunderstanding of the relationship between info-gap decision theory and Wald's Maximin paradigm.

All I need to do to this end is to remind the reader to keep in mind that info-gap's robustness model is a simple instance of Wald's Maximin model (see the official mobile maximin theorem and its proof). This means of course that because an instance of a prototype cannot possibly generalize the prototype, info-gap decision theory cannot possibly generalize Wald's Maximin paradigm.

Hence, the claim that info-gap's alleged generalization of Wald's Maximin strategy `permits' the generation of `robustness curves' is doubly in error. Not only is it false on the "generalization" claim, it errs with regard to Wald's Maximin capabilities. It thus gives the badly misleading impression that, unlike Wald's Maximin theory, info-gap decision theory does `permit' the construction of such curves. The fact of the matter is of course that the same procedure/method that is used to create `robustness curves' in the framework of an info-gap robustness model can be used to create such curves in the framework of a Maximin model. And this is so simply because this procedure has got nothing to do with the Maximin model as such nor with info-gap's robustness model as such.

Indeed, the `robustness curves' in question are no more and no less than simple instances of what are known universally as Pareto Efficiency curves. The typical Pareto Efficiency curve and the explanatory text shown below are taken from Wikipedia:

Looking at the Production-possibility frontier, shows how productive efficiency is a precondition for Pareto efficiency. Point A is not efficient in production because you can produce more of either one or both goods (Butter and Guns) without producing less of the other. Thus, moving from A to D enables you to make one person better off without making anyone else worse off (rise in Pareto efficiency). Moving to point C from point A, however, is not Pareto efficient, as fewer guns are produced. Likewise, moving to point B from point A is not Pareto efficient, as less butter is produced. A point on the frontier curve with the same x or y coordinate will be Pareto efficient.

One wonders, therefore, on what grounds do Wintle et al. (2011) state that info-gap generalizes Wald's maximin strategy? And on what ground do they insinuate that Wald's Maximin strategy does not `permit' the construction of `robustness curves'?

This error may well be due to the fact that the info-gap literature, (its primary texts Ben-Haim (2001, 2006, 2010) included) is practically mum on the connection between info-gap's robustness curves and Pareto Optimization notably Pareto Efficiency. Consequently, those info-gap adherents who are not conversant with these topics labor under the misconception that the so-called info-gap robustness curves are an info-gap innovation.

I need hardly add that this is yet another illustration of how cut off the info-gap literature is from areas of expertise that bear directly on what info-gap decision theory claims to be doing. In particular, the discussion in Ben-Haim (2001, 2006, 2010) is completely oblivious to the connection between info-gap decision theory and areas such as Robust Optimization and Pareto Optimization. However, given that Pareto efficiency is a central concept in economics, it is inexcusable that the connection between info-gap's robustness curves and this fundamental concept is not so much as mentioned in the latest book on info-gap decision theory, namely Info-Gap Economics: An Operational Introduction (Ben-Haim, 2010) (see Review 14).

I should also point out that Wintle et al. (2011) continue to propound the myth that info-gap decision theory is suitable for the management of severe uncertainty of the type that it postulates (emphasis added):

Because climate adaptation strategies will be developed under severe uncertainty, it is critical to incorporate uncertainty in decisions using a method such as info-gap, and plan for reducing uncertainty by learning about management effectiveness and other key parameters.
Wintle et al. (2011, p. 358)

Thus, readers of Wintle et al. (2011) are being doubly mislead by this statement. Not only are they being misinformed about the capabilities of info-gap's robustness model, they are given no clue to work out for themselves why `... a method such as info-gap ...' is the wrong method for the task. That is, readers would have no clue that '... a method such as info-gap ...' is in fact utterly unsuitable for this task because its robustness model is inherently a model of local robustness. Namely, it defines robustness as the smallest perturbation in a given nominal value of the parameter of interest that can cause a violation of the performance constraint. I therefore remind the reader of Hayes' (2011, p. 88) recent interesting observation (emphasis added):

Analysts who were attracted to IGT because they are very uncertain, and hence reluctant to specify a probability distribution for a model's parameters, may be disappointed to find that they need to specify the plausibility of possible parameter values in order to identify a robust management strategy.

Apparently, unlike Hayes (2011), Wintle et al. (2011) are not disappointed at all. Indeed, they have no qualms whatsoever about using a model of local robustness that operates in the neighborhood of a point estimate of the parameter of interest, without specifying the likelihood of possible parameter values.

And recall Rout et al.'s (2009, p. 785) reflections on this issue:

Thus, the method challenges us to question our belief in the nominal estimate, so that we evaluate whether differences within the horizon of uncertainty are `plausible'. Our uncertainty should not be so severe that a reasonable nominal estimate cannot be selected.

In contrast, Wintle et al. (2011) have not the slightest concern that under severe uncertainty of the type stipulated by info-gap decision theory the point estimate's poor quality may not justify the use of a model of local robustness.

But ... this should come as no surprise. Because, as indicated above, this stance is very much of a piece with what is being advocated in Wintle et al. (2010). Indeed, Wintle et al. (2010) even goes a step further to propose the use of a model of local robustness as a suitable means for dealing with Black Swans and Unknown Unknowns.

Stay tuned, there is more to come ...

Other Reviews

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

  34. 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-Gap is Wald's Maximin Principle in disguise. (December 31, 2006)
    This is a very short article entitled Eureka! Info-Gap is Worst Case (maximin) in Disguise! (PDF File)
    It shows that Info-Gap is not a new theory but rather a simple instance of Wald's famous Maximin Principle dating back to 1945, which in turn goes back to von Neumann's work on Maximin problems in the context of Game 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 because Info-Gap deploys 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 the ASOR 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.

Disclaimer: This page, its contents and style, are the responsibility of the author (Moshe Sniedovich) and do not represent the views, policies or opinions of the organizations he is associated/affiliated with.

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