Foundations and Philosophy

Info-gap theory deals with epistemic uncertainty – limitations on what we do know and what we can know. The attempt to model and manage epistemic uncertainty connects to a range of questions in epistemology.

  • Yakov Ben-Haim, 2006, Info-gap Decision Theory: Decisions Under Severe Uncertainty, 2nd edition, Academic Press, London.
    Section 2.2: Is ignorance probabilistic?
    Chapter 4: Value judgments.
    Section 11.1: The Ellsberg paradox.
    Section 11.2: The Allais paradox.
    Chapter 13: Implications of info-gap uncertainty.

    • Section 13.1: Holism and uncertainty.
    • Section 13.2: Language, meaning and uncertainty.
    • Section 13.3: Warrant and uncertainty.
    • Section 13.4: Credance for info-gap inference.
    • Section 13.5: Risk and uncertainty.
  • Yakov Ben-Haim, 2019, Info-gap decision theory, in V.A.W.J. Marchau, W.E. Walker, P. Bloemen, and S.W. Popper (eds.), Decision Making Under Deep Uncertainty: From Theory to Practice, Springer. Link to the open-access online version.
  • Yakov Ben-Haim, 2019, Assessing ‘beyond a reasonable doubt’ without probability: An info-gap perspective, Law, Probability and Risk, Link to abstract. Link to full paper.
  • Yakov Ben-Haim and Mike Smithson, 2018, Data-Based Prediction under Uncertainty: A Dual Approach. Journal of Mathematical Psychology, to appear. Abstract.
  • Yakov Ben-Haim, The innovative engineer: Qualitative reasoning in response to uncertainty, in the book The Engineer with a Humanistic Soul. The place and role of humanistic issues in technological discourse, edited by Krzysztof Baranowski, to appear. Abstract.
  • Yakov Ben-Haim, 2017, Does a better model yield a better argument? An info-gap analysis, Proceedings of the Royal Society, A, 5 April 2017. AbstractPre-publication version. Link to PRSA site. Summarized on here.
  • Yakov Ben-Haim, Order and indeterminism: An info-gap perspective, appearing in Error and Uncertainty in Scientific Practice, Marcel Boumans, Giora Hon and Arthur Petersen, eds., 2014, Pickering & Chatto Publishers, London, pp.157-175. Pre-publication version.
  • Yakov Ben-Haim, 2010, Info-Gap Economics: An Operational Introduction, Palgrave-Macmillan.
    Chapter 8: Positivism, F-twist and Robust-Satisficing.
  • Michael Smithson and Yakov Ben-Haim, 2015, Reasoned Decision Making Without Math? Adaptability and Robustness in Response to Surprise, Risk Analysis, vol.35, #10, pp.1911-1918. Pre-print.
  • Yakov Ben-Haim, 2012, Doing Our Best: Optimization and the Management of Risk, Risk Analysis, 32(8): 1326-1332. Pre-print, The published version, The definitive version is at


    Tools and concepts of optimization are widespread in decision-making, design and planning. There is a moral imperative to ‘do our best’. Optimization underlies theories in physics and biology, and economic theories often presume that economic agents are optimizers. We argue that, in decisions under uncertainty, what should be optimized is robustness rather than performance. We discuss the equity premium puzzle from financial economics, and explain that the puzzle can be resolved by using the strategy of satisficing rather than optimizing. We discuss design of critical technological infrastructure, showing that satisficing of performance requirements – rather than optimizing them – is a preferable design concept. We explore the need for disaster recovery capability and its methodological dilemma. The disparate domains – economics and engineering – illuminate different aspects of the challenge of uncertainty and of the significance of robust-satisficing.


    optimizing, satisficing, robustness, uncertainty, info-gap, financial investment, equity premium puzzle, technological infrastructure, moral hazard, disaster recovery

  • Yakov Ben-Haim, 2012, Why risk analysis is difficult, and some thoughts on how to proceed, Risk Analysis,32(10): 1638-1646. pre-print, The published version, The definitive version is at


    Risk analysis is challenged in three ways by uncertainty. Our understanding of the world and its uncertainties is evolving; indeterminism is an inherent part of the open universe in which we live; and learning from experience involves untestable assumptions. We discuss several concepts of robustness as tools for responding to these epistemological challenges. The use of models is justified, even though they are known to err. A concept of robustness is illustrated in choosing between a conventional technology and an innovative, promising, but more uncertain technology. We explain that non-probabilistic robust decisions are sometimes good probabilistic bets. Info-gap and worst-case concepts of robustness are compared. Finally, we examine the exploitation of favorable but uncertain opportunities and its relation to robust decision making.


    robustness, uncertainty, info-gap theory, satisficing, optimizing

  • Mark A. Burgman and Helen M. Regan, 2012, Information-gap decision theory fills a gap in ecological applications, Letter to the Editors, Ecological Applications, 24(1), pp. 227-228.
  • Mark A. Burgman, 2008, Shakespeare, Wald and decision making under uncertainty, Decision Point #23, p.10. On-line version (see p.10).
  • Barry Schwartz, Yakov Ben-Haim, and Cliff Dacso, 2011, What Makes a Good Decision?  Robust Satisficing as a Normative Standard of Rational Behaviour, The Journal for the Theory of Social Behaviour, 41(2): 209-227. Pre-print.
  • Yakov Ben-Haim and Francois Hemez, 2012, Robustness, Fidelity and Prediction-Looseness of Models,Proceedings of the Royal Society, A, 468: 227-244. Pre-print.
  • Yiping Li, Jianwen Chen, and Ling Feng, Dealing with uncertainty: A survey of theories and practices, IEEE Transactions on Knowledge and Data Engineering, vol.25, issue 11, November 2013, pages 2463-2482.


    Uncertainty accompanies our life processes and covers almost all fields of scientific studies. Two general categories of uncertainty, namely, aleatory uncertainty and epistemic uncertainty, exist in the world. While aleatory uncertainty refers to the inherent randomness in nature, derived from natural variability of the physical world (e.g., random show of a flipped coin), epistemic uncertainty origins from human’s lack of knowledge of the physical world, as well as ability of measuring and modeling the physical world (e.g., computation of the distance between two cities). Different kinds of uncertainty call for different handling methods. Aggarwal, Yu, Sarma, and Zhang et al. have made good surveys on uncertain database management based on the probability theory. This paper reviews multidisciplinary uncertainty processing activities in diverse fields. Beyond the dominant probability theory and fuzzy theory, we also review information-gap theory and recently derived uncertainty theory. Practices of these uncertainty handling theories in the domains of economics, engineering, ecology, and information sciences are also described. It is our hope that this study could provide insights to the database community on how uncertainty is managed in other disciplines, and further challenge and inspire database researchers to develop more advanced data management techniques and tools to cope with a variety of uncertainty issues in the real world.


    Uncertainty management, probability theory, Dempster-Shafer theory, fuzzy theory, info-gap theory, probabilistic database, fuzzy database

  • Yakov Ben-Haim, 2010, Uncertainty, Probability and Robust Preferences, working paper.
  • Yakov Ben-Haim, 2011, When is non-probabilistic robustness a good probabilistic bet? Working paper.
  • Yakov Ben-Haim, 2014, Robust satisficing and the probability of survival, Intl. J. of System Science, 45: 3-19, appearing on-line 9 May 2012. Online preview.
  • Yakov Ben-Haim, 2011, Optimizing and Satisficing in Quantum Mechanics: An Info-Gap Approach, working paper.
  • Yakov Ben-Haim, 2007, Peirce, Haack and Info-gaps, pp.150-164 in Susan Haack, A Lady of Distinctions: The Philosopher Responds to Her Critics, edited by Cornelis de Waal, Prometheus Books. Pre-print.
  • Yakov Ben-Haim, 2004, Uncertainty, probability and information-gaps, Reliability Engineering and System Safety, 85: 249-266. Pre-print.
  • Yakov Ben-Haim, 2000, Why the best engineers should study humanities, International Journal for Mechanical Engineering Education, 28: 195-200. Pre-print.
  • Yakov Ben-Haim, 2000, Robust rationality and decisions under severe uncertainty, Journal of the Franklin Institute, 337: 171-199. Pre-print.
  • Yakov Ben-Haim, 1999, Set-models of information-gap uncertainty: Axioms and an inference scheme, Journal of the Franklin Institute, 336: 1093-1117. Pre-print.
  • Yakov Ben-Haim, 1994, Convex models of uncertainty: Applications and Implications, Erkenntnis: An International Journal of Analytic Philosophy, 41:139-156. Re-print.
  • George J. Klir, 2006, Uncertainty and Information: Foundations of Generalized Information Theory, Wiley Publishers. Prof. Klir discusses possible relations between info-gap models of uncertainty and the measure-theoretic models of uncertainty in Generalized Information Theory.

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