Skip to main content
SpringerLink
Log in

Decision Making Under Ignorance

  • Chapter
Fusion Methodologies in Crisis Management

Abstract

Ignorance is an extreme form of uncertainty. In most narrow and technical sense, it means inability to assign a meaningful probability to the phenomena of interest. In more general sense, the state of ignorance is the result of the absence of knowledge about structural factors that influence the issues, the lack of reliable information or inability to completely determine the space of alternatives and consequences. We argue that the practice of casually papering over the ignorance with subjective judgments and analytic assumptions can have serious consequences. This chapter provides a structured survey (and necessarily selective) of significant ideas and proposals for decision making under ignorance, from the ground breaking work by Hurwicz and Arrow to the latest result of τ-anchor utility theory. A careful analysis and isolation of ignorance in the system of knowledge about a subject or a problem is of particular importance in the context of risk assessment and risk management.

This is a preview of subscription content, log in via an institution to check access.

Access this chapter

Log in via an institution
Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 129.00
Price excludes VAT (USA)
  • Available as EPUB and PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 169.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info
Hardcover Book
USD 169.99
Price excludes VAT (USA)
  • Durable hardcover edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

Notes

  1. 1.

    For the context of the quip, the entire transcript of the news briefing can be found here: http://www.defense.gov/transcripts/transcript.aspx?transcriptid=2636.

  2. 2.

    http://library.rumsfeld.com/doclib/20110202_20020909toMyersreWMD.pdf.

  3. 3.

    A bag is different from a set in the sense that a bag can contain the same item multiple times while all the elements in a set are distinct.

References

  • Arrow KJ, Hurwicz L (1977) An optimality criterion for decision making under ignorance. In: Arrow KJ, Hurwicz L (eds) Studies in resource allocation processes. Cambridge University Press, Cambridge

    Chapter  Google Scholar 

  • Aven T, Steen R (2010) The concept of ignorance in a risk assessment and risk management context. Reliab Eng Syst Saf 95:1117–1122

    Article  Google Scholar 

  • Barbera S, Bossert W, Pattanaik PK (2004) Ranking sets of objects. In: Barbera S, Hammond P, Seidl C (eds) Handbook of utility theory: extensions, vol 2. Springer, Berlin, pp 893–978

    Chapter  Google Scholar 

  • Cohen M, Jaffray J-Y (1980) Rational behavior under complete ignorance. Econometrica 48(5):1281–1299

    Article  MathSciNet  MATH  Google Scholar 

  • Congar R, Maniquet F (2010) A trichotomy of attitudes for decision-making under complete ignorance. Math Soc Sci 59:15–25

    Article  MathSciNet  MATH  Google Scholar 

  • Ellsberg D (1961) Risk, ambiguity and the Savage’s axioms. Q J Econ 75(4):643–669

    Article  MATH  Google Scholar 

  • Epstein LG (1999) A definition of uncertainty aversion. Rev Econ Stud 66:579–608

    Article  MATH  Google Scholar 

  • Giang PH (2011) Dynamic consistency and decision making under vacuous belief. In: Cozman FG, Pfeffer A (eds) Uncertainty in artificial intelligence: proceedings of the 27nd conference (UAI–2011). AUAI Press, pp 230–237

    Google Scholar 

  • Gilboa I, Postlewaite A, Schmeidler D (2009) Is it always rational to satisfy Savage’s axioms? Econ Philos 25:285–296

    Article  Google Scholar 

  • Graham DA (2014) Rumsfeld’s knowns and unknowns: the intellectual history of a quip. Atl Mag. http://www.theatlantic.com/politics/archive/2014/03/rumsfelds-knowns-and-unknowns-the-intellectual-history-of-a-quip/359719/

  • Gravel N, Marchant T, Sen A (2012) Uniform expected utility criteria for decision making under ignorance or objective ambiguity. J Math Psychol 56:297–315

    Article  MathSciNet  MATH  Google Scholar 

  • Health and Safety Executive (UK) (2001) Reducing risks, protecting people: HSE’s decision-making process. HSE Books, London

    Google Scholar 

  • Hogarth RM, Kunreuther H (1995) Decision making under ignorance: arguing with yourself. J Risk Uncertain 10:15–36

    Article  MATH  Google Scholar 

  • Keynes JM (1921) A treatise on probability. Macmillan, London

    MATH  Google Scholar 

  • Knight FH (1921) Risk, uncertainty and profit. Houghton Mifllin, Boston

    Google Scholar 

  • Maskin E (1979) Decision-making under ignorance with implications for social choice. Theor Decis 11:319–337

    Article  MathSciNet  MATH  Google Scholar 

  • Nehring K, Puppe C (1996) Continuous extensions of an order on a set to the power set. J Econ Theory 68:456–479

    Article  MathSciNet  MATH  Google Scholar 

  • Nitzan S, Pattanaik PK (1984) Median-based extensions of an ordering over a set to the power set: an axiomatic characterization. J Econ Theory 34:252–261

    Article  MathSciNet  MATH  Google Scholar 

  • Puppe C, Schlag KH (2009) Choice under complete uncertainty when outcome spaces are state dependent. Theor Decis 66:1–16

    Article  MathSciNet  MATH  Google Scholar 

  • Pushkarskaya H, Liu X, Smithson M, Joseph JE (2010) Beyond risk and ambiguity: deciding under ignorance. Cogn Affect Behav Neurosci 10(3):382–391

    Article  Google Scholar 

  • Shackle GLS (1949) Expectations in economics. Cambridge University Press, Cambridge

    Google Scholar 

  • Smets P (2005) Decision making in the TBM: the necessity of the pignistic transformation. Int J Approx Reason 38(2):133–147

    Article  MathSciNet  MATH  Google Scholar 

  • von Neumann J, Morgenstern O (1953) Theory of games and economic behavior, 3rd edn. Princeton University Press, Princeton, NJ

    MATH  Google Scholar 

  • Walley P (1996) Inferences from multinomial data: learning about a bag of marbles. J R Stat Soc Ser B 58(1):3–57

    MathSciNet  MATH  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. George Mason University, MS 1J3, 4400 University Dr., Fairfax, VA, 22030, USA

    Phan H. Giang

Authors
  1. Phan H. Giang
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Phan H. Giang .

Editor information

Editors and Affiliations

  1. State University of New York at Buffalo, Buffalo, New York, USA

    Galina Rogova

  2. State University of New Yorkat Buffalo, Buffalo, New York, USA

    Peter Scott

Rights and permissions

Reprints and permissions

Copyright information

© 2016 Springer International Publishing Switzerland

About this chapter

Cite this chapter

Giang, P.H. (2016). Decision Making Under Ignorance. In: Rogova, G., Scott, P. (eds) Fusion Methodologies in Crisis Management. Springer, Cham. https://doi.org/10.1007/978-3-319-22527-2_20

Download citation

  • DOI: https://doi.org/10.1007/978-3-319-22527-2_20

  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-319-22526-5

  • Online ISBN: 978-3-319-22527-2

  • eBook Packages: EngineeringEngineering (R0)

Publish with us

Policies and ethics

Search

Navigation