Daniel Ellsberg on J.M. Keynes and F.H. Knight: Risk, Ambiguity, and Uncertainty

  • Yasuhiro Sakai
Part of the Evolutionary Economics and Social Complexity Science book series (EESCS, volume 18)


This paper aims to focus on the life and work of Daniel Ellsberg, with an intensive discussion on its relation to J.M. Keynes and F.H. Knight, the two great pioneers of the economics of uncertainty. Ellsberg seems to be a man in paradox. When he was young, he was an outstanding researcher at Harvard University and the RAND Corporation; at the December Meeting of the Econometric Society in 1960, he presented his remarkable paper in which he successfully demonstrated what we may now call Ellsberg’s paradox against the traditional expected theory a la Daniel Bernoulli and von Neumann. Although it was published with the title Risk, Ambiguity and Decision in the November issue of the Quarterly Journal of Economics, it was not paid due attention for a long time. It was partly because he was so preoccupied in the 1960s and onward by letting the general public know the Pentagon Papers that he could virtually have no time left to engage in purely academic activities. In the twenty-first century, however, the times have changed in favor of Ellsberg: we can see the dramatic return of interest in decision-making under ambiguity.

This chapter will first deal with uncertainties that are not risks. A focal point of discussion will be the similarity and difference between Keynes and Knight. Kenneth Arrow’s skepticism about Knight on uncertainty will also be paid due attention. We will next turn to the concept of ambiguity that was first introduced by Ellsberg. This is really the main part of this chapter. Both the two-color problem and the three-color problem will systematically be examined by help of numerical representations. We will demonstrate many possible ways to solve the so-called Ellsberg paradox. Presumably, the Keynesian approach by means of interval-valued probabilities will be shown to be very simple and highly effective. In our opinion, the most amazing Ellsberg paradox lies in the fact that an accomplished economist specialized in risk aversion dared to make a personal choice to risk everything such as degrading his social status and putting him in prison for a long period. Surely, the intellectual legacy of Ellsberg seems to be an intriguing research in paradox.


Ellsberg Keynes Knight Risk Ambiguity Uncertainty 


  1. Akerlof GA, Shiller RJ (2009) Animal spirits: how human psychology drives the economy, and why it matters for global capitalism. Princeton University Press, PrincetonGoogle Scholar
  2. Arrow KJ (1951) Alternative approaches to theory of choice in risk-taking situations. Econometrica 19:404–437. Contained in Arrow (1970), Chapter 1CrossRefGoogle Scholar
  3. Arrow KJ (1970) Essays in the theory of risk-bearing. North Holland, AmsterdamGoogle Scholar
  4. Arrow KJ, Hahn EH (1971) General competitive analysis. Holden-Day, San FranciscoGoogle Scholar
  5. Bernoulli D (1738) Specimen theorie novae de mensura sortis (in Latin). Commentarii Academiae Scientiarum Imperialis Petropolitanae (Papers of the Imperial Science Sciences in Petersburg) 1:175–195. English Translation by Sommer L (1954) Exposition of a new theory of the measurement of risk. Econometrica: 22, 23–36Google Scholar
  6. Boyd R (1997) Knight FH, 1935, The ethics of competition: a new introduction to the transaction edition. Transaction Publishers, New Brunswick/LondonGoogle Scholar
  7. Brady ME (2004) J.M. Keynes’ theory of decision making, induction, and analogy: the role of interval valued probability in his approach. Xlibris Corporation, BloomingtonGoogle Scholar
  8. Ellsberg D (1961) Risk, ambiguity and the Savage axioms. Q J Econ 75(4):643–669CrossRefGoogle Scholar
  9. Ellsberg D (1962/2001) Risk, ambiguity and decision. Routledge, London/New YorkCrossRefGoogle Scholar
  10. Ellsberg D (2002). Secrets: a memoir of Vietnam and the Pentagon papersGoogle Scholar
  11. Emmett RB (1999a) Selected essays by Frank H. Knight, volume one. University of Chicago Press, ChicagoGoogle Scholar
  12. Emmett RB (1999b) Selected essays by Frank H. Knight, volume two. University of Chicago Press, ChicagoGoogle Scholar
  13. Frank P (1949) Einstein’s philosophy of science. Rev Mod Phys:21–23Google Scholar
  14. Gilboa I, Schmeidler D (1989) Maxmin expected utility with non-unique prior. J Math Econ 18:141–153CrossRefGoogle Scholar
  15. Hicks JR (1979) Causality in economics. Basic Blackell, OxfordGoogle Scholar
  16. Keynes JM (1921) A treatise on probability. Macmillan, LondonGoogle Scholar
  17. Keynes JM (1936) The general theory of employment, interest and money. Macmillan, LondonGoogle Scholar
  18. Keynes JM (1937) The general theory of employment. Q J Econ 51(2):209–223CrossRefGoogle Scholar
  19. Knight FH (1921) Risk, uncertainty and profit. University of Chicago Press, ChicagoGoogle Scholar
  20. Knight FH (1951) The role of principles in economics and politics. Am Econ Rev 41:1–29Google Scholar
  21. Levi I (2001) Introduction to risk, ambiguity and decision. Contained in the new edition of Ellsberg (2001), pp ix–xxxviiGoogle Scholar
  22. Nishimura GK, Ozaki H (2017) Economics of pessimism and optimism: theory of Knightian uncertainty and its applications. Springer, TokyoCrossRefGoogle Scholar
  23. Sakai Y (2015) J.M. Keynes versus F.H. Knight (in Japanese). Minerva Publishing Company, KyotoGoogle Scholar
  24. Sakai Y (2016) J.M. Keynes on probability versus F.H. Knight on uncertainty: reflections on the miracle year of 1921. Evol Inst Econ Rev 13(1):1–21CrossRefGoogle Scholar
  25. Sakai Y (2018) Daniel Ellsberg on J.M. Keynes and F.H. Knight: risk, ambiguity and uncertainty. CRR Discussion Paper No. A-31, Shiga University, Japan, pp 1–21Google Scholar
  26. Sakai Y (2019a) Economics of pessimism and optimism: theory of Knightian uncertainty and its applications, Kiyohiko G. Nishimura and Hiroyuki Ozaki, Springer Japan (2017). J Econ Psychol 72:51–53CrossRefGoogle Scholar
  27. Sakai Y (2019b) Daniel Ellsberg on J.M. Keynes and F.H. Knight: Risk, ambiguity and uncertainty. Evolutionary and Institutional Economics Review, forthcomingGoogle Scholar
  28. Schmeidler D (1989) Subjective probability and expected utility without additivity. Econometrica 57:571–587CrossRefGoogle Scholar
  29. Sen A (1987) On ethics and economics. Blackwell PublishingGoogle Scholar
  30. Skidelsky R (2009) Keynes: the return of the master. Public Affairs, New YorkGoogle Scholar
  31. Taleb N (2007) The black swan: the impact of the highly improbable. Allen Lane, New YorkGoogle Scholar
  32. Thaler RH (2015) Misbehaving: The making of behavioral economics. Norton, New YorkGoogle Scholar
  33. Zappia C (2016) Daniel Ellsberg and the validation of normative propositions. Œconomia (6–1):57–79Google Scholar

Copyright information

© Springer Nature Singapore Pte Ltd. 2019

Authors and Affiliations

  • Yasuhiro Sakai
    • 1
  1. 1.Department of EconomicsCenter for Risk Research, Shiga UniversityHikoneJapan

Personalised recommendations