Abstract
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.
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Notes
- 1.
In retrospect, the 1960s were truly turbulent years. While the Vietnam war was raging in Indochina, many young men and hippies in the USA and Japan were involved in social protest movements. So many scandals such as the Pentagon Papers scandal and the Watergate scandal took place, eventually leading to the resignation of Richard Nixon, the then American President.
- 2.
- 3.
Skidelsky has enthusiastically argued that “the economics of John Maynard Keynes is back in fashion. The guardian of free-market orthodoxy the Wall Street Journal devoted a full page spread to him on 8 January 2009. The reason is obvious. The global economy is slumping; ‘stimulus packages’ are all the rage” (Skidelsky 2009, Preface, p. xi). It seems that we are now living in the second age of Keynes.
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- 5.
Although Arrow described his strong skepticism about Knightian uncertainty, it would sound rather strange that Arrow’s comment on Keynesian uncertainty was not so critical. In fact, in Arrow and Hahn (1971), Arrow was so kind to discuss the position of the Keynesian model in relation to general competitive model.
- 6.
It is recalled that usefulness of the interval probability approach was later advocated by Hicks (1979), an outstanding Keynesian economist
- 7.
Gustave Choquet (1915–2006) is a contemporary French mathematician. His contributions include work in functional analysis, potential theory, and measure theory. He is well-known for creating Choquet integral and Choquet theory. Choquet integral may be regarded as an extension of Lebesgue integral, which was created by Henri-Léon Lebesgue (1875–1941), another famed French mathematician. Although Choquet integral per se belongs to a highly advanced branch of mathematics, it has recently been applied to economic theory by Schmeidler (1989), Gilboa and Schmeidler (1989), and Nishimura and Ozaki (2017). We have bear in mind, however, that there should be an insurmountable trade-off between intuitive simplicity and mathematical complexity. For a detailed review of Nishimura and Ozaki (2017), see Sakai (2019a).
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Sakai, Y. (2019). Daniel Ellsberg on J.M. Keynes and F.H. Knight: Risk, Ambiguity, and Uncertainty. In: J.M. Keynes Versus F.H. Knight. Evolutionary Economics and Social Complexity Science, vol 18. Springer, Singapore. https://doi.org/10.1007/978-981-13-8000-6_4
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