Daniel Ellsberg on J.M. Keynes and F.H. Knight: risk ambiguity and uncertainty

Abstract

This paper aims to critically evaluate the life and work of Daniel Ellsberg, with an intensive discussion on their 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. Although his remarkable paper on ambiguity and decision was published in a prestigious journal in 1962, it had not received due attention for a long time. Because he was so preoccupied in the 1960s and onward by letting the general public know the Pentagon papers, he could virtually have no time left to engage in purely academic activities. In the 21st century, however, the times have changed in favor of Ellsberg: we can see the dramatic return of interest in decision making under ambiguity. In this paper, we 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 then turn to the main part of this paper, that is, the concept of ambiguity that was first introduced by Ellsberg. Both the two-color and the three-color problems will systematically be examined by help of numerical representations. While there are a variety of ways including the Nishimura–Ozaki approach for the resolution of the so-called Ellsberg paradox, the Keynesian approach by means of interval-valued probabilities, which was recently revived by Brady and applied by Sakai in many ways, is very simple and highly effective. In our opinion, the most amazing Ellsberg paradox lies in the fact that an accomplished economist specialized in the aversion of risk and uncertainty has 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.