Ambiguity and uncertainty in Ellsberg and Shackle

This paper argues that the similarities between Ellsberg's and Shackle's frameworks for discussing the limits of the probabilistic approach to decision theory are more important than usually admitted. The paper discusses the grounds on which the ambiguity surrounding the decision-maker in Ellsberg's urn experiments can be deemed analogous to the uncertainty faced by Shackle's entrepreneur taking 'crucial decisions'. The two authors' insights are assessed, and special attention is paid to the criteria for decision under uncertainty they put forward. The paper establishes a link between Ellsberg's and Shackle's perspectives and the non-additive probability approach of Gilboa and Schmeidler, an approach that offers an alternative to standard probability calculus, which can be of use to analyse both ambiguity and uncertainty. The comparison between Ellsberg and Shackle draws on an interpretation of Keynes's Treatise on Probability emphasising Keynes's rejection of both well-defined probability functions and maximisation as a guide to human conduct. It is shown that Keynes's viewpoint implies a reconsideration of the boundaries of probability theory that is in the same vein of Ellsberg's and Shackle's concern in the years of the consolidation of Savage's new probabilistic mainstream.