Ambiguity and uncertainty in Ellsberg and Shackle

This paper argues that Ellsberg’s and Shackle’s frameworks for discussing the limits of the (subjective) probabilistic approach to decision theory are not as different as they may appear. To stress the common elements in their theories Keynes’s Treatise on Probability provides an essential starting point. Keynes’s rejection of well-defined probability functions, and of maximisation as a guide to human conduct, is shown to imply a reconsideration of what probability theory can encompass, 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. The parallel between Keynes and the two decision theorists is drawn by means of a particular assessment of Shackle’s theory of decision, namely, it is interpreted in the light of Ellsberg’s doctoral dissertation. In this thesis, published only as late as 2001, Ellsberg developed the details and devised the philosophical background of his criticism of Savage as first put forward in the famed 1961 QJE article. The paper discusses the grounds on which the ambiguity surrounding the decision maker in Ellsberg’s urn experiment can be deemed analogous to the uncertainty faced by Shackle’s entrepreneur taking “unique decisions.” The paper argues also that the insights at the basis of the work of both Shackle and Ellsberg, as well as the criteria for decision under uncertainty they put forward, are relevant to understand the development of modern decision theory.uncertainty, weight of argument, non-additive probability

Shackle versus Savage: non-probabilistic alternatives to subjective probability theory in the 1950s

G.L.S Shackle’s rejection of the probability tradition stemming from Knight's definition of uncertainty was a crucial episode in the development of modern decision theory. A set of methodological statements characterizing Shackle’s stance, abandoned for long, especially after Savage’s Foundations, have been re-discovered and are at the basis of current non-expected utility theories, in particular of the non-additive probability approach to decision making. This paper examines the discussion between Shackle and his critics in the 1950s. Drawing on Shackle’s papers housed at Cambridge University Library as well as on printed matter, we show that some critics correctly understood two aspects of Shackle’s theory which are of the utmost importance in our view: the non-additive character of the theory and the possibility of interpreting Shackle’s ascendancy functions as a specific distortion of the weighting function of the decision maker. It is argued that Shackle neither completely understood criticisms nor appropriately developed suggestions put forward by scholars like Kenneth Arrow, Ward Edwards, Nicholas Georgescu- Roegen. Had he succeeded in doing so, we contend, his theory might have been a more satisfactory alternative to Savage’s theory than it actually was.uncertainty, decision theory, non-additive measures

Production of a New Drug: A Sequential Investment ProcessUnder Uncertainty

On the basis of a database of more than 80 thousand records on total retails and production costs of the pharmaceutical industry worldwide we consider four classes of drugs. We evaluate the expected profits of an investment in a new drug in the four classes of pharmaceutical products by considering the standard NPV evaluation. We compare these outcomes with the evaluation of the expected profits of the four new drugs obtained by the real option approach. Interestingly enough quite different outcomes are obtained. These results loom on the capacity of standard methods to give a reliable evaluation of real investment projects that are analogous to compound optionscompound option, real option valuation, net present value, drugs

A Comment on Anna Carabelli’s «Keynes’s Uncertainty as a Tragic Rational Dilemma»

The paper comments on Anna Carabelli's view on Keynes's probability theor

A Comment on Donald Gillies’s «Difficulties in the Logical Interpretation of Probability»

The paper comments on Donald Gillies's views of Keynes's probability theor

On measurable uncertainty and the fight for taking uncertainty seriously in economics

This paper discusses the engagement of economists with the issue of the measurability of uncertainty. Since Knight’s seminal distinction between risk, intended as measurable uncertainty, and unmeasurable uncertainty, the question has been to what extent the extension of the theory of choice from certainty to risk through von Neumann and Morgenstern’s expected utility hypothesis would allow dealing with uncertain events. The paper develops from a study of the rationale underlying the theories of those authors who objected to the mainstream view that the axiomatic approach developed in the early 1950s, mainly through Leonard Savage’s generalization of expected utility, makes it, indeed, possible to reduce uncertainty to risk. After a summary of the meaning attributed by authors such as Knight, Keynes, Shackle and Ellsberg to the contention that uncertainty is irreducible to risk and unmeasurable, the paper aims to investigate why this view did not emerge as a significant alternative to the mainstream up until recently. A main reason, at times alluded to but never openly discussed in the literature, is shown to be the close link between Savage and the group of decision theorists at the Cowles Commission for Research in Economics under the directorship of Jacob Marschak and Tjalling Koopmans. Archival evidence suggests that arguing that a theory of decision under uncertainty could be developed on the basis of “axioms that seem unobjectionable,” as Koopmans put it, was indeed an integral part of the attempt undertook at Cowles to move forward in economic theory by prioritizing scientific rigour in the form of mathematical models engaging with new mathematical tools

Confessing Characters: Coming to Faith in the Gospel of John

There are at least seventy-two characters in the Fourth Gospel. Given its statement of purpose in 20:30-31, which suggests that it is for the sake of narrating miracles to produce faith, this observation is of interest. According to traditional counting there are seven miracles in John. Nonetheless, much of the Gospel is the retelling not of miracles but of conversations and other encounters between Jesus and a wide variety of characters, many of whom are not directly tied to these miracles. Given the number and variety of characters in John, questions arise: What function do characters as characters serve in the Fourth Gospel? Why include these particular characters? What do they contribute to John’s work? My goal in this study will be to examine one specific set of characters—those who make a confession of faith—and seek to understand the reason for their presence in the Gospel. Through this group of characters, I intend to show that these Johannine figures exist to articulate a specific theological and confessional proclamation. “Confessing characters,” as I will call them, manifest John’s understanding of spiritual transformation. Mary Magdalene will act as my principal test case (others will include Nathanael, the Samaritan Woman, the Man Born Blind, and Thomas). My hypothesis is that Mary Magdalene\u27s narrative in 20:11-18, and the pericopes of other confessing characters, depict what John expresses in the Prologue, Jesus’ dialogues, the narrator’s interjections, and John the Baptist’s teachings concerning spiritual transformation. In other words, these characters’ stories portray what is merely stated elsewhere in the Gospel

Keynes’s Treatise on Probability at 100: A Symposium. Introduction

This paper introduces the symposium reproducing the four papers presented at the STOREP 2021 Annual Conference, in the virtual session especially dedicated to celebrate the centennial anniversary of the Treatise. The papers testify well to the diversity of views about the significance of Keynes’s volume for both the probability theory and the main theme in Keynes’s economics, namely, the pervasiveness of uncertainty in the economy and its substantial neglect by «classical» economists