Carlo Zappia

Shackle and Modern Decision Theory

The paper discusses the role of George L.S. Shackle in fostering an unconventional approach to individual decision making. Up until the early 1970s Shackle was the single critic of the probabilistic approach to decision making who proposed an alternative formal corpus for dealing with uncertainty. The main aim of the paper is to analyse Shackles non-probabilistic conceptualization of individual decisions under uncertainty from a specific viewpoint, namely that of a possible connection between his theory and one of the most interesting recent approaches to decision under uncertainty, the so-called non-additive probability approach of Gilboa and Schmeidler. The paper shows that these developments in modern decision theory take Shackles issue seriously and confirm that the reliance of strict Bayesian theory on probabilistic judgements based on point-probability estimates, a reliance that Shackle intended to oppose, is untenable. Non-additive decision theory also provides a usage of non-additive probability distributions in choice that is an alternative to Shackles approach of using a qualitative notion of probability, such as potential surprise.

Probabilistic versus Non-probabilistic Decision Making: Savage, Shackle and Beyond

This paper discusses the evolution of decision theory after Savages Foundations. Two developments are examined. First, it is presented the rationale of Shackles proposal to abandon probabilistic decision making. Second, it is discussed the axiomatisation provided by the non-additive probability approach to account for the experimental evidence originated by the Ellsberg Paradox. An attempt is made to establish a connection between Shackles non-probabilistic instances and non-additive probabilistic decision making. The main outgrowth of the paper is that the similarities between the non-additive approach and Shackles theory are not limited to a number of methodological statements. In fact, it is also the formal measures used in the two contexts for representing individual preferences in uncertain environments that resemble each other.

De Finetti on the insurance of risks and uncertainties

In the insurance literature, it is often argued that private markets can provide insurance against ‘risks’ but not against ‘uncertainties’ in the sense of Knight ([1921]) or Keynes ([1921]). This claim is at odds with the standard economic model of risk exchange which, in assuming that decision-makers are always guided by point-valued subjective probabilities, predicts that all uncertainties can, in theory, be insured. Supporters of the standard model argue that the insuring of highly idiosyncratic risks by Lloyds of London proves that this is so even in practice. The purpose of this article is to show that Bruno de Finetti, famous as one of the three founding fathers of the subjective approach to probability assumed by the standard model, actually made a theoretical case for uncertainty within the subjectivist approach. We draw on empirical evidence from the practice of underwriters to show how this case may help explain the reluctance of insurers to cover highly uncertain contingencies. 1 Introduction 2 Knight and Keynes on the Philosophy of Unknown Probabilities and Lloyds of London   2.1 Knight   2.2 Keynes 3 Insuring Unique Events: The Subjectivist Viewpoint as Represented by de Finetti 4 The ‘Philosophy’ of Practitioners 5 De Finetti on Uncertainty in Knight and Keynes and on Insurability   5.1 De Finetti on Knight   5.2 De Finetti on Keynes 6 Empirical Evidence on Insurance Under Ambiguity 7 Conclusion 1 Introduction 2 Knight and Keynes on the Philosophy of Unknown Probabilities and Lloyds of London   2.1 Knight   2.2 Keynes   2.1 Knight   2.2 Keynes 3 Insuring Unique Events: The Subjectivist Viewpoint as Represented by de Finetti 4 The ‘Philosophy’ of Practitioners 5 De Finetti on Uncertainty in Knight and Keynes and on Insurability   5.1 De Finetti on Knight   5.2 De Finetti on Keynes   5.1 De Finetti on Knight   5.2 De Finetti on Keynes 6 Empirical Evidence on Insurance Under Ambiguity 7 Conclusion

The Weight of Argument and Non-Additive Measures: A Note

This note argues that a representation of the epistemic state of the individual through a non-additive measure provides a novel account of Keynes’s view of probability theory proposed in his Treatise on Probability. The paper shows, first, that Keynes’s “non-numerical probabilities” can be interpreted in terms of decisional weights and distorsions of the probability priors. Second, that the degree of non-additivity of the probability measure can account for the confidence in the assessment without any reference to a second order probability. And, third, that the criterion for decision making under uncertainty derived in the non-additive literature incorporates a measure of the degree of confidence in the probability assessment. The paper emphasises the Keynesian derivation of Ellsberg’s analysis: the parallel between Keynes and Ellsberg is deemed to be significant since Ellsberg’s insights represent the main starting point of the modern developments of decision theory under uncertainty and ambiguity.

Radical Ignorance in Individual Decision Making: Assessing Austrian Subjectivism

In recent years most Austrian developments have argued for a definitive shift away from the search for equilibrium constructs and in favor of the analysis of those institutions which favor ordered outcomes of the market process. These developments imply an inevitable withdrawal from methodological individualism and are based on the contention that a probabilistic approach to subjective decision making is flawed. Our aim in this paper is to point out that a withdrawal from equilibrium theorizing is not justified by the inability of pure economic theory to deal with radical ignorance. We argue that the kind of formal representation of decision making under uncertainty one finds in recent developments in microeconomic theory, namely the non-additive approach to subjectively probable assessments, recognizes as a starting point for research the view that ignorance is an inherent feature of every decision regarding future events. In this, it resembles the Shackleian assertion that the future is the unpredictable consequence of creative choices made by individual agents. A critical, but positive, attitude towards recent attempts to formalize radical ignorance suggests that the Austrian tradition may actually influence future research rather than merely constitute an optional supplement to it.

Shackle's Economic Agent and Modern Decision Theory

This paper assesses the rationale of George Shackles argument against Bayesian decision making in the light of recent developments of modern decision theory. The focus is on the so-called non-additive probability approach to decision theory under uncertainty, which, not unlike Shackles analysis, stresses the inability of agents to describe uncertain environments. A discussion of the pros and cons of the parallel between Shackles theory and the non-additive developments is provided.

Re-Reading Keynes after the Crisis: Probability and Decision

The recent financial crisis has renewed the interest in Keyness thought and his analysis of the role played by individual agents in financial markets. George Akerlof and Robert Shiller, in particular, have drawn on the growing interest in behavioural interpretations of financial markets to hold that Keynes’s insistence on “the spontaneous urge to action” of individuals is the most relevant message conveyed by the General Theory. This paper starts off from a brief summary of Akerlof and Shiller’s influential stance and aims to provide an historically motivated assessment of their claim. The paper mostly concentrates on Keynes’s Treatise on Probability and discusses how Keynes applied his philosophy of probability to decision-making. It is argued that a fresh reading of this part of Keynes’s work can contribute to an understanding of how individual agents behave under uncertainty, and that the violations of the Bayesian creed scrutinized in behavioural finance, and in some current proposals to amend mainstream decision theory, were already implicitly discussed by Keynes in his critique of frequency probability

De Finetti and Savage on the normative relevance of imprecise reasoning: a reply to Arthmar and Brady

This paper examines the claim that de Finetti and Savage completely rejected the notion of indeterminate, as distinct from imprecise, probabilities. It argues that their examination of imprecise reasoning refers both to descriptive and normative issues, and that the inability for a decisionmaker to commit to a single prior cannot be limited to measurement problems, as argued by Arthmar and Brady in a recent contribution to this Journal. The paper shows that de Finetti and Savage admitted that having an interval of initial probabilities may sometimes have normative relevance, thereby leaving an opening for indeterminate probabilities.

Whither Keynesian Probability? Impolite Techniques for Decision-Making

Abstract The critical literature on Keynes has provided extensive analysis of why individual agents may find convenient to adopt a “conventional judgement”, and what he meant by “polite techniques” used to save their faces as “rational, economic men.” This paper concentrates instead on impolite techniques of thought suited to deal with Keynesian uncertainty. The paper suggests that the thread going from Keyness Treatise on Probability to the General Theory and its defence provides a positive analysis of decision-making under uncertainty, and that placing emphasis on this positive analysis simply means adhering to Keyness long-standing commitment to a (surely peculiar) probabilistic set-up.