STOREP CONFERENCES, STOREP 2017 - Investments, Finance, and Instability

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Rationality under Uncertainty: Daniel Ellsberg's Criticism of the Consistency Viewpoint
Carlo Zappia

Last modified: 2017-05-27

Abstract


Modern decision theory mostly developed as an attempt to justify the maximization of utility even under risk and uncertainty. The axiomatic approach to decision-making flourished in the years following von Neumann and Morgenstern’s introduction of expected utility. On the basis a series of postulates, extending ‘rules of conventional logic … into the realm of decision’, Marschak argued that both ‘statisticians and businessmen’ should maximize expected utility when making decisions. This logical extension was developed further by Savage who offered a representation theorem through which axioms for a ideally rational decision-maker facing uncertainty imply a subjective expected utility function to maximise. Since then rationality have been equated with a theory prescribing what individual should do in view of axioms such as completeness, transitivity and, in particular, the independence axiom (under risk) and the sure-thing principle (under uncertainty).

This normative turn in decision theory, emphasizing the prescriptive component of theoretical analysis and moving beyond the traditional normative as ethically motivated viewpoint, incorporates a specific notion of rationality. Developed under what came to be known as the Bayesian paradigm, rational decision-making is identified with consistent decision-making. On this view, probabilistic reasoning has a normative connotation, since shows how economic agents should reason, even when degrees of beliefs do not hinge on objective probabilities. Attributing probabilities to any kind of event guarantees the kind of consistency necessary to avoid accepting losing prospects as in the Dutch Book example.

The paper discusses Daniel Ellsberg’s early 1960s critique of this consistency notion of rationality. First, it presents the Ellsberg Paradox and Savage’s reaction to it, emphasizing the differences with the Allais Paradox. Second, it concentrates on Ellsberg’s view of the significance of rationality as consistency promoted within the Bayesians approach. It is shown that Ellsberg’s view, long unnoticed since hidden in his doctoral thesis, consists of a generalization of the Bayesian viewpoint to inter-valued probabilities admitting for kind of inertia in decision-making when the decisional context is too ambiguous to be interpreted thorough sharp probability priors. Third, it helps clarify the origins of a related interpretation of rationality, i.e. that a decision is rational for a decision-maker if, when exposed to the analysis of her choices, she does not regret having made it. The paper argues that this third aspect, suggesting that the validity of normative assumptions should be tested in view of reflective behaviour, was a core element of Ellsberg’s critique.

 


Keywords


rationality, uncertainty, Ellsberg Paradox

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