Uncertainty and computational complexity

Modern theories of decision-making typically model uncertainty about decision options using the tools of probability theory. This is exemplified by the Savage framework, the most popular framework in decision-making research. There, decision-makers are assumed to choose from among available decision options as if they maximized subjective expected utility, which is given by the utilities of outcomes in different states weighted with subjective beliefs about the occurrence of those states. Beliefs are captured by probabilities and new information is incorporated using Bayes’ Law. The primary concern of the Savage framework is to ensure that decision-makers’ choices are rational . Here, we use concepts from computational complexity theory to expose two major weaknesses of the framework. Firstly, we argue that in most situations, subjective utility maximization is computationally intractable, which means that the Savage axioms are implausible. We discuss empirical evidence supporting this claim. Secondly, we argue that there exist many decision situations in which the nature of uncertainty is such that (random) sampling in combination with Bayes’ Law is an ineffective strategy to reduce uncertainty. We discuss several implications of these weaknesses from both an empirical and a normative perspective. This article is part of the theme issue ‘Risk taking and impulsive behaviour: fundamental discoveries, theoretical perspectives and clinical implications’.

Is There an Ellsberg-Fellner Paradox? A Note on its Resolution

The Ellsberg-Fellner Paradox can be shown to be nonparadoxical if Keynes' concept of weight-of-evidence is incorporated in decision making under risk and/or uncertainty. Keynes' concept is a more advanced version of C. S. Peirce's “second number” approach and is identical to R. Carnap's reliability-unreliability index. The Ellsberg-Fellner Paradox is paradoxical only to decision theorists who accept the Von Neumann-Morgenstern-Savage axioms. Decision theorists who accept the logical approach to probability can bypass this problem.