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...

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Bibliographic Details
Published in:Philosophical transactions of the Royal Society of London. Series B. Biological sciences Vol. 374; no. 1766; p. 20180138
Main Authors: Bossaerts, Peter, Yadav, Nitin, Murawski, Carsten
Format: Journal Article
Language:English
Published: England 18.02.2019
Subjects:
Bayes Theorem
Decision Making
Humans
Probability
Uncertainty
expected utility
uncertainty
Bayesian
computational complexity
ISSN:1471-2970, 1471-2970
Online Access:Get more information
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Summary: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'.
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ISSN:1471-2970
1471-2970
DOI:10.1098/rstb.2018.0138