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Counting is the type of measurement that is free from uncertainty, provided the number of objects being counted does not change during the process. Such measurements result in exact numbers. By counting the eggs in a carton, for instance, one can determine exactly how many eggs are there in the carton. Similarly, the numbers of defined quantities are also exact. For example, 1 foot is exactly 12 inches, 1 inch is exactly 2.54 centimeters, and 1 gram is exactly 0.001 kilograms. Quantities...
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Uncertainty and computational complexity.

Peter Bossaerts1,2, Nitin Yadav1, Carsten Murawski1

  • 11 Brain, Mind and Markets Laboratory, Department of Finance, The University of Melbourne , Parkville, Victoria 3010 , Australia.

Philosophical Transactions of the Royal Society of London. Series B, Biological Sciences
|April 11, 2019
PubMed
Summary
This summary is machine-generated.

The Savage framework for decision-making under uncertainty is computationally intractable and Bayes

Keywords:
Bayesiancomputational complexityexpected utilityuncertainty

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Area of Science:

  • Decision-making theory
  • Computational complexity
  • Probability theory

Background:

  • Modern decision-making theories use probability theory to model uncertainty.
  • The Savage framework, popular in research, assumes rational choices via subjective expected utility maximization.
  • Beliefs are probabilities, updated with Bayes' Law.

Purpose of the Study:

  • To expose computational and strategic weaknesses in the Savage framework for decision-making.
  • To challenge the plausibility of Savage axioms using computational complexity.
  • To identify limitations of Bayes' Law for uncertainty reduction in certain decision scenarios.

Main Methods:

  • Application of computational complexity theory to analyze decision-making frameworks.
  • Examination of the tractability of subjective utility maximization.
  • Analysis of the effectiveness of random sampling and Bayes' Law in reducing uncertainty.

Main Results:

  • Subjective utility maximization is computationally intractable in most situations, questioning Savage axioms.
  • Bayes' Law combined with random sampling can be ineffective for reducing uncertainty in specific decision contexts.
  • Empirical evidence supports the computational intractability claim.

Conclusions:

  • The Savage framework's assumptions may be implausible due to computational intractability.
  • Alternative strategies are needed for decision-making under uncertainty where Bayes' Law is insufficient.
  • Weaknesses have significant empirical and normative implications for understanding rational choice.