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Entropy 2019, 21(4), 375; https://doi.org/10.3390/e21040375

Bounded Rational Decision-Making from Elementary Computations That Reduce Uncertainty

Institute of Neural Information Processing, Ulm University, 89081 Ulm, Germany
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Received: 19 February 2019 / Revised: 2 April 2019 / Accepted: 4 April 2019 / Published: 6 April 2019
PDF [2531 KB, uploaded 6 April 2019]

Abstract

In its most basic form, decision-making can be viewed as a computational process that
progressively eliminates alternatives, thereby reducing uncertainty. Such processes are generally
costly, meaning that the amount of uncertainty that can be reduced is limited by the amount of
available computational resources. Here, we introduce the notion of elementary computation based
on a fundamental principle for probability transfers that reduce uncertainty. Elementary computations
can be considered as the inverse of Pigou–Dalton transfers applied to probability distributions, closely
related to the concepts of majorization, T-transforms, and generalized entropies that induce a preorder
on the space of probability distributions. Consequently, we can define resource cost functions that are
order-preserving and therefore monotonic with respect to the uncertainty reduction. This leads to
a comprehensive notion of decision-making processes with limited resources. Along the way, we
prove several new results on majorization theory, as well as on entropy and divergence measures.
Keywords: uncertainty; entropy; divergence; majorization; decision-making; bounded rationality; limited resources; Bayesian inference uncertainty; entropy; divergence; majorization; decision-making; bounded rationality; limited resources; Bayesian inference
This is an open access article distributed under the Creative Commons Attribution License which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited (CC BY 4.0).
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Gottwald, S.; Braun, D.A. Bounded Rational Decision-Making from Elementary Computations That Reduce Uncertainty. Entropy 2019, 21, 375.

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