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Bounded Rational Decision-Making from Elementary Computations That Reduce Uncertainty

Institute of Neural Information Processing, Ulm University, 89081 Ulm, Germany
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Entropy 2019, 21(4), 375; https://doi.org/10.3390/e21040375
Received: 19 February 2019 / Revised: 2 April 2019 / Accepted: 4 April 2019 / Published: 6 April 2019
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. View Full-Text
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
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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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