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Bounded Rational Decision-Making from Elementary Computations That Reduce Uncertainty
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 computation...
Autores principales: | , |
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Formato: | Online Artículo Texto |
Lenguaje: | English |
Publicado: |
MDPI
2019
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Materias: | |
Acceso en línea: | https://www.ncbi.nlm.nih.gov/pmc/articles/PMC7514859/ https://www.ncbi.nlm.nih.gov/pubmed/33267089 http://dx.doi.org/10.3390/e21040375 |
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author | Gottwald, Sebastian Braun, Daniel A. |
author_facet | Gottwald, Sebastian Braun, Daniel A. |
author_sort | Gottwald, Sebastian |
collection | PubMed |
description | 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. |
format | Online Article Text |
id | pubmed-7514859 |
institution | National Center for Biotechnology Information |
language | English |
publishDate | 2019 |
publisher | MDPI |
record_format | MEDLINE/PubMed |
spelling | pubmed-75148592020-11-09 Bounded Rational Decision-Making from Elementary Computations That Reduce Uncertainty Gottwald, Sebastian Braun, Daniel A. Entropy (Basel) Article 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. MDPI 2019-04-06 /pmc/articles/PMC7514859/ /pubmed/33267089 http://dx.doi.org/10.3390/e21040375 Text en © 2019 by the authors. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (http://creativecommons.org/licenses/by/4.0/). |
spellingShingle | Article Gottwald, Sebastian Braun, Daniel A. Bounded Rational Decision-Making from Elementary Computations That Reduce Uncertainty |
title | Bounded Rational Decision-Making from Elementary Computations That Reduce Uncertainty |
title_full | Bounded Rational Decision-Making from Elementary Computations That Reduce Uncertainty |
title_fullStr | Bounded Rational Decision-Making from Elementary Computations That Reduce Uncertainty |
title_full_unstemmed | Bounded Rational Decision-Making from Elementary Computations That Reduce Uncertainty |
title_short | Bounded Rational Decision-Making from Elementary Computations That Reduce Uncertainty |
title_sort | bounded rational decision-making from elementary computations that reduce uncertainty |
topic | Article |
url | https://www.ncbi.nlm.nih.gov/pmc/articles/PMC7514859/ https://www.ncbi.nlm.nih.gov/pubmed/33267089 http://dx.doi.org/10.3390/e21040375 |
work_keys_str_mv | AT gottwaldsebastian boundedrationaldecisionmakingfromelementarycomputationsthatreduceuncertainty AT braundaniela boundedrationaldecisionmakingfromelementarycomputationsthatreduceuncertainty |