The foundations of decision theory: an intuitive, operational approach with mathematical extensions
type: Item
instance of: scholarly article
title: The foundations of decision theory: an intuitive, operational approach with mathematical extensions
zbMATH Open document ID: 0578.62008
DOI: 10.1007/BF00132439
author: J. R. Ferrandiz
author: Jose M. Bernardo
author: A. F. M. Smith
published in: Theory and Decision
publication date: 1985-01-01T00:00:00Z
review text: The notion that ''quantitative coherence'' should provide the normative basis for decision making under uncertainty has found formal expression in a wide variety of axiom systems, building upon the original ideas of \textit{F. P. Ramsey} [``Truth and probability.'' in: The foundations of mathematics and other logical essays (1931; Zbl 0002.00501)] and the influential work of \textit{L. J. Savage}, The foundations of statistics. Wiley (1954; Zbl 0055.12604). All such axiom systems lead to essentially the same conclusions: uncertainty \(= probability\), preference \(= utility\), decision criterion \(= \max imize\) expected utility. However, they differ considerably in their trade-offs between intuitive appeal (simplicity- interpretability) and their range of applicability (structural flexibility). We would add to these considerations the need for clear operational definitions of key concepts. A new axiomatic basis for the foundations of decision theory is introduced and its mathematical development outlined. The system combines direct intuitive operational appeal with considerable structural flexibility in the resulting mathematical framework.
Mathematics Subject Classification ID: 62C05
Mathematics Subject Classification ID: 62C10
Mathematics Subject Classification ID: 91B06
Mathematics Subject Classification ID: 60A05
Mathematics Subject Classification ID: 62A01
zbMATH DE Number: 3925964
zbMATH Keywords: quantitative coherence
zbMATH Keywords: uncertainty
zbMATH Keywords: probability
zbMATH Keywords: preference
zbMATH Keywords: utility
zbMATH Keywords: new axiomatic basis
MaRDI profile type: Publication
cites work: Q4094173
cites work: Q4181540
cites work: Q5615833
cites work: Subjective expected utility: A review of normative theories
cites work: The Foundations of Decision Under Uncertainty: An Elementary Exposition
cites work: Q5826088
description: scientific article; zbMATH DE number 3925964