The foundations of decision theory: an intuitive, operational approach with mathematical extensions (Q1066568)

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.