Journal ArticleDOI
On the varieties of matrix probabilities in nonarchimedean decision theory
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TLDR
In this paper, it was shown that matrix probabilities can be represented by matrix probabilities that 1) may be taller than broad 2) remain finitely additive 3) can embody non-archimedean notions of relative likelihood.About:
This article is published in Journal of Mathematical Economics.The article was published on 1996-01-01. It has received 15 citations till now. The article focuses on the topics: Matrix (mathematics) & Axiom.read more
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Preference structures and their numerical representations
TL;DR: A selective survey of numerical representations of preference structures from the perspective of the representational theory of measurement, then describes recent contributions to ordinal, additive, and expected utility theories.
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Quantum information processing, operational quantum logic, convexity, and the foundations of physics
TL;DR: In this paper, the authors discuss general frameworks for operational theories, in which convexity plays key role, and show that any such theory naturally gives rise to a weak effect algebra when outcomes having the same probability in all states are identified and in the introduction of a notion of operation algebra that also takes account of sequential and conditional operations.
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Non-Archimedean subjective probabilities in decision theory and games
TL;DR: Blume et al. as discussed by the authors considered a suitable minimal field that is a complete metric space and used axioms similar to those in Anscombe and Aumann to characterize preferences which reveal unique non-Archimedean subjective probabilities within the field; and can be represented by the subjective expected value of any real-valued von Neumann-Morgenstern utility function in a unique cardinal equivalence class.
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Subjective expected lexicographic utility:Axioms and assessment
TL;DR: The theory of subjective expected lexicographic utility brings together two classical developments in expected utility theory, which produces representations of preference in decision under uncertainty in which utilities are finite-dimensional real vectors ordered lexicographically and subjective probabilities are real matrices.
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Subjective expected lexicographic utility with infinite state sets
TL;DR: In this paper, a theory of subjective expected lexicographic utility for decision under uncertainty with finite state sets was extended to an infinite state set S, where prior axioms yield a lexico-graph utility representation with matrix probabilities for preferences between mixtures of acts that are constant on finite partitions of S.
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The foundations of expected utility
TL;DR: The subjective linear utility with conditional preference comparison was proposed in this article for partially ordered preference comparison, and the subjective expected utility for arbitrary state sets was proposed as a generalization of the linear utility.
Journal ArticleDOI
Lexicographic probabilities and choice under uncertainty
TL;DR: In this paper, a non-Archimedean variant of subjective expected utility where decisionmakers have lexicographic beliefs is developed, which can be made to satisfy admissibility and yield well-defined conditional probabilities and at the same time allow for "null" events.