The shape of incomplete preferences

• 成果类型: Article
• 署名作者: Nau, Robert
• 署名单位: Duke University
• 刊物名称: ANNALS OF STATISTICS
• ISSN/ISSBN: 0090-5364
• DOI: 10.1214/009053606000000740
• 发表日期: 2006
• 页码: 2430-2448
• 关键词: state-dependent preferences; subjective probabilities; completeness axiom; decision-analysis; utility-theory; INFORMATION; definition

摘要

Incomplete preferences provide the epistemic foundation for models of imprecise subjective probabilities and utilities that are used in robust Bayesian analysis and in theories of bounded rationality. This paper presents a simple axiomatization of incomplete preferences and characterizes the shape of their representing sets of probabilities and utilities. Deletion of the completeness assumption from the axiom system of Anscombe and Aumann yields preferences represented by a convex set of state-dependent expected utilities, of which at least one must be a probability/utility pair. A strengthening of the state-independence axiom is needed to obtain a representation purely in terms of a set of probability/utility pairs.