Information and the dispersion of posterior expectations

• 成果类型: Article
• 署名作者: Brandt, Nikolai; Drees, Burkhard; Eckwert, Bernhard; Vardy, Felix
• 署名单位: University of Bielefeld; International Monetary Fund
• 刊物名称: JOURNAL OF ECONOMIC THEORY
• ISSN/ISSBN: 0022-0531
• DOI: 10.1016/j.jet.2014.10.004
• 发表日期: 2014
• 页码: 604-611
• 关键词: information; Dispersion orderings; Decision making under uncertainty

摘要

We explore the intuitive idea that more information leads to greater dispersion of posterior beliefs about the expected state of the world. First, we show that two dispersion orders that have been widely used as informativeness criteria do not satisfy the desirable property of ordinality of states (OS), i.e., invariance to increasing monotone state transformations. Then, for the class of monotone information systems, we characterize the weakest information criteria that respect OS and imply the dispersion orders. Our characterizations consist of intuitive conditions on the joint distributions of signals and states. Because of OS, the information criteria induce the dispersion orders not only on the posterior expectations of states, but also of state utilities, under any strictly increasing vNM utility function. (c) 2014 Elsevier Inc. All rights reserved.