Monotone Additive Statistics

• 成果类型: Article
• 署名作者: Mu, Xiaosheng; Pomatto, Luciano; Strack, Philipp; Tamuz, Omer
• 署名单位: Princeton University; California Institute of Technology; Yale University
• 刊物名称: ECONOMETRICA
• ISSN/ISSBN: 0012-9682
• DOI: 10.3982/ECTA19967
• 发表日期: 2024
• 页码: 995-1031
• 关键词: collective dynamic choice; DESCRIPTIVE STATISTICS; nonparametric models; time; RISK; INDEPENDENCE; aggregation; preferences; dominance; ambiguity

摘要

The expectation is an example of a descriptive statistic that is monotone with respect to stochastic dominance, and additive for sums of independent random variables. We provide a complete characterization of such statistics, and explore a number of applications to models of individual and group decision-making. These include a representation of stationary monotone time preferences, extending the work of Fishburn and Rubinstein (1982) to time lotteries. This extension offers a new perspective on risk attitudes toward time, as well as on the aggregation of multiple discount factors. We also offer a novel class of non-expected utility preferences over gambles which satisfy invariance to background risk as well as betweenness, but are versatile enough to capture mixed risk attitudes.