Monotone Additive Statistics
Xiaosheng Mu, Luciano Pomatto, Philipp Strack, Omer Tamuz
Econometrica · 2024 · Volume 92 · Issue 4
Abstract
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.
Keywords
Statistics, time preferences, stochastic dominance
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