Monotone additive statistics
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 nonexpected utility preferences over gambles which satisfy invariance to background risk as well as betweenness, but are versatile enough to capture mixed risk attitudes.
Cite
@article{arxiv.2102.00618,
title = {Monotone additive statistics},
author = {Xiaosheng Mu and Luciano Pomatto and Philipp Strack and Omer Tamuz},
journal= {arXiv preprint arXiv:2102.00618},
year = {2024}
}
Comments
59 pages, two figures