Monotone additive statistics

TL;DR

This paper characterizes monotone additive statistics, explores their applications in decision-making models, and introduces new preference classes that capture complex risk attitudes and invariance properties.

Contribution

It provides a complete characterization of monotone additive statistics and develops new models of decision-making with diverse risk attitudes and invariance features.

Findings

Complete characterization of monotone additive statistics

Representation of stationary monotone time preferences

Introduction of versatile nonexpected utility preference classes

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.