Monotone Additive Statistics

doi:10.3982/ECTA19967

Monotone Additive Statistics

2024-01-01

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DOI：10.3982/ECTA19967

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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

Monotone Additive Statistics

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