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Monotone Additive Statistics

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  • Xiaosheng Mu
  • Luciano Pomatto
  • Philipp Strack
  • Omer Tamuz

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.

Suggested Citation

  • Xiaosheng Mu & Luciano Pomatto & Philipp Strack & Omer Tamuz, 2024. "Monotone Additive Statistics," Econometrica, Econometric Society, vol. 92(4), pages 995-1031, July.
    • Handle: RePEc:wly:emetrp:v:92:y:2024:i:4:p:995-1031
    DOI: 10.3982/ECTA19967
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