We study statistics: mappings from distributions to real numbers. We characterize all statistics that are monotone with respect to first-order stochastic dominance, and additive for sums of independent random variables. We  explore a number of applications , including a representation of stationary, monotone time preferences, generalizing Fishburn and Rubinstein (1982) to time lotteries  .
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 , as well as a characterization of risk-averse preferences over monetary gambles that are invariant to mean-zero background risks .
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We study statistics: mappings from distributions to real numbers. We characterize all statistics that are
The expectation is an example of a descriptive statistic that is
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first-order
A
provide a complete characterization of such statistics, and
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, including
to models of individual and group decision-making. These include
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generalizing
extending the work of
A
, as well as a characterization of risk-averse preferences over monetary gambles that are invariant to mean-zero background risks