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.
Building on Pomatto, Strack, and Tamuz (2020), we identify a tight condition for when background risk can induce first-order stochastic dominance. Using this condition, we show that under plausible levels of background risk, no theory of choice under risk can simultaneously satisfy the following three economic postulates: (i) decision-makers are risk averse over small gambles, (ii) their preferences respect stochastic dominance, and (iii) they account for background risk. This impossibility result applies to expected utility theory, prospect theory, rank-dependent utility, and many other models.
We develop an axiomatic theory of information acquisition that captures the idea of constant marginal costs in information production: the cost of generating two independent signals is the sum of their costs, and generating a signal with probability half costs half its original cost. Together with Blackwell monotonicity and a continuity condition, these axioms determine the cost of a signal up to a vector of parameters. These parameters have a clear economic interpretation and determine the difficulty of distinguishing states.