Nash welfarism and the distributive implications of informational constraints

We study two informational simplicity conditions for aggregating von Neumann–Morgenstern preferences. When the best relevant alternative for each individual cannot be ascertained with confidence (as when allocating an uncertain endowment of goods), Independence of Harmless Expansions requires that the social ranking of lotteries be unaffected by the addition of any alternative that every agent deems at least as good as the one she originally found worst. This axiom, along with the Weak Pareto Principle and Anonymity, characterizes bottom-calibrated Nash welfarism: utilities are calibrated so that the worst alternative is worth zero and lotteries are ranked according to the product of such bottom-calibrated utilities. When the worst relevant alternatives are difficult to identify, replacing Independence of Harmless Expansions by the dual axiom of Independence of Useless Expansions yields a characterization of top-calibrated Nash welfarism: lotteries are ranked according to the opposite of the product of the absolute values of top-calibrated utilities. The distributive implications of our two informational simplicity axioms are thus drastically different: while bottom-calibrated Nash welfarism recommends randomizing between two alternatives that it deems equally good, top-calibrated Nash welfarism is randomization-averse.