Uncertainty and critical-level population principles

This paper analyzes variable-population social-evaluation principles in a framework where outcomes are uncertain, We provide characterizations of expected-utility versions of critical-level generalized utilitarian rules, These principles evaluate lotteries over possible states of the world on the basis of the sum of the expected values of differences between transformed utility levels and a transformed critical level, conditional on the agents' being alive in the states under consideration. Equivalently, the critical-level utilitarian value functions applied to weighted individual expected utilities can be employed, Weights are determined by the anonymity axiom.