Variable-population extensions of social aggregation theorems

This paper examines principles for social evaluation under uncertainty in environments with a variable population. In contrast to most of the literature, we employ a model that is formulated in terms of prospects rather than lotteries. Starting from a fixed-population result, a multi-profile variant of Harsanyi’s social aggregation theorem is extended to a variable-population environment. Two nested classes of population principles under uncertainty are characterized. Each is a variable-population extension of ex-ante utilitarianism. The results continue to apply if the probability distribution may vary, as long as probabilities are objectively known or agreed upon by all individuals and society.