Generalized Probabilistic Egalitarianism

For over 60 years, Lerner's (1944) probabilistic approach to the welfare evaluation of income distributions has aroused controversy. Lerner's famous theorem is that, under ignorance regarding who has which utility function, the optimal distribution of income is completely equal. However, Lerner's probabilistic approach can only be applied to compare distributions with equal means when the number of possible utility functions equals the number of individuals in the population. Lerner's most controversial assumption that each assignment of utility functions to individuals is equally likely. This paper generalizes Lerner's probabilistic approach to the welfare analysis of income distributions by weakening the restrictions of utilitarian welfare, equal means, equal numbers, and equal probabilities and a homogeneous population. We show there is a tradeoff between invariance (measurability and comparability) and the information about the assignment of utility functions to individuals required to evaluate expected social welfare.