The present paper is a selective overview, very considerably based on work in which the author himself has been involved, of the difficulties which can arise in the measurement of poverty and inequality when one compares populations of differing size. The paper begins with certain problems attending the measurement of poverty when the overall population size is fixed but the numbers of the poor are permitted to vary: one discovers a certain commonality of outcomes between Derek Parfit's quest for a satisfactory theory of wellbeing and the economist's quest for a satisfactory measure of poverty. Complications arising from both the poverty and inequality rankings of distributions when the aggregate size of the population is allowed to vary are also investigated. It is suggested in the paper that, from the perspectives of both logical consistency and ethical appeal, there are problems involved in variable population comparisons of poverty and inequality which deserve to be taken note of and enquired into.
poverty inequality total principle average principle fixed population axioms variable population axioms impossibility theorems