This paper demonstrates that the property of 'replication invariance', generally considered to be an innocuous requirement for the extension of fixed-population poverty comparisons to variable-population contexts, is incompatible with other plausible variable- and fixed-population axioms. --...

A natural way of viewing an inequality or a poverty measure is in terms of the vector distance between an actual (empirical) distribution of incomes and some appropriately normative distribution (reflecting a perfectly equal distribution of incomes, or a distribution with the smallest mean that...