Multidimensional inequality with variable population size

Summary. We study inequality in a context of more than one variable by extending a celebrated result of Hardy, Littlewood and Pölya (1934) to the case of distributions with variable population sizes, whose individuals differ in many characteristics besides income. A new ordering between rectangular matrices, representing such distributions, is provided and characterized by convexity theory.Received: 19 October 2003, Revised: 7 September 2004, JEL Classification Numbers: D31, D63, I31.I am indebted to C. d’Aspremont, V. Dardanoni, G. Koshevoy, K. Mosler and especially J. Weymark and an anonymous referee for many useful comments.