We discuss a method of ranking allocations in economic environments which applies when we do not know the names or preferences of individual agents. We require that two allocations can be ranked with the knowledge only of agents present, their aggregate bundles, and community indifference sets—a condition we refer to as aggregate independence. We also postulate a basic Pareto and continuity property, and a property stating that when two disjoint economies and allocations are put together, the ranking in the large economy should be consistent with the rankings in the two smaller economies (reinforcement). We show that a ranking method satisfies these axioms if and only if there is a probability measure over the strictly positive prices for which the rule ranks allocations on the basis of the random-price money-metric utilitarian rule. This is a rule which computes the money-metric utility for each agent at each price, sums these, and then takes an expectation according to the probability measure
© Springer-Verlag 2011. Received: 4 May 2010 / Accepted: 23 April 2011 / Published online: 8 June 2011. We are grateful to David Donaldson, Federico Echenique, François Maniquet, and John Weymark for useful comments. We are especially indebted to Marc Fleurbaey for many detailed comments and suggestions. Finally, we are extremely grateful to two anonymous referees and the associate editor, whose detailed comments and careful reading greatly improved the manuscript. All errors are our own. Formerly SSWP 1295.