Ranking Income Distributions

Abstract

A large variety of policy questions involve choices between social states and a consequent ordering of the feasible alternatives. When these social states are related to the levels of experienced by individuals or households, two central issues stand out in determining the relative desirability of different social outcomes. One of these is the essentially positive exercise of achieving comparability between households with different characteristics (such as composition or preferences) operating in different environments (for example, facing different price structures). The other concerns the normative judgments implicit in the evaluation of alternative allocations of resourcesthe emphasis placed on inequality between households and the extent to which greater inequality can be compensated by higher average living standards. This paper focuses on the second of these issues, and in doing so we abstract from the problem of household comparability by considering a population of n households, identical in all respects except for their incomes.' The question of ordering social states then becomes one of ranking income distributions over a group of anonymous households or individuals. Borrowing the usual assumptions imposed on consumer preferences, we may suppose that a social ordering of income distributions can be represented by a welfare function2