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The literature on inequality measurement has been largely concerned with single-dimensioned indicators. This paper explores some of the issues which arise when there are several dimensions to inequality, and these are not readily reduced to a single index, concentrating particularly on the two-dimensioned case. We make use of results on multi-variate stochastic dominance in portfolio theory, extending these and applying them to the measurement of inequality. The use of the dominance conditions is illustrated by an application to the international distribution of income and life expectancy.
Atkinson et al. (Thu,) studied this question.