The above observations on the principle of population and the principle of (income-related)
health transfers suggest that it may be desirable to study multivariate concepts of inequality: the
policymaker generally cares not only about the distribution of health, but also about the distribution
of other attributes, e.g. income, educational attainment, etc. To characterize health inequality
measures in such a setting requires that additional assumptions be imposed. In particular,we should
assume that the social decision maker’s preferences over the various attributes are separable in the
attributes. Also, the conditions imposed in Section 3 should be rephrased in a multidimensional
setting, which raises complications for the formulation of the principle of (income-related) health
transfers and additivity. The translation of the other conditions is straightforward. Theoretical
treatments of multidimensional inequality measurement have been provided by Tsui (1995) and
Gajdos and Weymark (2005) but we are not aware of any empirical applications other than the
initial attempt of Atkinson and Bourguignon (1982) to illustrate their dominance conditions for
the comparison of inequality in two dimensions (per capita incomes and life expectancy).