We consider a policy maker who has to make a choice between distributions of health for a
population of fixed size n≥2. Let hi denote the amount of health of individual i. A health profile
(h1, . . ., hn) specifies the health of each individual in society. Amounts of health are nonnegative
real numbers and, hence, health profiles are elements of IRn
+.4 The policy maker’s preferences
over health profiles are expressed by a preference relation , denoting “at least as preferred
as”. As usual, denotes strict preference and ∼ denotes indifference. The preference ordering
over health profiles does not depend on other variables such as the level of consumption. This
is a consequence of the fact that the purpose of the paper is to characterize common measures
of health inequality and these measures depend only on health and not on other variables. The
restrictiveness of the assumption that we can focus on health alone, which is implicit in these
measures, will become apparent when we discuss the conditions that we introduce next