Theorem 5 shows that under the single-series CI model the principle of population implies
Wagstaff’s (2002) achievement index, which is, in fact, the abbreviated social welfare function
underlying the extended concentration index. As noted in Section 2, the parameter ν captures
distributional concerns; the higher ν, the more sensitive the policy maker is to the distribution
of health. If we replace the principle of health transfers (the principle of income-related health
transfers) in the single-series Gini model (single-series CI model) by the Gini condition (CI
condition) then we obtain a preference foundation for the Gini index (concentration index) for
variable population size