To obtain (10), i.e. the social welfare function underlying the Gini index, we replace the
principle of health transfers by the following condition: for all h ∈K, for all j, and for all α>0,
h + (−(2j−1)α)1αj0 ∈K implies h + (−(2j−1)α)1αj0∼h. We will refer to this condition as the
Gini condition. In the definition of the Gini condition the subscript 1 refers to the individual
who is best-off in terms of health. The Gini condition specifies the trade-off in units of health
between the best-off individual and any other individual that leaves the policy maker indifferent.
The requirement that h + (−(2j−1)α)1αj0 ∈K reflects that the health transfer should not change
the rank ordering of the individuals in terms of health. The Gini condition implies for example
that h = (0.8,0.4)∼(0.5,0.5). In this example α = 0.1
To obtain (10), i.e. the social welfare function underlying the Gini index, we replace theprinciple of health transfers by the following condition: for all h ∈K, for all j, and for all α>0,h + (−(2j−1)α)1αj0 ∈K implies h + (−(2j−1)α)1αj0∼h. We will refer to this condition as theGini condition. In the definition of the Gini condition the subscript 1 refers to the individualwho is best-off in terms of health. The Gini condition specifies the trade-off in units of healthbetween the best-off individual and any other individual that leaves the policy maker indifferent.The requirement that h + (−(2j−1)α)1αj0 ∈K reflects that the health transfer should not changethe rank ordering of the individuals in terms of health. The Gini condition implies for examplethat h = (0.8,0.4)∼(0.5,0.5). In this example α = 0.1
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