Note that the Gini condition is stronger than the principle of health transfers. The Gini condition
implies the principle of health transfers given the other conditions in Theorem 1. The principle of
health transfers, however, does not imply the Gini condition: the principle of health transfers does
not imply the indifference h + (−(2j−1)α)1αj0∼h. It only says that h + (−α)1αj0)h whenever
h and h + (−α)1αj0 both belong to K. Hence, the Gini condition can be interpreted as a stronger
or more restrictive version of the principle of health transfers.
To summarize,