To formalize the principle of income-related health transfers, let Kid be the set of health profiles
such that the numbering of the individuals corresponds to their rank in terms of socioeconomic
status: h1 is the health of the individual with the highest socioeconomic status, hi is the health of
the individual who has rank i in terms of socioeconomic status and hn is the health of the individual
with the worst socioeconomic status. That is, Kid = {h: R1 < . . . < Rn}. The principle of incomerelated
health transfers holds if for all h ∈Kid, for all i < j and for all α>0, h + (−α)iαj0 ∈Kid
implies h + (−α)iαj0h. The requirement that h + (−α)iαj0 ∈Kid reflects that the health transfer
should not affect the rank ordering of the individuals in terms of socioeconomic status