This paper analyses the question of how to redistribute individual inc
omes if those incomes are determined by the agents' characteristics. I
t is assumed that some of these characteristics are to be considered '
relevant', whereas others should be 'irrelevant'. A redistribution mec
hanism assigns a post-tax income distribution to each characteristics
profile. The objective is to eliminate the influence of irrelevant cha
racteristics while preserving the contributions of relevant characteri
stics to the individual pre-tax incomes. An axiomatic approach is used
to provide characterizations of a specific redistribution mechanism.
Furthermore, it is shown that the income function (the function linkin
g pre-tax incomes to characteristics) must have a separability propert
y if some plausible conditions are imposed on a redistribution mechani
sm.