The ratio between the equally distributed income and the mean income yields Atkinson’s (1970) and Kolm’s (1969) measure of inequality. If equally distributed income is close to mean income, little can be gained by redistributing income equally (low aversion to inequality). Conversely, if equally distributed income is much smaller than mean income, larger welfare gains can be reaped from a more equal distribution. Hence adopting a social welfare function allows considering various normative options on distribution.