How much total income would you throw away to make what’s left perfectly equal? That fraction is the Atkinson index — inequality measured as the society’s own aversion to it. Slide (or tap) to level the distribution and watch the ‘equally-distributed equivalent’ income rise to the mean and the index fall to zero.
The Atkinson index, computed live at inequality-aversion ε=0.5: the equally-distributed-equivalent income is EDE = (mean of xᵢ^(1−ε))^(1/(1−ε)), and A = 1 − EDE/mean. EDE is the equal income that a society with aversion ε would accept in place of the unequal one; the gap to the mean is the deadweight of the inequality, so A is the fraction of total income that could be ‘wasted’ to buy perfect equality without loss of welfare. A=0 is equality (EDE=mean); a fail-loud self-check throws unless A≈0 at full equality and A>0 for the unequal base.
ε=0.5 is one choice of aversion (higher ε weights the poor more; Atkinson is a family, not one number), and the 10-person base is illustrative. The EDE and A arithmetic at the stated ε is exact.