We can derive the Atkinson inequality index by assuming a consumer withpreferences in the face of the Von Neumann-Morgenstern type risk that is placed behind theveil of ignorance and asked to estimate distributions of income. Since heis behind the veil of ignorance, this consumer does not know what income he will get inthe distribution. It therefore evaluates an income distribution having a density fY (y) by maximizing its expected utility. Suppose that the welfare index SW(fY ) is the valueof this distribution of income:

Umax u(y) fy (y) dy.1-E u(y) - E