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This paper examines a robust operational denition of "opportunity equalization"
for skills acquisition among children of dierent family background. The criteria
allow to compare societies are described as collections of distributions of outcome
(lotteries), one such distribution for every family background type. Societies are
confronted from the view point of a philosopher placed behind a veil of ignorance
with respect to the type he/she sould have in this society. Under established axioms
of choice under ambiguity, we show that the preferences of this philosopher involve
comparison of the expectation of some concave function of the expectations of the
consequences of skills lotteries on children well-being. We provide an empirical
criterion for comparing societies that coincide with the unanimity of all rankings that
would command agreement among these philosophers when they exhibit aversion to
inequality of opportunity. This last result is used to assess the evolution of inequality
of opportunity for skills acquisition across PISA countries, decomposing inequalities
developed early in life from the contribution of the education systems.
