Measuring the progress of equality of educational opportunity in absence of cardinal comparability

There are many situations in which measures of the full diversity of a collection of distributions is necessary and where simple comparisons of limited numbers of distributional moments are inadequate since they cast a veil of ignorance over the full extent of distributional differences. An example is the equality of opportunity imperative which demands equal chances for diverse circumstance groups. It requires comparison of distributional differences over the full range of their variation since only then can complete equality of chances be guaranteed. Here new techniques in the form of Gini-like coefficients for quantifying multilateral distributional differences in absence of cardinal comparability are introduced and employed to study changes in the German educational system in the first decade of this century.