This paper proposes two dominance criteria for evaluating education systems described as joint distributions of the pupils' cognitive skill achievements and family backgrounds. The first criterion is the smallest transitive ranking of education systems compatible with three elementary principles. The first principle requires the favorable recording of any improvement in the cognitive skill of a child with a given family background . The second principle demands that any child's cognitive skill be all the more favourably appraised as the child is coming from an unfavourable background. The third principle states that when two different skills and family backgrounds are allocated between two children, it is preferable that the high skill be given to the low background child than the other way around. Our second criterion adds to the three principles the elitist requirement that a mean-preserving spread in the skills of two children with the same background be recorded favorably. We apply our criteria to the ranking of education systems of 43 countries, where we measure cognitive skills by PISA score in mathematics and famly background by the largest of the two parents'International Socio Economic Index. Our criteria conclusively compare about 19% of all the possible pairs of countries.