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This paper proposes two dominance criteria for evaluating education
systems, based on the joint distributions of the pupils cognitive skill
achievements and their family backgrounds. The first criterion is shown to be
the smallest transitive ranking of education systems compatible with three
elementary principles. The first principle considers that any improvement
in the cognitive skill of a child with a given family background is
good. The second principle requires any child's cognitive skill to be all
the more favorably appraised as the child is coming from an unfavorable
background. The third principle asserts that, for any two levels of skill
and background, it is preferable that the high skill be given to the child
with the low background than the other way around. The criterion considers
that system A is better than system B if, for any pair of reference
background and skill, the fraction of children with both a a lower background
and a better skill than the reference is larger in A than in B. Our
second criterion completes the first one by adding to these 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 criterian to the ranking of education systems of 43 countries, taking
the PISA score in mathematics as the measure of cognitive skills and
the largest of the two parents International Socio Economic Index as the
indicator of background. We show that, albeit incomplete, our criteria enables
the comparisons of quite a few educatio systems. Education systems
of fast growing asian economies - and in particular Vietnam - appear at
the top of our rankings while those of wealthy arabic countries such as
Arab Emirates are at the bottom. The fraction of the countries that can
be ranked successfully increases substantially as a result of adding elitism
to to the three other principles.
