Evaluating Education Systems

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This paper proposes two dominance criteria for evaluating education systems describedas joint distributions of the pupils’ cognitive skill achievements and family backgrounds. Thefirst criterion is shown to be the smallest transitive ranking of education systems compatiblewith three elementary principles. The first principle requires any improvement in the cognitiveskill of a child with a given family background to be recorded favorably. The secondprinciple demands that any child’s cognitive skill be all the more favorably appraised as thechild is coming from an unfavorable background. The third principle states that when twodifferent skills and family backgrounds are allocated between two children, it is preferablethat the high skill be given to the low background child than the other way around. Thecriterion considers system A to be better than system B when, for every pair of referencebackground and skill, the fraction of children with both a lower background and a betterskill than the reference is larger in A than in B. Our second criterion completes the first byadding to the three principles the elitist requirement that a mean-preserving spread in theskills of two children with the same background be recorded favorably. We apply our criteriato the ranking of education systems of 43 countries, taking the PISA score in mathematicsas the measure of cognitive skills and the largest of the two parents International Socio EconomicIndex as the indicator of background. We show that, albeit incomplete, our criteriaenables conclusive comparisons of about 19% of all the possible pairs of countries. Educationsystems of fast-growing Asian economies - in particular Vietnam - appear at the topof our rankings while those of relatively wealthy Arabic countries such as Lebanon, UnitedArab Emirates and Jordan are at the bottom. The fraction of countries that can be rankedsuccessfully happens to be only mildly increased as a result of adding elitism to the threeother principles.