We compare distributions of body mass index (BMI) categories among genders in France, the United States, and the United Kingdom on the basis of efficiency and inequality considerations. The new normative criteria that we propose are well suited to the ordinal nature of this variable. Our empirical results, which are supported by robust statistical inference, are twofold. First, BMI categories for the two genders are better distributed in France than in the UK, and in the UK than in the US. Second, BMI categories happen to be more equally distributed among men than among women in all three countries.

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.

This article establishes an equivalence between four incomplete rankings of distributions of income among agents who are vertically differentiated with respect to some nonincome characteristic (health, household size, etc.). The first ranking is the possibility of going from one distribution to the other by a finite sequence of income transfers from richer and more highly ranked agents to poorer and less highly ranked ones. The second ranking is the unanimity among utilitarian planners who assume that agents' marginal utility of income is decreasing with respect to both income and the source of vertical differentiation. The third ranking is the Bourguignon (Journal of Econometrics, 42 (1989), 67-80) Ordered Poverty Gap dominance criterion. The fourth ranking is a new dominance criterion based on cumulative lowest incomes.

We examine the problem of providing a non-rival and excludable public good to individuals with the same preferences and differing contributing capacities. Exclusion from the public good is costly in the sense that if two different quantities of the public good are consumed in the community, then the sum of the costs of providing the two quantities must be borne. By contrast, costless exclusion only requires the cost of the largest quantity consumed of the public good to be financed. We show that despite its important cost, providing public goods in different quantities is often part of any optimal provision of public good when the public authority is imperfectly informed about the agents' contributive capacities. In the specific situation where individuals have an additively separable logarithmic utility function, we provide a complete characterization of the optimal exclusion structure in the two-type case. We also show that the preference for such a costly exclusion is more likely when the heterogeneity in the population or income is large, and when the aversion to utility inequality is important.