 The first development is related to the application of theories of equality of opportunity, and involves the construction of mixed social welfare functions which combine utilitarianism and maximin. Suppose that there is a double partition of the population, such that one would like the social welfare function to display infinite inequality aversion within subgroups of the first partition, and zero inequality aversion within subgroups of the second partition. For instance, subgroups of the first partition consist of equally deserving individuals, for which one would like to obtain equality of outcomes, whereas subgroups of the second partition consist of individuals who have equal opportunities, so that inequalities among them do not matter. Van de gaer (1993) proposes to apply average utilitarianism within each subgroup of the second partition, and to apply the maximin criterion to the vector of average utilities obtained in this way. In other words, the average utilities measure the value of the opportunity sets offered to individuals, and one applies the maximin criterion to such values, in order to equalize the value of opportunity sets. Roemer (1998) proposes to apply the maximin criterion within each subgroup of the first partition, and then to apply average utilitarianism to the vector of minimum utilities obtained in this way. In other words, one tries to equalize outcomes for equally deserving individuals first, and then applies a utilitarian calculus. These may not be the only possible combinations of utilitarianism and maximin, but they are given an axiomatic justification which suggests that they are indeed salient, in Ooghe, Schokkaert and Van de gaer (2007) and Fleurbaey (2008). For a survey on the applications of Roemer’s criterion, see Roemer (2002b) and, more recently, Ferreira and Peragine (2016), Roemer and Trannoy (2016), Ramos and Van de gaer (2016).