“…A widely accepted conception of equality of opportunity is about the implementation of a meritocracy: only merits matter (see, for example, Lucas, 1995). A second conception, which has been developed over the last decade (see, among others, Roemer, 1993, 1998, Van de Gaer, 1993, Fleurbaey, 1995, Roemer et al, 2003, RuizCastillo, 2003, Peragine, 2002, Lefranc et al, 2006aand 2006b, MorenoTernero, 2007, Ooghe et al, 2007, Fleurbaey and Maniquet, 2007, and Rodríguez, 2009 We focus in the second approach but first we provide some notation and definitions.…”