Abstract: In this paper we study the problem of ranking profiles of opportunity sets, one for each agent in the society. An interesting way of capturing the notion of equality of opportunities is to consider the intersection of all agents’ opportunity sets for each profile, since it coincides with the set of opportunities to which all individuals have access. A family of rankings fulfilling different domain requirements is considered. For any ranking in that family, a way of ranking individual sets emerges. We propose three ways of ranking opportunity profiles, all of them looking first at the common opportunity set. If this is not decisive, additional criteria are used in a lexicographic way. We provide axiomatic characterizations for each of these methods.