In this paper we study the problem of ranking profiles of opportunity
sets, one for each agent in the society. An interesting way of capturi
ng the notion of equality of opportunities is to consider the intersec
tion of all agents' opportunity sets for each profile, since it coinci
des with the set of opportunities to which all individuals have access
. A family of rankings fulfilling different domain requirements is con
sidered, For any ranking in that family, a way of ranking individual s
ets emerges. We propose three ways of ranking opportunity profiles, al
l of them looking first at the common opportunity set. If this is not
decisive, additional criteria are used in a lexicographic way. We prov
ide axiomatic characterizations for each of these methods. (C) 1998 El
sevier Science B.V.