Equality of opportunities: cardinality-based criteria

Abstract

In this paper we study possible rankings of opportunity profiles. An opportunity profile is a list of sets of alternative opportunities, one set for each agent in the society. We compare such opportunity profiles on the basis of the notion of “equality of opportunities”. Our main results show the necessary and sufficient conditions for this comparison to be made using exclusively the information provided by two cardinal measures: the number of common alternatives for all sets in a given profile and/or the difference between the number of alternatives of individual sets. We also show that, under given circumstances, the only way to solve conflicts between these two numbers is to combine them in a lexicographic procedure.