Equitable opportunities: An axiomatic approach

We propose an axiomatic approach to ranking lists of opportunity sets of the form O = (O-1, ..., O-n) on the basis of fairness. First, we consider two agents each of whom faces a finite set of opportunities. To demonstrate the tractability of our approach, we axiomatically characterize the cardinality difference relation according to which O is more equitable than O' if the difference between the cardinalities of the sets in O is less than the difference in O'. We then generalize the analysis to include an arbitrary number of agents, and we characterize the class of relations that admit of a linear representation. (C) 1996 Academic Press, Inc.