On opportunity inequality measurement

I study the problem of ranking distributions of opportunity sets on the basis of equality. The analysis begins by developing alternative ways of formulating the notion ofequalizing transfersin the context of opportunity distributions. It is readily observed that any such formulation must rely on agents' preferences over individual opportunity sets, and therefore, a theory of opportunity inequality measurement must be conditional upon the "social" opportunity set ranking one postulates. Unfortunately, the results make it clear that such a theory can be constructed only when one uses the cardinality ordering of Pattanaik and Xu (1990). More precisely put, I show that it is essentially impossible to extend Dalton's transfer principle to the context of opportunity distributions unless one is content with ranking the opportunity setsonlyon the basis of their cardinalities.Journal of Economic LiteratureClassification Numbers: D31, D63, D71.