When economists talk about equality, they typically have equality of outcomes, like welfare or income in mind. However such a view of equality is not entirely satisfactory and theories of equality of opportunity have been developed and proposed as an alternative. While there has been some theoretical discussion of equality of opportunity in the public choice literature, the empirical implementation of many of these issues has been limited. In this paper we develop a nonparametric estimator of the opportunity sets facing individuals with different characteristics. This estimator allows us to visualise the choices available to individuals of different types. We then use this estimator to reexamine the intergenerational transmission process. Our estimates indicate that even for children who exhibit the same degree of responsibility, those from richer families earn substantially more than those from poorer families.