On fair allocations and monetary compensations

In this paper we study fair division problems with the special feature that there exists only one transferable good that everyone likes. This good will be used to compensate some individuals for their differences in other non-transferable resources (like talents or handicaps). In this context we test the traditional no-envy solution and we verify that: 1) its ethical content can be a matter of discussion, and 2) frequently it does not select a non-empty set of allocations. We propose an extension of this criterion that partially solves the existence problem while also retaining the main ethical properties of the preceding solution.