Prioritizing the 'worse off' under attainability constraints: An indeterminacy problem for distributive fairness

Numerous theories of distributive fairness promote the idea that we ought to give extra weight to benefits to the worse off and can thereby be seen as promoting gap closures. This paper underlines the relevance of making a distinction between attainable and ideal target levels for individuals in populations affected by distributive fairness and show that in cases of scarce resources, theories that promote aggregate gap closures and prioritization of the worse off can in view of this distinction be interpreted in three mutually inconsistent ways.