Fair Division With Uncertain Needs and Tastes

This article examines the extent to which utilitarian social welfare maximization results in an egalitarian outcome for the classic n-agent cake-cutting problem when the agents are characterized by heterogenous subsistence needs as well as by heterogeneous tastes. It is shown that utilitarian social welfare maximization results in surplus-egalitarianism---i.e., first meeting needs, then equally dividing the remaining cake---when tastes are uncertain but needs are known, can be met, and are required to be met by prior restriction. If the meeting of needs is not imposed as a lexicographically prior principal of fairness, however, then---due to the fundamental non-concavity of individual agent utility functions resulting from the introduction of subsistence needs---utilitarian social welfare maximization requires that agents with high subsistence needs be allowed to die with zero shares as a matter of general policy. Moreover, when needs and tastes are both uncertain, an egalitarian allocation only results if the meaning of subsistence needs is suitably weakened to a poverty line definition. Annotated pointers to related work can be accessed here: http://www2.econ.iastate.edu/tesfatsi/dehome.htm