A discussion of the consistency axiom in cost-allocation problems

The recent literature on cost allocation lacks consensus on what is an appropriate definition of the consistency axiom. We take this as evidence that a careful reexamination is necessary. The starting point of our critique is the widely adopted definition proposed in Moulin and Shenker (1994), which we show to be conceptually flawed. Rectifying this flaw leads to a definition of consistency which already appeared in the recent literature though without satisfactory conceptual justification. We offer a classification of the existing definitions of the consistency axiom by relating them to the definitions of consistency in cooperative games suggested in Davis and Maschler (1965) and Hart and Mas-Colell (1989). We argue that only the latter leads to a meaningful interpretation of consistency when production externalities are present.