We exploit the similarity between the problem of risk adjustment with prospective reimbursement schemes in the health care sector and the problem of fair compensation analysed in the social choice literature. The starting point is the distinction between two sets of variables in the explanation of medical expenditures: those for which the insurers (or the providers) can be held responsible, and those for which they have to be compensated. Using this partitioning the objectives of cost-efficiency and no risk selection can be expressed in terms of two simple axioms. If the medical expenditure function is additively separable in the two sets of variables, there exists a natural division rule which is analogous to the standard linear risk adjustment schemes. We show how this rule should be applied if the total level of actual medical expenditures is different from the budget to be divided over the insurers (or providers) and how information from the disturbances in the regression equation can be used in an optimal way. We discuss the analogy with mixed reimbursement systems. If the medical expenditure function is not additively separable in the two sets of variables, the conflict between efficiency and risk selection is unavoidable, even if one has perfect information about that function. The theoretical results are illustrated with empirical results derived from the Belgian setting where the move towards prospective reimbursement of the mutualities has necessitated the introduction of a risk adjustment formula.