Mixing Solutions in Claims Problems

The literature on solutions to claims problems mainly orbits on three canonical rules: The proportional, the Constrained Equal Awards and the Constrained Equal Losses. Mixtures of these solutions have been proposed to design alternative approaches to solve claims problems. We consider piece-wise and convex mixtures as two relevant tools. Piece-wise mixture guarantees that each agent obtains a minimal reimbursement, when it is available, while the remaining is distributed according an alternative distribution criterion. Convex mixture shares the relevance of each distributive criterion according an exogenously given weight. In this framework we explore which properties are preserved by mixed solutions. Alternatively, we propose to design mixed solutions according the compromising degree, an endogenous parameter capturing the relative relevance of the rationing that agents have to share collectively. By using our mixing parameter we obtain that the Proportional rule appears as a piece-wise mixture of the Constrained Equal Awards and the Constrained Equal Losses solutions. The convex mixture of these solutions is explored from a normative point of view.