Mixing solutions for claims problems

The literature on solutions for 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 to an alternative distribution criterion. Convex mixture shares the relevance of each distributive criterion according to an exogenously given weight. In this framework we explore which properties are preserved by mixed solutions. Moreover, we propose to design mixed solutions according to the compromising degree, an endogenous parameter capturing the relative relevance of the rationing that agents have to share collectively. We characterize the Proportional solution as the piece-wise mixture of any two solutions. The convex mixture of the Constrained Equal Awards and the Constrained Equal Losses solutions is explored from a normative point of view.