Self-dual solutions to claims problems with ex-ante conditions

Abstract

A claims problem involves the distribution of a divisible and scarce resource within a group of individuals with a specific right over this endowment. In the classic model, the final allocation of the estate among the agents is based on a single criterion: their own claims. However, what happens when the initial conditions of the individuals are not equal?. To answer this, we provide an extension of two of the most well-known rules: the proportional rule and the Talmudic rule. These extensions include new relevant information that characterizes the claimants and impacts the final distribution. We provide a formal definition for these generalized rules, check the properties that each of these satisfies, and give a respective characterization to each of them. Finally, we propose an empirical approach for the analysis of this kind of problems, and the perceptions from the agents among them, with and without ex-ante conditions. From this, we found a significant preference among the proportional rule in situations with ex-ante conditions. While for the cases with ex-ate conditions the perceptions tend to vary depending on the role played by the agent.