Lower bounds and recursive methods for the problem of adjudicating conflicting claims

For the problem of adjudicating conflicting claims, we propose the following method to extend a lower bound rule: (i) for each problem, assign the amounts recommended by the lower bound rule and revise the problem accordingly; (ii) assign the amounts recommended by the lower bound rule to the revised problem. The “recursive-extension” of a lower bound rule is obtained by recursive application of this procedure. We show that if a lower bound rule satisfies positivity then it’s recursive extension singles out a unique awards rule.We then study the relation between desirable properties satisfied by a lower bound rule and properties satisfied by its recursive extension. Copyright Springer-Verlag 2013