The average-of-awards rule for claims problems

Abstract

Given a claims problem, the average-of-awards rule ($${\text {AA}}$$ AA ) selects the expected value of the uniform distribution over the set of awards vectors. The $${\text {AA}}$$ AA rule is the center of gravity of the core of the coalitional game associated with a claims problem, so it corresponds to the core-center. We show that this rule satisfies a good number of properties so as to be included in the inventory of division rules. We also provide several representations of the $${\text {AA}}$$ AA rule and a procedure to compute it in terms of the parameters that define the problem.

Refining the Lorenz‐ranking of rules for claims problems on restricted domains

“…The formal definitions are given in Appendix A. Table 1, adapted from Thomson (2019) and Mirás Calvo et al (2022b), summarizes which of the above properties are satisfied by these rules. A check mark, $$\text{}\checkmark \text{}$$, in a cell means that the property in the row is satisfied by the rule indexing the column.…”

“…The set of all the allocations that meet these basic properties is the set of awards vectors for the claims problem. The average‐of‐awards rule, introduced by Mirás Calvo et al (2022b), selects for each claims problem the expected value of the (continuous) uniform distribution over its set of awards vectors. O'Neill (1982) associates to each claims problem a coalitional game whose core is the set of awards vectors of the problem.…”