We consider the problem of adjudicating conflicting claims in the context of a variable population. A property of rules is "lifted" if whenever a rule satisfies it in the two-claimant case, and the rule is bilaterally consistent, it satisfies it for any number of claimants. We identify a number...

It is well known that on the domain of convex games, the Dutta-Ray solution satisfies many desirable properties such as population-monotonicity, max consistency, converse max consistency, and conditional self-consistency. In this paper, we define a family of possibly non-symmetric and...

We investigate the existence of consistent rules for the resolution of conflicting claims that generalize the Talmud rule but do not necessarily satisfy equal treatment of equal. The first approach we follow starts from the description of the Talmud rule in the two-claimant case as...

The Dutta-Ray solution and the Shapley value are two well-known examples of population-monotonic solutions on the domain of convex games. We provide a new formula for the Dutta-Ray solution from which population-monotonicity immediately follows. Then we define a new family of...

We show that the nucleolus is not aggregate-monotonic on the domain of convex games, and that this lack of monotonicity holds even if there are as few as four agents.