Wary of the worst: Maximizing award guarantees when new claimants may arrive

When rationing a resource or adjudicating conflicting claims, the arrival of new agents necessitates revision. Adopting a worst-case perspective, we introduce guarantee structures to measure the protection a rule provides to either individuals or groups in these circumstances. With the goal of maximizing guarantees for those in the original group, we characterize the constrained equal awards rule. Requiring that a rule provide protection for both the original and arriving agents, so that both gains and losses are shared, we characterize the Talmud rule.