Rights on what is left

Allocating property rights on an open access resource which has been freely exploited in the past is often very problematic. Involved agents typically rely on one of two competing principles to determine future allocation. The first priority principle, "first in time, first in rights" favors the status quo while the other one, "historical accountability", is a corrective justice argument. We construct a simple model inspired by the claims problem literature to show that these two positions are in fact compatible: they define bounds to the set of possible allocations. We detail a family of methods which meets these bounds and characterize the two extreme points of this family: the equal sharing and the uniform gains methods.