We study ordered claims problems in which availability of a resource changes across locations according to a stationary linear transition. Our motivating example is sharing water along a river when water is lost on the way due to evaporation and infiltration. In such environments, allocations assigned to agents at different positions have different implications for feasibility. We characterise a class of geometric allocation rules in which claims are weighted by a constant multiplicative factor along the ordering and then scaled to the feasibility boundary. The main result provides an axiomatic foundation for this class. We then apply the geometric allocation rules to two environmental applications. In river water allocation with conveyance losses, the rule yields a compromise between reducing water loss and equal treatment. In pollution allocation with decay and a downstream cap, the same logic implies an allocation with geometric weighing of claims to emission rights.
This will be a hybrid seminar. If you are interested in joining this seminar, please send an email to the secretariat of ASF at asf-feb@uva.nl.