How to pollute a river if you must

We propose the river pollution claims problem to distribute a pollution budget among agents located along a river. A key distinction with the standard claims problem is that agents are ordered exogenously. For environmental reasons, the location of pollution along the river is an important concern in addition to fairness. We characterize the class of externality-adjusted proportional rules and argue that they strike a balance between fairness and minimizing environmental damage in the river. We also propose two novel axioms that are motivated by the river pollution context and use them to characterize two priority rules.