How to pollute a river if you must

We propose the river pollution claims problem to distribute a budget of emissions permits among agents located along a river. A key distinction from the standard claims problem is that agents are ordered exogenously. For environmental reasons, the specific location along the river where pollutants are emitted is an important concern. In our analysis, we combine this environmental concern with standard fairness considerations. We characterize the class of externality-adjusted proportional rules and show 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. We illustrate the rules through a case study of the Tuojiang Basin in China.