On the fair abatement of riparian pollution

We study the design of fair allocation rules for the abatement of riparian pollution. To do so, we consider the so-called river pollution claims model, recently introduced by Yang et al. (2025) to distribute a budget of emissions permits among agents (cities, provinces, or countries) located along a river. In such a model, each agent has a claim reflecting population, emission history, and business-as-usual emissions, and the issue is to allocate among them a budget that is lower (or equal) than the aggregate claim. For environmental reasons, the specific location along the river where pollutants are emitted is an important concern (the more upstream the location is the higher the damage of polluting the river). We characterize a class of geometric rules that adjust proportional allocations to account for externalities, thus compromising between fairness and environmental concerns. Our class is an alternative to the one studied by Yang et al. (2025). We compare both alternatives through an axiomatic study, as well as an illustration for the case study of the Tuojiang Basin in China.