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On the fair abatement of riparian pollution

Ricardo Martinez, Juan D. Moreno-Ternero

Abstract

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 compromise between fairness and environmental concerns. Our class is an alternative to the one proposed 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.

On the fair abatement of riparian pollution

Abstract

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 compromise between fairness and environmental concerns. Our class is an alternative to the one proposed 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.
Paper Structure (7 sections, 5 theorems, 25 equations, 2 figures, 4 tables)

This paper contains 7 sections, 5 theorems, 25 equations, 2 figures, 4 tables.

Table of Contents

  1. Introduction
  2. The model
  3. Axioms and characterizations
  4. Case study
  5. Further insights
  6. Discussion
  7. Appendix B. Excerpts from the Water Pollution Prevention and Control Law of the People's Republic of China (Amended in 2017)

Key Result

Lemma 1

Let $\varphi$ and $\varphi'$ be two rules that satisfy budget additivity. If, for each $(c,E)\in \mathcal{R}$, $\varphi(c,E)=\varphi'(c,E)$, then it follows that for each $(c,E)\in \mathcal{D}$, $\varphi(c,E)=\varphi'(c,E)$.

Figures (2)

  • Figure 1: Paths of awards for geometric rules when $\gamma$ varies from $0$ to $1$.
  • Figure 2: Examples of basin structures: (a) line; (b) hierarchy; (c) boundary river.

Theorems & Definitions (7)

  • Remark 1
  • Example 1
  • Lemma 1
  • Theorem 1
  • Theorem 2
  • Theorem 3
  • Theorem 4