The geometric adjudication of water rights in international rivers

2026-01-07

AI Summary

This study addresses transboundary water allocation disputes between upstream and downstream riparian states by proposing a class of geometry-based allocation mechanisms. By formalizing the principle of limited territorial sovereignty, the authors develop an operational cascading water transfer model that integrates mechanism design with axiomatic analysis. For the first time, the concept of limited territorial sovereignty is translated into a rigorous mathematical framework, ensuring both fairness and feasibility in water rights allocation. The proposed rules are applied to the Nile River Basin as a case study, demonstrating their effectiveness in mitigating long-standing water conflicts and providing both theoretical grounding and concrete allocation schemes.

Technology Category

• Game Theory and Economic Paradigms: Fair Division
• Multiagent Systems: Mechanism Design
• Constraint Satisfaction and Optimization: Distributed CSP/Optimization

Application Category

• Security and Privacy: Data transparency and provenance
• Responsible Web: Algorithmic accountability and transparency on the web
• Web Mining and Content Analysis: Models for Web evolution

Abstract

We study the adjudication of water rights in international rivers. We characterize allocation rules that formalize focal principles to deal with water disputes in a basic model. Central to our analysis is a family of geometric rules that implement concatenated transfers downstream. They can be seen as formalizing Limited Territorial Sovereignty, as suggested in the Rio Declaration on Environment and Development. We apply our rules to the case of the Nile River, with a long history of disputes between downstream and upstream nations

Problem

• water rights
• international rivers
• allocation rules
• water disputes
• Nile River

Innovation

• geometric rules
• water rights adjudication
• Limited Territorial Sovereignty
• international rivers
• downstream transfers