Distributive Justice in Multi-Objective Optimization: A Priori vs. A Posteriori Approaches in Eastern Nile Basin Management

Addressing global water scarcity requires effective, sustainable water resource management. However, water resources management problems are complex challenges with multiple, often contradicting, objectives. Moreover, increasingly, questions are raised regarding the fair allocation of scarce water resources. In this study, we use multi-objective optimization as an approach to explore the trade-offs between these conflicting objectives. Questions pertaining to fair allocation are commonly integrated a posteriori. In contrast, this study explores their a priori incorporation and the impact of doing so on the trade-offs identified through multi-objective optimization. We investigate utilitarianism, egalitarianism, and prioritarianism, representing diverse theories of distributive justice. These theories guide the translation of justice principles into mathematical models, offering insights into how societal values influence water distribution. Our research centers on the management of the heavily disputed shared water resources within the Eastern Nile River Basin. We compare a priori and a posteriori integration of distributive justice principles to find Pareto-optimal trade-offs across irrigation, hydropower, and urban supply objectives for Sudan, Egypt, and Ethiopia. Our findings demonstrate that the a priori integration produces trade-offs that differ significantly from those obtained through analyses that omit distributive justice principles during optimization and only incorporate them post-optimization for filtering. Utilitarian integration enhances overall system performance, egalitarian integration diversifies solutions, and prioritarian integration produces sharper trade-offs, highlighting the challenges in reconciling distributive justice principles. Our findings contribute to the broader discourse on ethics in many-objective optimization, offering valuable insights for policymakers and water resource managers, especially in contexts where sustainability and fair distribution of water resources are essential.