Addressing the global challenge of water scarcity, particularly in the context of Sustainable Development Goal 6, underscores the critical need for effective water resource management. Central to this management is the control of dams in river basins, which poses complex decision-making challenges often labeled as wicked problems. Many-Objective Optimization, a powerful tool in modeling water systems, grapples with conflicting objectives, and the complexity heightens when integrating Distributive Justice principles. Distributive Justice, aiming to equitably distribute resources, is crucial in the context of water distribution for reservoir management. While current modeling approaches predominantly apply Distributive Justice principles A Posteriori, this study focuses on their A Priori incorporation, evaluating their impact on trade-offs and decision-making processes within the framework of Many-Objective Optimization.The investigation delves into Utilitarianism, Egalitarianism, and Prioritarianism, representing varied Distributive Justice perspectives. These frameworks are translated into mathematical models to provide insights into how societal values influence water resource allocation. The research centers on managing contentious shared water resources within the Eastern Nile River Basin. A comparative analysis between A Priori and A Posteriori integration of Distributive justice principles reveals distinct Pareto-optimal trade-offs. The findings underscore significant differences between a priori and a posteriori approaches, with Utilitarian integration enhancing overall system performance, egalitarian integration diversifying solutions, and prioritarian integration yielding sharper trade-offs. This study contributes valuable insights to the ethical considerations in many-objective optimization. It also offers guidance for policymakers and water resource managers by providing clear terminology to discuss and evaluate different approaches that are fitting within the policymaker's scope.