Water management usually considers economic and ecological objectives, and involves tradeoffs, conflicts, compromise, and cooperation among objectives. Pareto optimality often is championed in water management, but its relationships with the mathematical representation of objectives, and implications of tradeoffs for Pareto optimal decisions, are rarely examined. We evaluate the mathematical properties of optimized tradeoffs to identify promising regions for compromise, suggest strategies for reducing conflicts, and better understand whether decision-makers are more or less likely to cooperate on environmental water allocations. Cooperation and compromise among objectives can be easier when tradeoff curves are concave and more adversarial when tradeoff curves are convex. “Knees,” or areas with maximum curvature, bulges, or breakpoints in concave Pareto frontiers, suggest more promising areas for compromise. Evaluating the shape of Pareto curves based on each objective's performance function can screen for the existence of knees amenable to compromise. We explore water management and restorations actions that improve and shift the location and prominence of knees in concave Pareto frontiers. Connecting river habitats and other non-flow management actions may add knees on locally concave regions of Pareto frontiers. Managing multiple streams regionally, rather than individually, can sometimes turn convex local tradeoffs into concave regional tradeoffs more amenable to compromise. Overall, this analysis provides a deep investigation of how the shape of tradeoffs influences the range and promise of decisions to improve performance, and illustrates that management actions may encourage cooperation and reduce conflict.

中文翻译：

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环境水管理的帕累托最优和妥协

水资源管理通常考虑经济和生态目标，涉及目标之间的权衡、冲突、妥协和合作。帕累托最优在水资源管理中经常受到拥护，但它与目标的数学表示的关系，以及对帕累托最优决策的权衡的影响，很少被研究。我们评估优化权衡的数学特性，以确定有希望的妥协区域，提出减少冲突的策略，并更好地了解决策者是否可能或多或少地在环境水资源分配上进行合作。当权衡曲线是凹的时，目标之间的合作和妥协会更容易，而当权衡曲线是凸的时，则更具对抗性。“膝盖”，或具有最大曲率、凸起、或凹帕累托边界中的断点，表明更有希望的妥协领域。根据每个目标的性能函数评估帕累托曲线的形状可以筛选是否存在可以妥协的膝盖。我们探索了水管理和恢复行动，以改善和改变凹形帕累托边界中膝盖的位置和突出度。连接河流栖息地和其他非流量管理行动可能会在帕累托边界的局部凹区增加膝盖。区域性地管理多个流，而不是单独管理，有时可以将凸局部权衡变成更易于妥协的凹区域权衡。总体而言，该分析深入研究了权衡的形状如何影响提高性能的决策范围和承诺，