Mon, Aug 02, 2021:On Demand
Background/Question/Methods
High-profile modeling studies often project that large-scale win-win solutions exist in environmental management, either improving aggregate objectives such as economic gains and conservation, or improving outcomes for multiple stakeholder groups. However, on-the-ground scholars and managers often approach win-win narratives skeptically, due to real-world complexity. Case-study meta-analyses also find win-wins are relatively rare. We show mathematically why complexity reduces the availability of win-wins. We also characterize two-dimensional tradeoffs with a meta-analysis, and show how to extrapolate results of two-dimensional studies to higher dimensional realities.
Results/Conclusions We provide a general proof that, under uncertainty, the probability a manager should assign to win-win outcomes existing (here meaning Pareto improvements) strictly decreases in: the number of objectives, the number of stakeholders, and the number of constraints. We show that the maximum fraction of single-objective best outcomes simultaneously achievable for all objectives, a measure of tradeoff severity, also decreases (i.e. tradeoff severity increases) in the number of objectives, and approaches a limit unaffected by tradeoff surface curvature. This is important because our meta-analysis shows that most (77%) of empirically estimated two-dimensional tradeoff surfaces are concave. Concave tradeoffs are less severe, and moreso in lower dimensions. Our model can extrapolate these estimated low-dimensional tradeoff severities to arbitrary higher dimensions. This work provides precise intuition and quantitative guidance for interpreting implications of simple tradeoff studies for complex realities.
Results/Conclusions We provide a general proof that, under uncertainty, the probability a manager should assign to win-win outcomes existing (here meaning Pareto improvements) strictly decreases in: the number of objectives, the number of stakeholders, and the number of constraints. We show that the maximum fraction of single-objective best outcomes simultaneously achievable for all objectives, a measure of tradeoff severity, also decreases (i.e. tradeoff severity increases) in the number of objectives, and approaches a limit unaffected by tradeoff surface curvature. This is important because our meta-analysis shows that most (77%) of empirically estimated two-dimensional tradeoff surfaces are concave. Concave tradeoffs are less severe, and moreso in lower dimensions. Our model can extrapolate these estimated low-dimensional tradeoff severities to arbitrary higher dimensions. This work provides precise intuition and quantitative guidance for interpreting implications of simple tradeoff studies for complex realities.