Why win-wins are rare in complex environmental management

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 find win-wins are relatively rare. Here, we show mathematically why complexity reduces the availability of win-wins. We provide a general proof that, under uncertainty, the probability a manager should assign to the existence of a win-win outcome (i.e. a Pareto improvement) strictly decreases in each of: the number of objectives, the number of stakeholders, and the number of constraints. We also prove that the maximum simultaneously achievable fraction of all objectives’ maxima strictly decreases in the number of objectives, and approaches a limit unaffected by the tradeoff surface’s curvature. This is important because most empirically estimated two-dimensional tradeoff surfaces are concave—77%, we show in a meta-analysis. Concave tradeoffs are less severe—moreso in lower dimensions—which could create misleading impressions of higher-dimensional tradeoffs. Our results link two important schools of thought regarding environmental tradeoffs, and provide quantitative guidance for interpreting the implications of empirical low-dimensional tradeoff studies for higher-dimensional realities.