Why win–wins are rare in complex environmental management

High-profile modelling studies often project that large-scale win–win solutions are widely available, but practitioners are often sceptical of win–win narratives, due to real-world complexity. Here we bridge this divide by showing mathematically why complexity makes win–wins elusive. We provide a general proof that increasing the number of objectives, the number of stakeholders or the number of constraints decreases the availability of win–win outcomes (here meaning Pareto improvements). We also show that a measure of tradeoff severity increases in the number of objectives. As the number of objectives approaches infinity, we show that this tradeoff severity measure approaches a limit unaffected by the curvature of the tradeoff surface. This is surprising because concave tradeoff-surface curvature results in less severe tradeoffs with fewer objectives. Our theory suggests that this difference gradually dissipates as objectives are added. In a meta-analysis, we show that 77% of empirically estimated two-objective tradeoff surfaces are concave. We then show how to approximately extrapolate our tradeoff severity measure to higher numbers of objectives, starting from estimated tradeoffs between fewer objectives. Our results provide modellers with precise intuition into practitioners’ scepticism of win–win narratives and practitioners with guidance for assessing the implications of simple tradeoff models.