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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.

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Fig. 1: Hypothetical fishery example.
Fig. 2: Tradeoff severity and number of objectives.
Fig. 3: Measuring and extrapolating empirical tradeoff severities.

Data availability

All data used in this study are available in Supplementary Data 1.

Code availability

Mathematica code for Figs. 2d and 3c,d is available as Supplementary Software 1. Supplementary Data 2 is the input data file for this code. It is a subset of the data contained in Supplementary Data 1.


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We thank P. Newton, T. Ippolito, W. Eichhorst and R. Marshall for feedback on earlier drafts of the manuscript, and C. Brooks, B. Wallace, D. Dorman, C. Burgess, D. Kaffine and attendees of several seminars for helpful feedback on and discussion of the concepts and mathematics discussed here. M.H. and M.G.B. acknowledge funding from the US Department of Agriculture (USDA) and National Institute of Food and Agriculture (NIFA) (Award number: 2020-38420-30727 to M.G.B.). R.E.L. and M.G.B. acknowledge funding from the University of Colorado Boulder (start-up grant to M.G.B.).

Author information

Authors and Affiliations



M.G.B. conceived the project, M.H. and R.E.L. assembled and analysed the data, and M.G.B., R.E.L. and M.H. completed the mathematical proofs. M.G.B., M.H. and R.E.L. wrote the paper.

Corresponding author

Correspondence to Matthew G. Burgess.

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The authors declare no competing interests.

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Nature Sustainability thanks Rebecca Shaw, Alex Strang and the other, anonymous, reviewer(s) for their contribution to the peer review of this work.

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Supplementary information

Supplementary Information

Supplementary methods.

Reporting Summary

Supplementary Data 1

Full meta-analysis data.

Supplementary Data 2

Data input file for Mathematica code.

Supplementary Software 1

Mathematica code for Figs. 2d and 3c,d.

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Hegwood, M., Langendorf, R.E. & Burgess, M.G. Why win–wins are rare in complex environmental management. Nat Sustain 5, 674–680 (2022).

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