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Utilitarian benchmarks for emissions and pledges promote equity, climate and development


Tools are needed to benchmark carbon emissions and pledges against criteria of equity and fairness. However, standard economic approaches, which use a transparent optimization framework, ignore equity. Models that do include equity benchmarks exist, but often use opaque methodologies. Here we propose a utilitarian benchmark computed in a transparent optimization framework, which could usefully inform the equity benchmark debate. Implementing the utilitarian benchmark, which we see as ethically minimal and conceptually parsimonious, in two leading climate–economy models allows for calculation of the optimal allocation of future emissions. We compare this optimum with historical emissions and initial nationally determined contributions. Compared with cost minimization, utilitarian optimization features better outcomes for human development, equity and the climate. Peak temperature is lower under utilitarianism because it reduces the human development cost of global mitigation. Utilitarianism therefore is a promising inclusion to a set of benchmarks for future explorations of climate equity.

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Fig. 1: Evaluating NDCs with the utilitarian benchmark.
Fig. 2: Human development and equity advantages of the utilitarian policy.
Fig. 3: Gains from adopting the utilitarian versus the cost-minimization optimal policy.
Fig. 4: Climate advantages of the utilitarian policy.

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Data availability

All data used in our version of the model is archived54 and freely available at

Code availability

All model code used to generate results and create figures for this article is archived54 and freely available at


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Research by D.S. is supported by the National Institute of Child Health and Human Development (NICHD) grants K01HD098313 and P2CHD042849. The content is solely the responsibility of the authors and does not necessarily represent the official views of the National Institutes of Health.

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Authors and Affiliations



All authors contributed equally to this work. M.B.B., D.A., F.D., N.K.D., F.E. and D.S. designed the research. F.D., F.E. and K.K. led the computer modelling, M.B.B., F.E., K.K. and D.S. designed the figures and F.E., K.K. and D.S. constructed the figures. M.B.B., N.K.D. and D.S. wrote the main paper and M.B.B. wrote the Supplementary Information. All authors discussed the results and implications and commented on the manuscript.

Corresponding authors

Correspondence to Mark B. Budolfson or Dean Spears.

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Competing interests

N.K.D. is a member of the committee advising the Government of India on analysis of low carbon trajectories. All other authors declare no competing interests.

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Peer review information Nature Climate Change thanks Diane Coyle and the other, anonymous, reviewer(s) for their contribution to the peer review of this work.

Publisher’s note Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.

Extended data

Extended Data Fig. 1 Cumulative emissions per capita converge over the 21st century under utilitarianism.

The vertical axis plots, for each year, (cumulative emissions by region since 1900 up to that year) divided by (the total population, measured as person-years, lived in that region since 1900 up to that year). The high levels for USA in 2020 are the result of far higher emissions through the 20th century than the poorer regions plotted. Only countries are presented for which we have adequate population and emissions data going back to 1900.

Extended Data Fig. 2 Multi-Model Robustness.

Implementing the utilitarian method in the FUND model. The top row replicates Fig. 2c-d for RICE, while the bottom row displays the analogous results in the FUND model, which is known to have substantively different assumptions and structure.50 (See FUND documentation for details of the FUND model.51) The main results of the paper—that regional emission allocations are heavily tilted towards developing countries in the utilitarian optimum—also hold in the FUND model. (See also Anthoff 2011.18) We optimize FUND through 2300 with the same discounting parameters and utilitarian objective function used to generate our main results with RICE. The FUND results assume that regional carbon taxes can go no higher than $5000/ton CO2 and remain constant after 2200.

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Budolfson, M.B., Anthoff, D., Dennig, F. et al. Utilitarian benchmarks for emissions and pledges promote equity, climate and development. Nat. Clim. Chang. 11, 827–833 (2021).

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