Expert elicitation studies have become important barometers of scientific knowledge about future climate change (Morgan and Keith, Environ Sci Technol 29(10), 1995; Reilly et al., Science 293(5529):430–433, 2001; Morgan et al., Climate Change 75(1–2):195–214, 2006; Zickfeld et al., Climatic Change 82(3–4):235–265, 2007, Proc Natl Acad Sci 2010; Kriegler et al., Proc Natl Acad Sci 106(13):5041–5046, 2009). Elicitations incorporate experts’ understanding of known flaws in climate models, thus potentially providing a more comprehensive picture of uncertainty than model-driven methods. The goal of standard elicitation procedures is to determine experts’ subjective probabilities for the values of key climate variables. These methods assume that experts’ knowledge can be captured by subjective probabilities—however, foundational work in decision theory has demonstrated this need not be the case when their information is ambiguous (Ellsberg, Q J Econ 75(4):643–669, 1961). We show that existing elicitation studies may qualitatively understate the extent of experts’ uncertainty about climate change. We designed a choice experiment that allows us to empirically determine whether experts’ knowledge about climate sensitivity (the equilibrium surface warming that results from a doubling of atmospheric CO2 concentration) can be captured by subjective probabilities. Our results show that, even for this much studied and well understood quantity, a non-negligible proportion of climate scientists violate the choice axioms that must be satisfied for subjective probabilities to adequately describe their beliefs. Moreover, the cause of their violation of the axioms is the ambiguity in their knowledge. We expect these results to hold to a greater extent for less understood climate variables, calling into question the veracity of previous elicitations for these quantities. Our experimental design provides an instrument for detecting ambiguity, a valuable new source of information when linking climate science and climate policy which can help policy makers select decision tools appropriate to our true state of knowledge.
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Kriegler et al. (2009) is an exception, however its results are difficult to interpret since it prompted experts for a range of probabilities (taking the existence of imprecise probabilities for granted), instead of inferring the non-existence of subjective probabilities from observed choices.
The precise definition of climate sensitivity we used is quoted in the Supplementary Information, and is also available on the survey website.
We computed a two-sided Wilcoxon rank-sum test at each of the three percentiles to test the hypotheses that the percentile estimates in our study and Zickfeld et al. (2010) were drawn from the same sampling distributions. All of the P-values from the three tests exceed the Bonferroni corrected 5 % threshold.
Experts in our sample were less likely to violate SEU on the Ellsberg Problem than in most other published studies, where SEU violation rates can be up to 80 % (Slovic and Tversky 1974; Camerer and Weber 1992). This most likely reflects the scientist’s mathematical training, and suggests that those SEU violations that we do observe are likely not due to lack of familiarity with the rules of probability theory.
Note that all we need to show is that SEU is violated once in order to conclude that an expert’s knowledge cannot be described by subjective probabilities. One might argue that it is easy to observe at least one violation of SEU by simply asking experts to make bets on a large number of values of S, however the larger the number of bets, the less power the experimental design has to detect correlations between behavior in the Ellsberg Problem and that in the Climate Problem. The current design achieves a balance between detecting SEU violations, and preserving sufficient statistical power to allow us to ascribe them to the presence of ambiguity.
We use a one-sided test as our hypothesis is that ambiguous beliefs about climate sensitivity cause SEU violations on the Climate Problem to be more likely amongst those who violate SEU on the Ellsberg Problem than amongst those who do not. Thus our alternative hypothesis is ‘positive dependence’ between SEU violations on the Ellsberg and Climate Problems.
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AM was supported by a Ciriacy-Wantrup postdoctoral fellowship at UC Berkeley during the course of this work. RC is supported by the UK Economic and Social Research Council (ESRC) and the Jan Wallander and Tom Hedelius Foundation. DAS acknowledges the support of the LSE’s Grantham Research Institute on Climate Change and the Environment and the ESRC Centre for Climate Change Economics and Policy, funded by the Economic and Social Research Council and Munich Re. We thank Rachel Denison for advice and comments.
Electronic Supplementary Material
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Appendix A: Methods summary
Participants were recruited by e-mail and word of mouth over a period of 3 months beginning in December 2010. Forty two respondents completed the survey (available in full online at http://www.climate.websperiment.org). All respondents consented to be identified as participants, and were informed that their responses would be anonymized. Thirteen respondents were removed from the sample as they either stated that they are not familiar with the literature on climate sensitivity estimation, or were not primarily engaged in climate science research at the time of the survey.
The 29 experts in our sample were: Gab Abramowitz, James Annan, Kyle Armour, David Easterling, Seita Emori, John Fasullo, Chris Folland, Chris Forest, Piers Forster, John Harte, Gabriele Hegerl, Gregory Jones, Reto Knutti, Gerald Meehl, James Murphy, Falk Niehoerster, Geert Jan van Oldenborgh, John Reilly, Gerard Roe, Ben Sanderson, Stephen Schwartz, Carolyn Snyder, Andrei Sokolov, Claudia Tebaldi, Simon Tett, Warren Washington, Andrew Weaver, Rob Wilby, Carl Wunsch. All reported results have been anonymized.
Each experts’ hypothesized 5th, 50th and 95th percentile of the distribution for S were initially elicited using standard probabilistic elicitation methods. They then completed four sets of betting tasks—three on the Climate Problem (one at each of the elicited percentiles of S), and one on the Ellsberg Problem. Full details of these betting tasks are available in the Supplementary Information. Participants could move back and forth through the survey at any time, and had access to help boxes on each screen with reminders about quantity definitions and judgmental biases to be aware of when forming their answers. They could also change their answers at any time. We used data only from those experts who completed the survey in full. There was no time limit on the survey, and experts were informed that they should take as much time as they need to form their best judgments. The Ellsberg Problem was presented at the very end of the survey, so as not to prime participants to think in terms of ambiguity.
Appendix B: Author contributions
AM conceived of the research. RC and AM designed the experiment. GM implemented the online survey. DAS provided guidance on the formulation of the survey questions. RC, AM, and DAS recruited participants and ran the experiment. RC analyzed the data, and AM wrote the paper.
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Millner, A., Calel, R., Stainforth, D.A. et al. Do probabilistic expert elicitations capture scientists’ uncertainty about climate change?. Climatic Change 116, 427–436 (2013). https://doi.org/10.1007/s10584-012-0620-4
- Climate Policy
- Climate Sensitivity
- Subjective Probability
- Climate Science
- Ambiguity Aversion