Ben Laude made a YouTube video in which he interviewed Eugene Chan about his analysis of the voting of the 2025 19th Chopin Competition.

I have thought a little about voting systems and the judges scores were made available on the Competition Web site, so I thought why not create some python code to analyze who the winners of the 19th competition under voting systems that were not used by the actual competition.

The github repository containing the processing code, input data files, and results, for all of the analysis described here is freely available. Feel free to copy it and modify it to perform your own preferred analyses.

[Since the original publication of this blog post, it has come to my attention that there is a another analysis of Chopin Competition voting at https://euge.ca/chopin-2025.]

VOTING SYSTEMS

Before discussing voting systems, it is useful to take note of Nobel Prize Winner Kenneth Arrow’s impossibility theorem. I’ll let you look into it on your own, but it shows mathematically that there is no perfect voting system, that every voting system has its flaws.

This motivates my attempt to use several reasonable voting systems. If several reasonable voting systems yield the same winner, then it is likely the best winner was chosen.

[Incidentally, I was able to participate in some seminars at Stanford in which Kenneth Arrow also participated. I feel very fortunate that, in my life, I have gotten to meet, or at least be in the room with. some towering giants of accomplishment.]

In all of the voting systems considered, I take the numerical scores of each judge and then use the scores to rank the preferences across the different contestants. If two contestants receive the same score, it is assumed the judge has no preference between the two of them.

“First past the post” : Most first choices

There is a voting system often known as “First past the post“.

In this voting system, whoever gets the most first choice votes wins. If a judge had two people rated as first choice, that would count as 1/2 a vote for each.

Then the person receiving the most first choice votes wins (assuming there is no tie, and there was not). That person is then removed from everyone’s list, and the process is repeated to determine the second place winner, and so on to the bottom of the list.

“Copeland’s method”: Most wins on pairwise comparisons

Copeland’s method is to take the judges’ ratings of the contestants, and compare how they would be judged by each judge in a pairwise comparison, and then take the person who would do best in the most pair-wise competition.

One point is added to each contestant’s score for winning a pairwise competition as judged independently by each judge, and a point is subtracted from each contestant’s score for losing a pairwise competition. A tie neither adds nor subtracts points.

The person who has the highest point score then wins.

If there is one person who is preferred over everybody else by over half the judges, this is known as a Condorcet winner. It may not be obvious that someone can score highest on Copeland’s method without being a Condorcet winner, but it is possible. In fact, this happened in the first round of this year’s competition.

“Instant Runoff Voting”: Top-down elimination

In instant runoff voting, the candidate with fewest first preference votes is eliminated, and everyone who had that candidate as a first choice now has that candidate eliminated from their ranking so now their second choice is their first choice.

This process is iterated until some candidate gets a majority of the votes.

To determine the second place winner, the first place winner is removed from every judge’s ranking and the process is repeated. To get the third place winner, we remove the first and second place winners and repeat the process and so on.

Bottom-elimination voting

Bottom-elimination voting is the same as instant runoff voting except the process starts from the bottom instead of the top.

It is essentially repeating instant runoff voting where you flip everyone’s ranking so that the judges’ last choices are at the top and their first choices are at the bottom, and then you see who got to the lowest rankings, etc.

If instant runoff voting tries to find the candidate liked by the greatest number of judges, bottom elimination voting tries to find the candidate disliked by the fewest number of judges.

THE RESULTS

The results of this exercise can be found in an excel file located here.

Stage 1

In Stage 1, with 84 contestants, the following five contestants got the highest scores on each of the voting systems:

Table 1: Stage 1 voting results

The first thing to notice is that all of these voting systems agree that Kevin Chen won the first round. Four out of the five methods agree that Eric Guo placed second. There is reasonable cause for argument about the remaining places.

Further note that 4 out of the people top-ranked by Copeland’s method appear in the same order as chosen in the Competition. Thus it seems the Competition method is closest to Copeland’s method.

Each of these voting systems have different implications for who would be one of the 40 contestants to pass on to Stage 2.

Under the first past the post system, there were 14 people who would have passed to Stage 2 but did not (and 14 people who did pass to Stage 2 but would not have). You can look at the linked excel file to look at names.

Under Copeland’s method, there were only 2 people who would or would not have passed to Stage 2, compared to who was actually chosen to continue to Stage 2. For the instant runoff voting, there was a discrepancy of 5 people either way, and for the bottom elimination method, the discrepancy was 6 people.

By this criterion also, the Competition method seems closest to Copeland’s method.

Stage 2

In Stage 2, of the 40 contestants competing, the following five contestants got the highest scores on each of the voting systems:

Table 2: Stage 2 voting results

There seems to be fairly broad agreement on the top two contestants in the second round, and arguably the third place winner.

Vincent Ong did not appear in the top five in any of the voting methods considered. Vincent came in 6th place in first past the post, 7th place in Copeland ranking, and 6th place in instant runoff voting. However, he came in 32nd place in the bottom-elimination method. This means that while there were many judges who gave Vincent Ong a high ranking, there were some who gave him a low ranking.

In terms of determining the 20 contestants to pass on to Stage 3, there were 14 discrepancies with the first past the post method, 2 discrepancies with the instant runoff voting, and 4 discrepancies with the bottom elimination voting.

For passing on to the Stage 3, Copeland’s method agreed 100% with the Competition method, providing more evidence that Copeland’s method is most similar to the Competition method in its effects.

Stage 3

In Stage 3, of the 20 contestants competing, the following five contestants got the highest scores on each of the voting systems:

Table 3: Stage 3 voting results

Every method agrees that Eric Lu was first place in this round, and all of the methods, except for the method actually used, predict that Zitong Wang came in second.

Interestingly, this time, the five top people chosen by the Jury were the same as the five top people chosen by the bottom-elimination method. It as if we have gone from asking who would win the most in pairwise competitions to asking who does nobody rank lowly.

In terms of the 11 contestants passing on to the Final Stage, there were 3 discrepancies with the first past the post method, 2 discrepancies with the instant runoff voting, and 2 discrepancies with the bottom elimination voting.

Once again, Copeland’s method agreed 100% with the Competition method on who should pass on to the Final Stage, providing yet more evidence that Copeland’s method is most similar to the Competition method in its effects.

Final stage

In the Final stage, of the 11 contestants competing, the following five contestants got the highest scores under each of the voting systems:

Table 4: Final Stage voting results

Two of the four voting methods considered here agree with the Competition method that Eric Lu was the winner, and Eric Lu appears in the top 4 under all voting systems considered.

Kevin Chen came in first on instant runoff voting, third on first past the post voting, and second with the other two methods, so the judgement of the Jury that Kevin Chen was second also seems fairly robust. (Although, the average position of Kevin Chen across the four voting systems was closer to first place than the average position of Eric Lu across the four systems.)

Zitong Wang was 7th in first past the post, 9th in Copeland ranking, and 8th in instant runoff voting. Zitong Wang seems to have made third place by not being near the bottom of anybody’s list, but he was favored by few.

Final stage, cumulative voting

I did an additional analysis where instead of considering the judges’ vote only in the Final Stage, I treated it as if there were 68 judges (4 x 17), considering all of the votes the contestants received from all of the judges in all of the rounds. I treated them as if Stage 1 Garrick Ohlsson was a different judge than Stage 2 Garrick Ohlsson. The link to the spreadsheet containing the full results of this analysis can be found here.

One could argue that it is good to take into consideration the scores from all the Stages in the final scoring, to reduce the influence of any one performance.

Under this cumulative voting approach, the following five contestants got the highest scores on each of the voting systems:

Table 5: Voting results taking into consideration votes by the judges across all stages.

CONCLUDING COMMENTS

Copeland’s method and instant runoff voting are both typically considered relatively good voting systems, and these two voting systems would have produced different first place winners for this year’s competiton.

There is no objective way to say what would be the “best” voting system. The right voting system to use for this year’s competition was the voting system defined in the rules of the competition.

I would suggest that in future years, the Competition consider using Copeland’s method. Copeland’s method produced the results that were closest to the results obtained under the current methodology, but is a simple and widely recognized approach that has been studied in detail by mathematicians and game theorists.

Copeland’s method is not guaranteed to produce a single winner, known as a Condorcet winner. Therefore, a tiebreak procedure might be considered. A reasonable tiebreak might be to choose which of the people tied for first place under Copeland’s method does best on instant runoff voting.

Purely numerical approaches give more weight to judges who use a wide range of values in their voting, whereas methods based on ranking are less amenable to one judge having more influence than another judge.

First past the post voting is generally considered to be a bad voting system, although it is used in the UK and many other places. Bottom elimination is better at weeding out the worst than at finding the best.

Lastly, I would encourage the competition to consider developing more awards, maybe not open to the first prize winner. Who played most emotively? Who displayed the greatest technical skill? Who was the most polarizing?

I’ve been listening to Eric Lu since the Competition’s results were announced, but now I want to go back and listen to some others, realizing the “best” is a matter of taste, and even one person’s taste can differ from day to day or even hour to hour.

In particular I want to look at which contestants produced the widest divergence of opinions among the judges. Which set of judges would I agree with? And who will I like the most?

The only way to find out is to listen.

ADDENDUM

Normalized mean analysis

The above looks at ranking voting systems, but one can approach this problem numerically.

Numerical voting systems have the problem that different judges have different amount of influence on rankings depending on both their average score and how large a range they use for their scoring.

One way to adjust for this is to subtract the mean score given by each judge and divide by the standard deviation of their scores. This gives each judge the same average and the same amount of variability.

We can then rank people at each stage by this normalized mean score of the judges. A spreadsheet that does this analysis can be found here.

For the Final Stage, the results for the top 5 contestants in terms of normalized mean scores are:

Table A1: Normalized mean analysis

Rank	Contestant	Normalized Mean ± 1 STD ERROR	Normalized Standard deviation
1	Kevin Chen	0.50 ± 0.20	0.83
2	Eric Lu	0.48 ± 0.19	0.72
3	Piotr Alexewicz	0.36 ± 0.19	0.79
4	Vincent Ong	0.18 ± 0.29	1.18
5	Shiori Kuwahara	0.13 ± 0.22	0.90

There is a mathematical way to estimate the uncertainty on these scores, how much the scores would be expected to vary if you hypothetically chose a different 17 judges from the same pool of possible judges (if such a thing exists). This amount is known as “standard error”.

In my scientific work, usually results need to differ by two standard errors before we consider them statistically significant. By this measure, none of the top competitors would be considered to differ to a statistically significant degree.

I would go further and say that the Kevin Chen and Eric Lu’s scores are statistically indistinguishable.

Least agreement analysis

Above, I said it would be interesting to know which pianists created the greatest difference of opinion among the judges.

Based on normalized standard deviations as described above, in Stage 1, the contestants with the most disagreement among judges was a mix of high , mid and low ranked contestants: Xiaoyu Hu, Piotr Pawlak, Vincent Ong, Xuanyi Mao, and Gabriele Strata. In contrast, the contestants where was the most agreement were all ranked low.

In Stage 2, the contestants where there was the most disagreement were William Yang, Yang (Jack) Gao, David Khrikuli, Gabriele Strata, and Vincent Ong, who were all high to middle ranked. Most of the contestants where there was high agreement were low ranked with the exception of Eric Lu, where there was high agreement that he was very good.

In Stage 3, the most disagreement were middle to low ranked contestants: Yang (Jack) Gao, Piotr Pawlak, David Khrikuli, William Yang, and Vincent Ong. The contestants where there was the most agreement were also middle to low ranked contestant, once again with the exception of Eric Lu, where there was high agreement that he was very good.

For the Final Stage, of the people in the top five shown in Table A1, there was the most disagreement about Vincent Ong, with the highest normalized standard deviation of any contestant in the Final Stage.

It looks to me like VIncent Ong wins the prize for being considered among the top finalists despite having the most disagreement among the judges. He is who I want to listen to now. (And then Kevin Chen.)

Duplicated from US State Department web site on 3 March 2025. Links to organizations under the DONATE heading have been updated.

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Ukraine – Fact Sheet: How You Can Help

Last Updated: March 14, 2022

UNITED WITH UKRAINE

How You Can Help

We understand many people want to help Ukraine and those suffering from ongoing Russian aggression. We strongly advise against U.S. citizens traveling to Ukraine. Please see the below resources on ways you can safely contribute.  

STAY INFORMED

To learn more about the crisis and how you can support the humanitarian needs of those impacted by the conflict, visit: 

• The Department of State United with Ukraine website.
• The U.S. Agency for International Development (USAID) Ukraine crisis website. 
• United Nations High Commissioner for Refugees (UNHCR) website.  
• United Nations Children’s Fund (UNICEF) appeal to help all children in Ukraine.

DONATE

The Department has partnered with GoFundMe.org, an independent charity, to help address the humanitarian needs of the people affected by the Russian aggression against Ukraine. [NOTE: I would not trust this GoFundMe link, as it will be distributed by the current US State Department.] In addition, a variety of relief organizations are responding to the situation in Ukraine. Sending cash donations to experienced humanitarian relief organizations working on the ground is generally the most effective way to help and save the most lives. Below are organizations responding to the crisis. 

Airlink                                                                 

All Hands and Hearts                                         

CARE                                                               

Catholic Relief Services     

ChildFund                                                                  

Food and Agriculture Organization of the UN

Humanity & Inclusion                                                 

ICRC                                                                     

International Medical Corps                                       

International Organization for Migration                    

Islamic Relief USA                                                 

KidSave                                                             

Medical Teams International

Project C.U.R.E

Project HOPE

Red Cross

Save the Children

UNFPA

UNHCR

UNICEF

UNICEF USA

UNOCHA

World Central Kitchen

World Food Program (WFP)

World Health Organization (WHO)

TRAUMA RESOURCES

The Child Mind Institute has prepared free trauma resources in Russian, Ukrainian, and English to assist parents, educators, and other adults in talking to children about traumatic events and identifying those who may benefit from professional attention.

CHILD PROTECTION PRINCIPLES IN TIMES OF EMERGENCY

We frequently receive inquiries from U.S. citizens concerned about refugee or conflict-affected children. We share these concerns for children, and we understand that some U.S. citizens want to respond by offering to adopt or host these children in need.  

It can be extremely difficult during crises to determine whether children who appear to be orphans are truly eligible for adoption and immigration under U.S. laws. Children may be temporarily separated from their family, and their parents or other caregivers may be looking for them. Families may make the difficult choice to send children on their own in search of safety. Even when it can be demonstrated that a child’s parents are deceased, children are often cared for by other relatives and caregivers.  During crises, many children who are not orphans temporarily live in orphanages for safety. Leaving orphanages may pose additional risks, including exploitation and abuse. 

During crises, it can be exceptionally difficult to fulfill the legal and documentation requirements for intercountry adoption of both the United States and the child’s country of origin. We recommend taking extra caution when considering adopting a child during a crisis and hiring an experienced immigration attorney may also be helpful.   

ADDITIONAL RESOURCES ON INTERNATIONAL STANDARDS FOR CHILDREN IN CRISES

• Statement on Ukraine by Department of State’s Special Advisor for Children’s Issues
• Statement on Ukraine by the Permanent Bureau of the Hague Conference on Private International Law.
• UNICEF and the UN High Commissioner on Refugees joint statement on supporting children in crises. 
• International Social Service fact sheet with guidance on the application of international standards for children in crises.
• Resources and guidance on Ukraine by non-profit Creating A Family.
• National Council for Adoption’s statement on refugee children.

OTHER GLOBAL GUIDANCE DOCUMENTS ON BEST PRACTICES FOR UNACCOMPANIED AND SEPARATED CHILDREN 

• Field Handbook on Unaccompanied and Separated Children 
• Toolkit on Unaccompanied and Separated Children 
• Minimum Standards for Child Protection in Humanitarian Action 
• Critical Considerations for Movement of Children During a Humanitarian Crisis

EVACUATION OF UKRAINIAN CHILDREN

Ukrainian authorities have jurisdiction over decisions regarding the safety and welfare of children in Ukraine, including whether to grant permission for children to exit the country. Ukrainian authorities have informed us they are moving children into Poland for safety and medical treatment. Child welfare and protection agencies that specialize in humanitarian crisis assistance, refugee issues, and family tracing are on the ground to assist and care for children who exit Ukraine.

INTERCOUNTRY ADOPTION REGULATIONS

For more information specifically about adoption issues in the Ukraine crisis, please visit: Information for U.S. Citizens in the Process of Adopting Children from Ukraine.  

Families who are currently in the process of adopting a child from Ukraine should direct questions and concerns to their accredited or approved Adoption Service Provider.   

HOSTING PROGRAMS

Some non-governmental organizations coordinate temporary hosting programs that have included exchanges with Ukrainian children in the past.  However, Ukrainian authorities have confirmed they are not approving children for participation in hosting programs at this time. The Department is therefore unable to seek approval for a child’s participation in a hosting program at this time. Please see Ukraine Adoption Update for additional information.  

Although often referred to as “orphan hosting” programs, those interested in hosting should be aware that many of the children who participate in these programs are not eligible for adoption. Children who travel to the United States for hosting programs do so with the Ukrainian government’s authorization and on a U.S. non-immigrant visa.  The visa is typically valid only for one entry to the United States during the narrow date range of the program.  A new visa is required before travelling to the United States again.  

HOSTING PROGRAMS (continued)

Previously-hosted children may apply for a nonimmigrant visa at a U.S. Embassy or Consulate outside Ukraine.  However, there is no “emergency hosting” visa category, and applicants must have permission from the appropriate guardian to travel and must meet the legal criteria for an existing category of non-immigrant visa, generally a B-2 visitor visa. Applications for nonimmigrant visas are evaluated under Section 214(b) of the Immigration and Nationality Act (INA) and require an applicant to demonstrate sufficient ties to a county other than the United States that would compel departure after a temporary stay.  Nonimmigrant visa applicants are “…presumed to be an immigrant until (s)he establishes to the satisfaction of the consular officer…that (s)he is entitled to nonimmigrant status…”. The presumption of immigration intent in Section 214(b) of the Immigration and Nationality Act can be difficult to overcome. Consular officers cannot issue visas based on assurances or recommendations by third parties or on the ability of a sponsor to provide financial support. Please see Visas for Ukrainian Nationals for additional information.  

Ukraine – Fact Sheet: How You Can Help

Northern Europe experienced a period of very low winds in 2021, adversely impacting Europe’s ability to generate climate-friendly electricity.

This led us to ask several questions:

— Is this level of variability in wind resources consistent with historical variability, or has this variability been increasing as a result of climate change?

— Where in the world are the winds most abundant and most reliable?

Enrico Antonini, who was a postdoc in our group, set about answering these questions by analyzing historical reconstructions of weather since 1979. He led the production of a very nice paper published in “Nature family” journal “communications earth & environment“.

Abundant and reliable

We have all seen maps of average wind power at different locations, but where are winds both abundant and reliable?

The areas in yellow above have strong winds, on average, whereas the areas in purplish colors have relatively weak winds.

Some places can have strong winds on average, but experience a large seasonal cycle. For example, some places have more wind in the winter and others and more wind in the summer. Enrico Antonini and colleagues developed the following map illustrating the magnitude of the seasonal cycle, indicating how much the average winds shown above vary from season to season. That map looks like this:

Details of the metric and methodology are explained in the paper, and some comments on the methods are offered below. Regardless, the areas in yellow above have winds that are relatively consistent from season to season, whereas the areas in blue exhibit a high degree of variation from season to season.

Some areas might have strong winds that are relatively consistent from season to season, but these areas might exhibit a large amount of weather variability. That is, due to weather variability, there could be weeks without much wind even if a season would typically be windy.

To estimate the degree of weather variability, Antonini and colleagues developed a metric of weather variability that indicated how much a typical year’s weather might depart from what you would expect on average. (Details in the paper, and some more discussion below.)

In the above figure, the yellow areas exhibit little weather variability, whereas in the dark area, the winds you actually get can differ markedly from what you would expect for that location and time of year.

Everyplace has its own particular needs, and certainly transmission and storage can be used to smooth out some variability in wind power production. Nevertheless, other things equal, one would like wind power that could provide a steady and reliable supply of electricity.

Now that we have maps of annual average wind power, seasonality of wind power, and weather variability in wind power, how do we combine these three metrics on a single map? Wind power is in units of power per square meter, whereas our variability metrics end up being in units of hours of storage that would be needed at mean demand levels. You can’t add together metrics with different units. You can multiply or divide them but that doesn’t make sense in this case.

We settled on the idea of percentile rank ordering each location from best (100th percentile) to worst (0th percentile) on each dimension, where best is highest mean power, lowest seasonal variability, and lowest weather variability. If someplace were the best on all of these metrics the minimum percentile ranking across the three metrics would be 100. If someplace were the worst on any of these metrics, the maximum across these three metrics would be zero. For someplace to have abundant and reliable winds (both with respect to seasonality and weather), the minimum percentile rankings should be high on all three metrics. We made a map based on this concept:

One thing that came out of this analysis is that parts of the American Midwest are among the places in the world with most abundant and reliable winds. There are other good places in Asia, in the Sahara and southern Africa, in Australia, and Argentina.

Obviously variants of this analysis could be performed making different assumptions about storage, transmission, variation in demand and so on. We hope others will perform these analyses.

Trends in abundance and reliability

One of the things that motivated this study was the deep wind drought in Northern Europe in 2021. Are these kinds of wind drought just a product of normal variability or is there an increasing trend in wind power or its reliability that might be associated with climate change?

Before we begin this discussion, it is probably a good idea to point out a few things:

1. It is possible that a trend is real and driven by real underlying physical causal factors, but the trend is masked by so much variability that the trend is not showing up as statistically significant on commonly used tests.

2. Even if there is a trend, the trend itself could be due to natural variability or any of a large number of causes. Further, there could be a climate-induced trend that is masked by natural variability of the opposite sign.

In short, our tests of statistical significance do not lead to any determinative claim for causality in any direction. Absence of evidence is not evidence of absence.

When we look for trends in annual mean wind speeds over the period from 1979 through 2022, we get a map that looks like this:

From the above figure we see that winds tend to be getting stronger in the equatorial region and in parts of the Southern Ocean. I am somewhat hesitant to ascribe too much significance to trends observed over land because we would expect 5% of the land area to show up as statistically significant at the 0.05 level just by chance. Nevertheless, there is an indication of a strengthening of winds in parts of the American Midwest and a weakening of wind over Northern Europe and India.

More investigation is needed to determine if these trends are real, and if so, whether climate change is an important causal factor.

We found very little evidence of trends in weather variability in wind power. However, winds seem to be strengthening in the American Midwest and weakening over much of India. The result is that wind droughts, according to the metric we discuss below, are becoming less severe in the American Midwest and more severe over parts of India.

Energy metric of wind drought

There have been previous studies of wind drought (periods of low wind) that use arbitrary cut-offs of different sorts, such as how low the winds need to fall, or how long the low winds need to last, to be considered a wind drought.

Sometimes there can be an extended period of low winds that is interrupted by a single windy day or windy hour. Or there can be an extended period of relatively low winds but no time when the winds are extremely low. We wanted to develop a metric that could handle all of these cases in a consistent way.

We discuss wind droughts in terms of an energy deficit relative to some background case. For example, imagine we want to characterize the amplitude of the seasonal cycle in winds. We could ask: If we had this annual cycle repeating, how much energy storage would we need to yield a constant output of energy at the annual mean rate?

If the winds were steady, you would need no storage. If the winds were 8760 times the mean for 1 hour and then zero for the rest of the year, you would need an amount of storage nearly equal to the entire annual wind output. Intermediate cases would need intermediate amounts of storage.

To estimate weather variability relative to seasonal averages, we construct a year where wind power follows the typical average profile for different times of the year, and then we ask how much storage would be needed to offset weather variability and provide the amount of power from climatologically expected winds.

The figure below illustrates this methodology for a more realistic case, where the blue curve in panel a represents wind generation and the red curve represents the required output. When the blue curve is greater than the red curve, excess power is available and the power could be thought of as adding to storage. When the red curve is greater than the curve, that means the wind energy in insufficient to meet the target and so energy must come out of storage.

Note that the illustrated period of energy deficit is interrupted by a brief period of excess generation on Day 6. However, the amount of storage that would be needed to make up for the energy deficit would be the sum of the two areas where the red is above the blue from Day 3 to Day 10, less the excess generation that occurred on Day 6.

The amount of storage needed by calculating the difference in energy between each local minimum in the integral of generation minus target and the preceding global maximum in this integral (as illustrated in panel b).

Details of this methodology are described in Antonini et al (2024) and the associated Supplemental Material. All codes, and high resolution versions of the figures shown here (and other figures) are available at the associated github repository.

Closing remarks

I am very much proud of this paper. I think Enrico Antonini did a fine job pulling all of this together. I also thank our co-authors who each helped in various ways.

In our group, we like to do geophysical studies that are relevant to energy systems. We chose steady power because we wanted this to be a geophysically-oriented study focused on basic principles and methodology. Our computer codes are publicly available and ready to be modified for specific applications.

It would have been easy for us to incorporate costs of turbines, and real electricity demand curves, and consider inefficiencies and costs of batteries and so on. Consideration of transmission would be a bit more challenging but could be done. However, a study like this that is purely geophysical will stand the test of time.

Studies that consider more things like real demand profiles, technical characteristics, and costs are very valuable, but will tend to age as these properties change over time. Studies could also consider mixes of wind and solar and perhaps other generation sources. We encourage others to do such studies. We may end up doing some of these studies ourselves.

Of course, we do not expect people to decide whether or not to build wind farms based on our study alone. However, we hope that our study provides incentive for people to look more carefully at the potential for wind power in areas that we have identified as having abundant and reliable wind resources.

Lei Duan, Juan Moreno-Cruz and I recently published a paper in Environmental Research Letters, titled “The value of reducing the Green Premium: cost-saving innovation, emissions abatement, and climate goals”.

The Green Premium is the difference in cost between a technology that reduces net greenhouse gas emissions and the cost of the currently-used greenhouse gas-emitting technology.

The Abstract of this paper provides a good overall summary of what we did and our findings. In this blog post, I want to highlight a few things that we have found in doing this investigation.

The COIN model

The idea for this model came in the discussion after I gave a talk for University of Waterloo on 3 Dec 2020. We wanted to have a model that was simpler than Nordhaus’s DICE model. We called it the COIN model, laughing that it was simpler than the DICE model — only two sides instead of six.

The COIN model is designed as a tool that can be used to explore conceptual issues, and to teach about climate change economics. It is not intended to produce numerically accurate results.

Among other simplifications, in the COIN model, the amount of warming is proportional to cumulative carbon emissions, climate damage is assumed to scale with the square of temperature change, population is held constant, and total factor productivity is assumed to increase exponentially with time.

For this paper, we added a second abatement technology to the COIN model with costs that followed an “experience curve” (also known as a “learning curve”). The optimizer was allowed to choose to invest in the new technology, even when it was more costly than the incumbent technology.

Stringency of carbon constraint

Sometimes people say things like, “We don’t have time to develop new technologies. We just have to deploy the technologies we already have.”

It is certainly true that we need to deploy the technologies that we already have, but it doesn’t follow from that that we should not put effort into developing new technologies or reducing the cost of existing technologies.

The idea that there is not enough time to develop new technologies or improve existing technologies is based on a mistaken notion. We can develop what does not exist while we deploy what does exist.

We found that the value of reducing the Green Premium increases with the stringency of carbon constraint. If we want to ramp down to zero net emissions by year 2050, there is even more value to reducing the Green Premium than if we were to, say, ramp down to zero net emissions by year 2100.

Rapidly decreasing emissions requires building a lot of costly infrastructure. Because of the way returns on investments and economic discounting works, you would need to invest more today to build something in year 2050 than you would to build the same thing in year 2100. If we have more ambitious climate goals, it becomes even more valuable to reduce technology costs.

Costs don’t stop when we reach net-zero emissions

In Figure 3 (above), the middle row of panels is the cost of emissions abatement. Columns are different levels of abatement stringency. Note that the cost of mitigation abatement remains high in these simulations, even after all emissions are eliminated.

Sometimes people act like all of the cost of zero net emissions is in the transition to zero net emissions, but to maintain zero net emissions can also be costly if we do not have low-cost technologies available to help us avoid emissions.

One of the key benefits of reducing the Green Premium is to reduce costs after we have already achieved net zero emissions.

Do investments in emission reduction come from current consumption or from other capital investment?

I didn’t know the answer to the title of this section. If investment in mitigation cannibalized other forms of capital investment this could slow economic growth, yielding knock-on costs to the economy.

A basic insight is that if you think the world is going to end tomorrow, there is little incentive to invest in the future.

However, in our model, investing in emissions reduction produces a better future, with less climate damage. This is especially true as the Green Premium is decreased.

Climate damage, and the cost of mitigation, can be thought of as akin to taxes, and expectation of lower future taxes provides an incentive for increased investment.

Thus, in our model, the capital for investment in mitigation comes from current consumption. In contrast, investment in other forms of capital (the “savings rate”) increases relative to the “no mitigation” case.

Learning subsidies

The COIN model uses an optimizer to determine the optimal partitioning of resources between consumption, capital investment, investment in abatement using the incumbent mitigation technologies (“COIN abatement”), and investment in abatement with a new technology with costs that decline following an “experience curve” (also known as a “learning curve”).

In Nordhaus’s DICE model, the marginal cost of abatement is equal to the marginal net-present-value of climate damage avoided. However, we find that in nearly all cases considered, the optimizer is willing to pay more for the new technology, because there is value in driving the new technology down the learning curve. This additional investment in the more costly technology is known as the “learning subsidy” (or “learning investment”).

We found it very interesting that the optimizer, in nearly all cases, was willing to pay a learning subsidy to help drive the new technology down the learning curve. This suggests that subsidies for new clean technologies can be an economically efficient way to produce a better future.

Summary

We have developed an extremely simple model, the COIN model, to investigate conceptual issues related to the economics of climate change mitigation in general, and the value of decreasing the Green Premium in particular.

We have found that there is substantial value in reducing the Green Premium, and the more stringent the climate goals, the greater the value of decreasing the Green Premium.

“Carbon-emitting technologies often cost less than carbon-emission-free alternatives; this difference in cost is known as the Green Premium.”

In our simulations, much of the value of developing cheaper abatement technologies accrued after net-zero targets were reached. Decreasing Green Premiums not only makes it easier to get to net-zero, it makes it cheaper to stay there.

In nearly every case considered, the optimizer chose to invest in a learning subsidy to bring down the cost of the new technology, even as it allocated substantial resources to deploy existing technologies. This suggests that it can be economically efficient to subsidize new technologies that are proceeding down a learning curve.

In our simulations, investment in emissions abatement induced higher rates of capital investment in other parts of the economy. Decreased costs of emissions abatement and climate damage are akin to expectations of lower future taxes, and expectations of lower future taxes, in an efficient economy, induce increased capital investment.

Lastly, I would like to close with a bit of homage to simple conceptual models. We do not pretend that our model provides reliable numerical results, but we do believe that our model provides conceptual insight that is applicable to the real world.

Reducing the Green Premium can contribute to achieving climate goals, and helps us to develop a better future.

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Citation: Caldeira, K, Duan, L., and Moreno-Cruz, J. The value of reducing the Green Premium: cost-saving innovation, emissions abatement, and climate goals, Environ. Res. Lett. 18 104051 (2023)

Over the past 50 years, the world has seen a substantial amount of global warming,

And there has been substantial regional variability in the rate of warming.

The world has also seen a lot of GDP growth, with substantial regional variation in the rate of GDP growth.

These observations led us (Lei Duan and myself) to ask whether there was a statistically significant relationship between country-level rates of warming and rates of GDP growth over the past half century.

We used country-level temperature change data from Berkeley Earth, kindly provided to us by Zeke Hausfather. We used GDP data in 2015 USD from the World Bank. For population, we used data from NASA’s SEDAC. We focus on the 50-year time period from 1971 to 2020, and include only countries that had data for the full 50 years. We performed country-level linear regressions, weighting countries in three different ways: (1) countries weighted equally; (2) countries weighted by GDP; and (3) countries weighted by population.

For each country, we estimated an average rate of temperature increase with a ordinary least-squares regression of country-level annual mean temperature versus time; estimated an average continuous rate of GDP increase with an ordinary least-squares regression of the logarithm of country-level annual GDP versus time. We report results for temperature increase in units of K/yr and for GDP growth rates in units of %/yr.

If for each country, we divide the GDP growth rate trend by the temperature rate trend, we get a slope in units of %GDP/yr per K/yr or, equivalently, %GDP/K. The histograms for the country level warming rates, GDP growth rates, and ratios of GDP growth to rates of warming looks like this:

The simple point of the above figure is to illustrate that every country has experienced a warming trend over the past half century, and every country has experienced positive GDP growth.

The ratio of GDP growth to warming rate has therefore been positive in every country. This is a reminder that there are many factors that influence GDP growth. Temperature increases may have slowed GDP growth in many countries but climate change has not been the primary determinant of GDP growth.

To investigate whether, on the half-century scale, there are robust relationships between country-level rates of warming and country-level rates of GDP growth, we performed linear regressions of each country’s GDP growth rate against its rate of warming, with those rates determined as described above.

Because countries are not normally distributed in their properties, we estimated uncertainties in the regression by using a bootstrap approach — doing 2,000 regressions sampling from our data by choosing countries for randomly from the set of complete countries, with replacement.

Our primary results are displayed in this figure:

Note that a horizontal line would be consistent with the 95% uncertainty range for all three country weightings. Our conclusion from this preliminary analysis was that there are too many other things affecting country-level GDP growth over the past 50 years for a climate signal to show up strongly in a global regression on annual-mean country-level temperature and GDP data.

The next thing we did was to look at whether there were differential impacts based on the GDP of the countries, so we stratified countries into three income groups with approximately equal number of countries in each group. There may be some indication of negative climate impact on GDP growth in the low- and high-income countries, but not at a level that would permit publication in a high-quality journal.

Regressions in the low-income countries are strongly influenced by India, which experienced both relatively modest warming and relatively high rates of GDP growth. Regressions in the middle-income countries are strongly influenced by China, which experienced both substantial warming and very high rates of GDP growth.

Some climate damage functions predict net benefits of global warming for cold countries and net harm for warm countries. Therefore, we did an analysis partitioning countries into three groups based on mean country-level temperature. The result of those regressions appear in the next figure:

Again, we do not see strong trends. One might project that warming would have the strongest negative influence in the highest-temperature countries, but no strong signal emerges from this data. The signal of climate damage, if it is there, appears to be overwhelmed by other factors that influence rates of GDP growth.

We understand that there are many things we could have done to try to account for other sources of variability with the aim of isolating the effects of climate change as a residual. However, after consideration, we decided this was not a good application of our time.

It is possible that future climate change might produce a large amount of damage even if historical climate change did not cause a lot of damage. (It should be noted that there are a number of studies identifying historical climate damage, for example Callahan and Mankin [2022].) Many so-called “climate damage functions” do not show substantial climate damage below 1 C of warming but then show substantial climate damage at higher warming levels.

We thought about preparing this analysis for peer-reviewed publication, but the basic conclusion is that there are many factors that affect GDP growth, and that without considering those factors it is difficult to discern a signal of multi-decadal warming trends on multi-decadal GDP growth .

In closing, I would like to remind people that I have spent most of my professional life working on better understanding climate change and helping to facilitate a transition to a global economy that does not rely on using the atmosphere and oceans as waste dumps for our CO2 pollution.

Our analysis comparing half-century trends in temperature change with half-century trends in GDP growth for the period 1971-2020 did not provide strong evidence for a relationship between these two parameters. However, our uncertainty range is so large that our analysis does not serve to exclude a very strong historical relationship between temperature change and GDP growth. Our failure to provide compelling evidence for this relationship is not evidence that this relationship does not exist.

NOTE: The calculations and figures presented here were done by Lei Duan, working interactively with me.

ALSO NOTE: Others, including Richard Newell and colleagues, have done more sophisticated analyses addressing this issue.

A colleague asked me about whether I would sign on to an effort that would effectively ban most research on solar geoengineering. Here is a lightly edited response.

A few points:

1. The main problem with this letter is that it is an assault on freedom of research that is in-itself benign. 

I don’t see that banning outdoor research on solar geoengineering is different in kind from the Catholic Church banning Galileo from dropping balls off the leaning tower of Pisa.

There should be a presumption that if an experiment is expected to lead to negligible direct harm, that the experiment can go forward unless it would lead to an expectation of imminent harm that could not easily be averted by other means.

2. I am increasing critical about people signing onto policy positions where it is not entirely clear whether the person has special expertise related to the issues contained therein.

If I sign a letter saying Trump should be prosecuted for his crimes, nobody will think that I have special insights into Trump’s crimes or appropriate legal processes.

But if I sign onto a letter like this, a reader might reasonably assume that I have special expertise on policy measures that would lead to international risk reduction. In fact, I have no such expertise.

I try to avoid signing anything that is in this grey zone, where it would not be clear to readers whether I was signing as a domain-area expert or merely as a concerned citizen with no special expertise.

3. As a matter of public policy, a no first use ban may or may not be effective at banning first use. I am not expert in the efficacy of such bans.

We can see how successful various international constraints were at stopping Russia from taking Crimea. Maybe having countries declare that they won’t do bad things helps to prevent bad things from happening, but maybe not. 

Were it clear that I was signing as a citizen, and not as someone with special expertise, I would sign onto a “no first use” ban.

4. As a practical matter, defining what is or is not solar geoengineering research will be very difficult as the definitions are based on establishing intent. 

Bad actors can still go ahead and study stratospheric chemistry, aerosol distribution techniques, effects of changes in diffuse radiation on ecosystems, climate effects of stratospheric aerosol loading, etc. They just need to do this without the intent of producing a system that would geoengineer the planet.

These sorts of bans will stop good actors and force bad actors to be less forthcoming about intent.

I recall with the iron fertilization experiments, many of the scientists could care less about iron fertilization as a climate mitigation tool, but they just saw the experiments as a chance to learn more about how marine ecosystems respond to nutrient additions. I think we can assume there are stratospheric chemists who might feel the same way about stratospheric aerosol release experiments.  

Politicians can fund these programs thinking of solar-geo as the use case with the scientists engaged in the study as pure science.

How are such cases to be adjudicated?  What are the proposed procedures if you do an experiment and I think your intent is really to learn about solar geoengineering? Do I take my charges to some sort of inquisition so that they can determine what is truly in your heart of hearts?

I was asked by a journalist to comment on a paper. Here is an edited form of part of my response.

Thought evolved over evolutionary time to mediate between sensory perception and muscular action. Models are tools for thought, and help us to mediate between our perceptions and our actions.

Models are like crutches that allow our thinking to advance where it might otherwise be hobbled.

It would seem that recommendations of what sorts of modeling should be done should start with a discussion of what actions we are considering and what tools might be most helpful for informing decisions related to those actions, and then proceed to a discussion of the feasibility and resources needed to construct a model that could usefully inform decisions.

This question is particularly problematic when it comes to models involving social systems.

Clearly, there is some predictability to social systems: We can reliably predict that if political leaders engage in racially or religiously discriminatory speech that there will be an uptick in racial or religious violence within the society.

On the other hand, our primary goal is to inform decisions, not predict those decisions. We do not necessarily want to predict whether political leaders will engage in racially or religiously discriminatory speech, but rather inform the political leaders of the likely outcomes of their actions.

Further, while there is some predictive skill in predicting that increased prices will have a negative influence on demand, for example, the evidence of predictive skill for what we might call “future history” is limited at best.

There remains a major challenge in thinking through what sorts of models of social systems at global scale can usefully improve understanding and decision making at a cost that is commensurate with the value of generated information.

Much of my work gets done by way of “productive procrastination”, that is, working on things other than what I “should” be working on. This in an example.

There have been differences of opinion about how best to address the question of temporal discounting, especially with respect to intergenerational equity and the climate problem. In its simplest form, this question is often framed:

How should we be valuing the future?

Lately, I have been taking a different tack on addressing this question, asking :

Why do we value the future as much as we do, and not more and not less?

One way of thinking about the discounting question is to ask: What is the relative value of consuming a thing versus owning a thing? How do we compare the consumption value of a thing versus asset value of a thing?

I have been working on a simple mathematical model to explore these issues, as a kind of “fiction science” – a make-believe world that I hope shares properties with the real world, to function as a mathematical metaphor.

From working with this model, I have convinced myself that we value the future as we do because organisms that valued the future (or at least, valued having an asset more than they valued consuming it) increased their evolutionary fitness.

The squirrel that buried the acorn was more likely to survive and successfully reproduce than the squirrel that didn’t bury the acorn.

The psychology of valuing the future is a product of an evolutionary process that tends to increase reproductive success and evolutionary fitness.

In an earlier version of my model, the agents hoarded assets until they had sufficient assets to achieve reproductive success. This led me to ask a question that I had never thought of before:

Why do we value current consumption as much as we do, and not more and not less?

If we are comparing consumption value versus asset value of a thing, we need to ask not only why we value the asset as much as we do, but also why we value consumption as much as we do.

And I think the understanding of consumption value largely parallels the understanding of asset value. We value consumption because consumption increases our evolutionary fitness.

If that squirrel did not eat acorns today, the squirrel will die and fail to reproduce. Note that the squirrel doesn’t die right now if it does not eat the acorn right now. Eating the acorn right now is another form of investing in the future.

Consumption value and asset value are two forms of investing in the future, and the balance between consumption value and asset value is the balance that tends to increase reproductive success and evolutionary fitness.

Humans are not squirrels. I doubt squirrels explicitly think very far into the future.

Evolution gives us psychological properties that manifest in unpredictable ways. Evolution, for example, did not select for the ability to play chess, but the ability to play chess is nevertheless a product of our evolutionary past.

One of the properties of human psychology is, when given the opportunity, we tend to consume far in excess of what might be thought to be optimal for maximizing fitness.

Diseases related to obesity and over-eating are rampant in wealthy societies.

Further, people who have enough money, often consume expensive clothing, automobiles, live in large and expensive homes, and so on. They display their consumptive behavior.

What is the explanation for the human tendency to want to consume far in excess of what might be thought sufficient to maximize fitness?

One possible contributing factor is that humans evolved in a resource limited environment, so that we evolved to consume as much as we possibly could, because in most of our evolutionary history, consuming as much as you possibly could directly maximized fitness.

However, one might also imagine that earlier in our past, consuming beyond what was needed to sustain life signaled to potential mates that a potential partner would have the resources to feed and care for offspring – and thus increase reproductive success.

Our drive to consume beyond what is needed to sustain our lives may be in part a consequence of a psychology that improved our evolutionary fitness by signaling our desirability as mates.

Observations indicate that financially successful people tend to be more sought after as mates than people who are living at a subsistence level.

The potential mate that is able to give valuable gifts is likely to be the potential mate that can provide for offspring, increasing reproductive success and evolutionary fitness.

People’s happiness tends to be associated with their amount of consumption relative to their peers, and less so to absolute levels of consumption. This is consistent with the drive to consume being closely tied to social signaling functions that increase evolutionary fitness.

Our drive to excessive consumption might be a bit like the peacock’s tail – something that, absent the signaling value, would decrease our evolutionary fitness; something that is maintained through sexual selection.

One might imagine that, in evolutionary equilibrium in a simple system with perfect information, the marginal benefit to fitness from consumption would equal the marginal benefit to fitness from savings. This, I think, is the conceptual underpinning of determination of the optimal savings rate from the perspective of evolutionary fitness.

Of course, we are not slaves to evolution.

We have a neo-cortex that not only allows us to play chess, but also allows us to be thoughtful about how we might increase our evolutionary fitness.

If our drive to excessive consumption is damaging the planet, we can use reason to develop ways to meet our psychological needs while lessening this damage. (An alternative is to deny our psychological desires, but this seems to be a much more difficult path both psychologically and politically.)

The increase in value from the service sector relative to the manufacturing sector (for example, the value we get from books, movies, music, and so on) points to ways that we can satisfy desires to consume with relatively little impact in the material world.

Rather than asking people to consume less, we can work on dematerialization of value generation. This can be done by expanding the service sector, for example by increasing the value of information and social relationships.

The internet is be a major step forward in human history. We are interacting with each other, often in real time, without the need for transportation. We are consuming music and videos and video games that can be replicated at very low marginal cost.

We may be entering a new era of increasingly dematerialized consumption may allow us to reconcile our evolutionary past with a future that places fewer material demands on our environment.

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I thank Harry Saunders and Juan Moreno Cruz for contributing to some of the ideas expressed here.

A CURATED TWITTER FEED

Twitter is interesting because if forces you to try to say things in 280 characters. This tends to lead one to speak in Yoda-like aphorisms or make gross over-simplifications. (And on Twitter, there is no shortage of people to remind you of the myriad ways in which you are over simplifying.)

Also, for those insufficiently disciplined to compose offline and tweet only carefully edited tweets, Twitter is all about rough first drafts, preserved forever, warts and all.

Twitter is odd because it is both ephemeral and eternal — ephemeral in the sense that thoughtful tweets tend to get lost in the sands of time; eternal in the sense that some thoughtless boneheaded comment is there to pursue you for the rest of your life.

That all said, this blog post, which I expect to evolve over time, will be my place to dust the sand off of some old tweets so that they might live on a bit longer.

By the way, my “not-so-professional” Twitter account is @KenCaldeira.

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A postdoc asked a question about being prescriptive and/or normative in academic papers, noting that some of the people with the most successful scientific careers were scientist/activists who did not shy away from saying in their technical work what we should do or what is good and what is bad.

My response:

It is fine to say “I think we should do XYZ” or “XYZ is good [or bad]” in an opinion piece in academic or informal settings.

But is it OK to make those kinds of statements in regular academic research papers?

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A starting point is that there are multiple paths and strategies to success and you have to do something that fits your personal style and also takes account the reality of the job market.

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I was trained on Hume’s distinction between empirical and prescriptive/normative statements.

My feeling has always been that we as scientists are trained to generate and disseminate information and our opining on public issues was just our hobby, not our profession.

That said, I am not above language of the sort: “Policy makers should consider doing XYZ” rather than coming right out and saying “Do XYZ”. 

This may seem rhetorical artifice, but there is implicit acknowledgement in that construct that I may be wrong in my recommendation when a broader range of facts is considered.

I am probably near one end of the spectrum of wanting to keep recommendations to a minimum in academic papers (research suggestions, factors for policy consideration).

Others say that the distinction between opinion/informal pieces and scientific/technical reports is artificial and all that is required is transparency.

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When something is written in an academic paper, it should be true and you should stand behind it for all time.

Usually the errors are not in what you did, but errors in interpreting the implications of what you did. Often the error is believing your result applies more generally than it does.

When I look back since graduate school, my policy prescriptions have evolved, but I stand by all of the basic findings I have published over the years.