The Carbon Footprint of Bitcoin

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JOURNAL Joule
ARTICLETITLE The Carbon Footprint of Bitcoin
AUTHORLIST Christian Stoll, Lena Klaaßen, Ulrich Gallersdörfer

The Carbon Footprint of Bitcoin
Christian Stoll,
1
,
2
,* Lena Klaaßen,
3
Ulrich Gallersdörfer
4
Abstract
Participation in the Bitcoin blockchain validation process requires specialized hardware and
vast amounts of electricity, which translate into a significant carbon footprint. Here we
demonstrate a methodology for estimating the power consumption associated with Bitcoin’s
blockchain based on IPO filings of major hardware manufacturers, insights on mining facility
operations, and mining pool compositions. We then translate our power consumption estimate
into carbon emissions, using the localization of IP-addresses. We determine the annual
electricity consumption of Bitcoin, as of November 2018, to be 48.2 TWh, and estimate that
annual carbon emissions range from 23.6 to 28.8 MtCO2. This means that the level of emissions
produced by Bitcoin sits between the levels produced by the nations of Jordan and Mongolia.
With this article, we aim to gauge the external costs of Bitcoin, and inform the broader debate
on the costs and benefits of cryptocurrencies. The externalities we discuss here may help policy-
makers in setting the right rules as the adoption journey of blockchain has just started.
1
MIT Center for Energy and Environmental Policy Research, Massachusetts Institute of Technology, Cambridge,
MA 02139, USA
2
TUM Center for Energy Markets, TUM School of Management, Technical University of Munich, Germany
3
TUM School of Management, Technical University of Munich, Germany
4
TUM Software Engineering for Business Information Systems, Department of Informatics, Technical University
of Munich, Germany
* Contact: cstoll@mit.edu

1
Introduction
In 2008, Satoshi, the pseudonymous founder of Bitcoin, published a vision of a digital currency
which, only a decade later, reached a peak market capitalization of over $800 billion.1,2 The
revolutionary element of Bitcoin was not the idea of a digital currency in itself, but the
underlying blockchain technology. Instead of a trusted third party, incentivized network
participants validate transactions and ensure the integrity of the network via the decentralized
administration of a data protocol. The distributed ledger protocol created by Satoshi has since
been referred to as the ‘first blockchain’.3
Bitcoin’s blockchain uses a Proof-of-Work consensus mechanism to avoid double-spending
and manipulation. The validation of ownership and transactions is based on search puzzles of
hash-functions. These search puzzles have to be solved by network participants in order to add
valid blocks to the chain. The difficulty of these puzzles adjusts regularly in order to account
for changes in connected computing power and to maintain approximately ten minutes between
the addition of each block.4
During 2018, the computing power required to solve a Bitcoin puzzle increased until October
more than fourfold, and heightened electricity consumption accordingly.5,6 Speculations about
the Bitcoin network’s source of fuel have suggested, among other things, Chinese coal,
Icelandic geothermal power, and Venezuelan subsidies.7 In order to keep global warming below
2°C – as internationally agreed in Paris COP21 – net-zero carbon emissions during the second
half of the century are crucial.8 To take the right measures, policy makers need to understand
the carbon footprint of cryptocurrencies.
We present a techno-economic model for determining electricity consumption in order to
provide an accurate estimate of the carbon footprint of Bitcoin. Firstly, we narrow down the
power consumption, based on mining hardware, facilities, and pools. Secondly, we develop
three scenarios representing the geographic footprint of Bitcoin mining, based on pool server
IP, miners’ IP, and device IP-addresses. Thirdly, we calculate the carbon footprint, based on
the regional carbon intensity of power generation.
In comparison to previous work, our analysis is based on empirical insights. We use hardware
data derived from recent IPO filings, which are key to a reliable estimate of power consumption
as the efficiency of the hardware in use is an essential parameter in this calculation.
Furthermore, we include assumptions about auxiliary factors which determine the power usage
effectiveness (PUE). Losses from cooling and IT-equipment have a significant impact, but have

2
been largely neglected in prior studies. Besides estimating the total power consumption, we
determine the geographical footprint of mining activity based on IP-addresses. This
geographical footprint allows for more accurate estimation of carbon emissions compared to
earlier work.
Previous academic studies, such as predictions of future carbon emissions,9 or comparisons of
cryptocurrency and metal mining,10 are based on simplistic estimates of power consumption,
and lack empirical foundations. Consequently, the estimates produced vary significantly among
studies, as listed in Table 1.
Power consumption [MW]
Carbon emissions [Mt CO2]
2017
2018
2017
2018
Vranken11
100-500a
Bevand12
470-540b
Mora9
69j
Foteinis13
43.9k
De Vries6
7,670e
Krause10
948c
3,441f
2.9-13.5l
McCook14
12,080g
63m
Digiconomist15
7,744h
25.8n
This study
364-1,727d
5,501i
23.6-28.8o
Table 1 | Power consumption and carbon emission estimates in previous studies. The data reflect the power
requirements at a specific date. Thus, the data are presented in power (W) rather than energy (J). a. power
consumption as of 1/1/2017, b. as of 2/1/2017, c. 2017 average, d. power consumption range in 2017; PUE of
1.11 considered, e. power consumption as of 03/2018; calculated by assuming miners spent 40% of all revenues
on hardware and 60% on electricity, f. first six months 2018 average, g. as of 07/2018; PUE of 1.25 considered,
h. as of 11/2018; calculated by assuming 60% of revenues are spent on operational costs including electricity,
hardware, and cooling costs, i. as of 11/2018; PUE of 1.11 considered, j. carbon emissions as of 2017;
calculation based on the flawed assumption that the number of transactions drives power consumption, k. carbon
emissions as of 02/2018; including Ethereum, l. carbon emission range calculated using the median daily power
consumption from 01/2016 to 06/2018 multiplied by CO2 emission factors of seven countries, assuming all
miners would be based in one of these countries, m. as of 07/2018; using a world average CO2 emission factor,
n. as of 11/2018; using an emission factor of 0.7 kg CO2 per kWh for 70% of the power consumption (based on
China’s average emission factor), and assuming clean energy for the remaining 30%, o. as of 11/2018; range
reflects three footprint scenarios with respective local carbon intensity of power generation.
We show that, as of November 2018, the annual electricity consumption of Bitcoin had a
realistic magnitude of 48.2 TWh. We further calculate that the resulting annual carbon
emissions range between 23.6 and 28.8 MtCO2; a ratio which sits between the levels produced
by Jordan and Mongolia.16 The magnitude of these carbon emissions, combined with the risk
of collusion and concerns about control over the monetary system, might justify regulatory
intervention to protect individuals from themselves and others from their actions.

3
Mining hardware
Bitcoin prices for 2017 chart a curve shaped like an upturned hockey stick, and boosted the
investment made by network participants in mining hardware. First-generation miners used
central processing units (CPU) in conventional personal computers with computing power of
less than 0.01 gigahashes per second (GH/s) and an efficiency of 9,000 joule per gigahashes
(J/GH). Over time, miners switched to graphics processing units (GPU), with 0.2-2 GH/s and
1,500-400 J/GH in 2010 and, starting in 2011, moved to field-programmable gate arrays
(FPGA) with 0.1-25 GH/s and 100-45 J/GH.17 Since 2012, application-specific integrated
circuit (ASIC) devices, with up to 18,000 GH/s and less than 0.1 J/GH have prevailed.18
Figure 1 charts the market price (in USD per Bitcoin (USD/BTC)), network hash rate (in
petahashes per second (PH/s)), and resulting profitability threshold (in J/GH), where miners’
income equals cost. Comparing this profitability threshold to the efficiencies of mining
hardware shows that only ASICs operate profitably nowadays.
Fig. 1 | Bitcoin market price, network hash rate, profitable efficiency, and hardware efficiencies of ASICs
released by major mining hardware producers. Values are charted at monthly intervals. Hash rate and market
price were retrieved from Blockchain.com (https://www.blockchain.com/charts)5. Calculations of the profitable
hardware efficiency are reported in Supplementary Notes Sheet 3.6. We assume an average electricity price of
USD 0.05/kWh as argued in previous estimates.12,15 A detailed overview of ASIC mining hardware releases can
be found in Supplementary Notes Sheet 4.1.
From IPO filings disclosed in 2018, we determine the distribution of market share held by the
three major mining hardware producers; Bitmain, Canaan, and Ebang. The hardware in use and
its efficiency are key to a reliable estimate of power consumption. Based on the IPO filings, we
conclude that, as of November 2018, Bitmain’s hardware provides 76% of the network’s
computing power, and the hardware of each of Canaan and Ebang provides 12% (see
Supplementary Notes Sheet 3.2; the IPO filings are embedded in Sheet 3.4).
0.0
0.2
0.4
0.6
0.8
1.0
1.2
1.4
1.6
1.8
2.0
2.2
0
5,000
10,000
15,000
20,000
25,000
30,000
35,000
40,000
45,000
50,000
55,000
[J/GH][USD/BTC] / [PH/s]
Canaan [J/GH]
Hash rate [PH/s]
Market price [USD/BTC]
Profitable efficiency [J/GH]
Ebang [J/GH]
Bitmain [J/GH]
Jul-16 Jan-17 Jul-17 Jan-18 Jul-18 Jan-19

4
Mining facilities
There is no typical size of cryptocurrency mining operations, but a wide scale ranging from
students who do not pay for their electricity (some of whom applied to support this research),19
to gamers who leverage their graphics cards whenever they are not playing (as reflected in
Nvidia’s volatile sales allocated to crypto),20 all the way up to dedicated, large-scale crypto-
mining farms (for instance, in abandoned olivine mines in Norway).21
Depending on the scale of mining operation, auxiliary efficiency losses may occur in addition
to losses caused by mining hardware. The two main categories of auxiliary losses are cooling
and IT-equipment. We classify miners into three groups according to the scale of their
operation: small (S) miners provide less than 0.1 PH/s (equal to seven of the most efficient
ASICs), medium (M) miners provide less than 10 PH/s, and large (L) miners provide more than
10 PH/s. This classification is based on our personal communications with miners.
For large-scale miners, we use the power usage effectiveness (PUE) of Google’s most efficient
data center of 1.09.22 For medium-scale miners, we use a PUE of 1.15, based on personal
communication with mining companies in Germany. For small-scale miners, we assume a
moderate efficiency of 1.12, as higher losses from dust and cable inefficiencies are more than
offset by the lack of a need for cooling (see Supplementary Notes Sheet 2 for a sensitivity
analysis of this assumption).
We determine the distribution among these three categories using Slushpool data, displayed in
Figure 2. Slushpool is a mining pool, which provides live statistics on the computing power of
connected users.23 By assuming that distribution is the same in the rest of the network, we
determine that 8% are small, 27% are medium, and 65% are large-scale miners, resulting in an
overall PUE of 1.11.
Fig. 2 | Hash rate distribution of Slushpool grouped by individual miners’ computing power. Data
generated in web scrawling of Slushpool pool statistics (https://slushpool.com/stats/?c=btc)23, data reported in
Supplementary Notes Sheet 3.7. Source code available under https://github.com/UliGall/cfootprint_bitcoin.
4.0
0.0
1.0
2.0
5.0
3.0
6.0
EH/s
11/01/18 11/30/18
S
M
L

5
Mining pools
Miners combine their computing power and share the block rewards and transaction fees in
order to reduce the time and variance of finding a new block. Back in January 2011, a miner
with an up-to-date GPU (2 GH/s) could expect to find more than two blocks a day. In November
2018, due to the increasing difficulty, the same miner could expect to find a block every 472,339
years. Even today’s most powerful ASIC (18,000 GH/s) yields an expected discovery rate of
one block every 52 years (the calculations can be found in Supplementary Notes Sheet 4.3).
The average time it takes to find a new block depends on the network’s current level of difficulty
and computing power of the hardware in use. The average number of hashes to be computed in
order to solve a block, is given by the difficulty multiplied by the number of hashes per block
(each block has 248/65535 hashes). The difficulty adjusts every 2016 blocks to account for
changes in connected computing power in order to maintain approximately ten minutes between
the addition of each block.4
Solving a block is rewarded with new Bitcoins and the fees of all newly-included transactions.
The reward per block in new Bitcoins started at 50 for the first blocks and halves every 210,000
blocks. At the current number of blocks in November 2018 (552,100), the block reward equals
12.5 Bitcoins per block and as a result, 1,800 (=12.5 x 24h x 6/h) new Bitcoins are currently
mined every day. As the time to solve one block remains constant and the reward continues to
halve, the last of about 21 million Bitcoins will be mined in 121 years from now.
Nowadays, nearly all network participants are organized in public pools or self-organized private
pools. Thereby, more than two-thirds of the current computing power is grouped by Chinese pools,
followed by the 11% of pools registered in the EU, as depicted in the chart in Figure 3.
Fig. 3 | Hash rate distribution among mining pools as of November 2018. Data pulled from btc.com
(https://btc.com/stats/pool?percent_mode=latest#pool-history)24 and reported in Supplementary Notes Sheet 4.2.
17%
12%
10%
9%
9%
5%
11%
10%
12%
3%
3%
BTC.com
AntPool
ViaBTC
SlushPool
DPOOL
BTC.TOP
Huobi.pool
F2Pool
Poolin
Others
Unknown
Chinese pools (68%)
European pools (11%)

6
Power consumption
Prior to estimating a realistic level of electricity consumption by Bitcoin, we narrow down the
solution range by calculating a lower and an upper limit. The lower limit is defined by a scenario
in which all miners use the most efficient hardware. The upper limit is defined as the break-
even point of mining revenues and electricity costs. Figure 4 charts the range including our
best-guess estimate, which follows the approach of the lower limit, but includes the anticipated
energy efficiency of the network, based on hardware sales and auxiliary losses (see Methods
for details).
Fig. 4 | Power consumption corridor. Values are charted at daily intervals. Data are reported in Supplementary
Notes Sheet 3.2-3.3. Sensitivities are shown in Supplementary Notes Sheet 2.
Figure 4 shows that the upper limit of power consumption is more volatile as it follows the
market price of Bitcoin. The lower limit is more stable as it is defined by hardware efficiency
and hash rate. We estimate a power consumption of 364 MW at the end of 2016, 1,727 MW at
the end of 2017, and 5,501 MW in November 2018, based on auxiliary losses and ASIC sales.
By multiplying the power consumption as of November 2018 with 8,760 hours, we get an
annual power consumption of 48.2 TWh.
0
10,000
20,000
30,000
40,000
50,000
Electricity load [MW]
Lower limit
Best-guess
Upper limit
Jul-16 Jan-17 Jul-17 Jan-18 Jul-18 Jan-19

7
Mining locations
Below, we develop three scenarios examining the regional footprint of Bitcoin, which are based
on the localization of pool IP, miners’ IP, and device IP-addresses. Some miners may use
services like TOR or VPN to disguise their locations, for instance, for legal reasons. However,
as a good overall network connection increases the probability of having a new block accepted
in the network, it is generally advantageous to propagate blocks through the fastest connection.
Based on pool IP-addresses on BTC.com and Slushpool, which are the largest mining pool
administrated in China and Europe, we find evidence that miners tend to allocate their
computing power to local pools. In both pools, regional miners comprise the vast majority of
participants. U.S-based miners tend to join the European pool as the operation of mining pools
is prohibited inside the U.S. Combining these insights from pool server IP-addresses with pool
shares in terms of their regional origin, we determine that there is 68% Asian, 17% European,
and 15% North American computing power in the network (see Supplementary Notes Sheet
3.1, 4.2 and 4.5).
Based on miner IP-addresses, we find a stronger U.S. presence. The full nodes and miners in
the network communicate via a peer-to-peer network. Information (such as new transactions or
blocks) are sent to connected peers via a gossip-protocol, reaching all nodes in a timely manner.
Therefore, we monitor the IP-addresses relaying new blocks recorded by Blockcypher.25 We
detect different patterns in the data: In some cases, single IP-addresses are responsible for many
blocks, while, in other cases, many addresses are only responsible for a small portion of blocks.
As for the location of our server, our data set is biased towards the U.S., as over 95% of the
mined blocks are on U.S. soil. If we assume a share of 15% for U.S.-based mining devices, we
find 34% of all blocks originate from Asia, 24% from Europe, and 24% from Canada, while the
rest of the world (South America, Africa, and Australia) are each responsible for less than 1%
of the blocks created. Uncertainties are introduced by the server location, the decentralized
nature of the network, and the resolution from IP-addresses to location by ipinfo.io. Figure 5
displays the origins of blocks on a world map (The source code is available under
https://github.com/UliGall/cfootprint_bitcoin).

8
Fig. 5 | Local footprint of Miner IPs. Locations are reported in Supplementary Notes Sheet 4.6.
Based on device IPs, we can confirm the U.S. concentration. We identify the location of ASICs
via the IoT-search engine Shodan. By searching for connected ASICs, we can view the
distribution on a national level. We are able to localize 2,260 ASICs of Bitmain, and the query
results support the U.S.-concentration (19%). Venezuela (16%), Russia (11%), Korea (7%),
Ukraine (5%), and China (4%) appear next on the list, and Figure 6 charts all the locations of
internet nodes with connected Antminers.
Fig. 6 | Local footprint of Device IPs. Map and data from IoT-search engine Shodan (https://www.shodan.io)26
as reported in Supplementary Notes Sheet 4.7.
Comparing Bitmain’s eleven mining farms in China – which total about 300 MW capacity – to
our estimated total network load of more than 6 GW leaves enough space for the North America
concentration instead of the expected China concentration. Bitmain’s publicly announced
projects in Texas, Tennessee, Washington State, and Quebec support these findings.27

9
Carbon footprint
We calculate Bitcoin’s carbon footprint based on its total power consumption and geographic
footprint. To determine the amount of carbon emitted in each country, we multiply the power
consumption by average and marginal emission factors of power generation. Our best guess is
based on average emission factors, which represent the carbon intensity of the power generation
resource mix, while marginal emission factors account for the carbon intensity of incremental
load change.
We find that the annual global carbon emissions of Bitcoin range between 23.6 and 28.8 MtCO2;
a ratio which sits between the levels produced by Jordan and Mongolia.16 23.6 MtCO2 is based
on the footprint derived from device IP-addresses, assuming the footprint of miner IP-addresses
totals in 24.3 MtCO2, and pool IP-addresses mark the upper limit with 28.8 MtCO2 (emission
factors from IEA28; the calculation of the three scenarios can be found in Supplementary Notes
Sheet 3.1.).
Many have argued that clean resources fuel Bitcoin to a significant degree. However, unless
there is excess zero-carbon power capacity, even the skimming of renewable electricity leads
to shortages in surrounding grid areas. These shortages are generally covered by fossil fuel
resources. If we assume that the additional load additional load accredited to Bitcoin mining
has to be covered by the additional consumption of fossil fuels such as coal or natural gas, we
find that annual carbon emissions caused by Bitcoin could be as high as 53.6 MtCO2, in a
footprint scenario of device IP-addresses and 100% coal based power generation (all remaining
combinations of footprint scenarios and marginal emission factors of gas and coal are depict in
Supplementary Notes Sheet 1). Therefore, we consider our best guess estimate as conservative.
Some have argued that miners do not operate continuously. We assume the hardware runs
continuously throughout the year. A comparison of break-even electricity prices for ASIC
mining hardware shows that this assumption is valid for most fixed rate retail tariffs, and
especially for regions with high mining activity (see Supplementary Notes Sheet 3.5). The
steadiness of hash rate distribution in Figure 2 supports this assumption. Therefore, we consider
potential additional sources of revenue from price volatility in the wholesale market or from
the provision of load-balancing services as irrelevant.
As listed in Table 1, recent estimates of the global carbon emissions of Bitcoin vary
significantly among studies between 2.9 and 63 MtCO2. Our approximation based on empirical
insights underlines the need to tackle the environmental externalities that result from Bitcoin.

10
Social cost and benefit
Our approximation of Bitcoin’s carbon footprint underlines the need to tackle the environmental
externalities that result from cryptocurrencies,29 and highlights the necessity of cost/benefit
trade-offs for blockchain applications in general. We do not question the efficiency gains that
blockchain technology could, in certain cases, provide. However, the current debate is focused
on anticipated benefits, and more attention needs to be given to costs. For cryptocurrencies with
proof-of-work protocols, policy-makers should not ignore the following aspects:
Carbon. As global electricity prices do not reflect the future damage caused by today’s
emissions, economic theory calls for government intervention to correct this market failure in
order to enhance social welfare. The issue of the social cost of carbon is of course not specific
to cryptocurrency. Nonetheless, regulating this gambling-driven source of carbon emissions
appears to be a simple means to decarbonize the economy.30
Concentration. The case of Bitcoin shows that the risk of concentration must not be ignored.
Irrespective of the decentralized nature of Bitcoin’s blockchain, the four largest Chinese pools
now provide almost 50% of the total hash rate, and Bitmain operates three of these four pools.
If one player controls the majority of computing power, it could start reversing new
transactions, double-spend coins, and systematically destroy trust in the cryptocurrency.
Control. With their idea, Satoshi intended for Bitcoin to increase privacy and reduce
dependency on trusted third parties.2 However, protecting individuals from themselves and
others from their actions might justify the downsides of central control, as the potential benefit
of anonymity spurs illegal conduct such as buying drugs, weapons, or child pornography.
Therefore, a use-case specific degree of central governance is essential. Today, most
intermediate parties serve useful functions, and a decentralized socio-economic construct like
blockchain should only replace them if it can ensure the same functionality.

11
Beyond Bitcoin
Bitcoin’s power consumption may only be the tip of the iceberg. Including estimates for three
other cryptocurrencies adds 30 TWh to our annual estimate for Bitcoin alone.31,32 If we assume
correlation to market capitalization, and only consider mineable currencies (unlike second layer
tokens or coins with other consensus mechanisms), the remaining 618 currencies could
potentially add a power demand over 40 TWh.1 This than more than doubles the power
consumption we estimate for Bitcoin.
While other blockchain platforms (e.g., the second largest cryptocurrency, Ethereum) develop
on switching protocols from Proof-of-Work to other, less energy-consuming consensus
mechanisms, such as Proof-of-Stake, it is likely that Bitcoin will continue to use the established
algorithm. Miners, who have a large influence on the development of Bitcoin, are not interested
in removing the algorithm, which is central to their own business. Therefore, it is likely that
Bitcoin will remain the largest energy consumer among public blockchain systems, and will
continue to consume a considerable amount of energy.
Besides cryptocurrencies, there are other uses for blockchain. Bitcoin has managed to establish
a global, decentralized monetary system, but fails as a general purpose blockchain platform.
For instance, Smart Contracts are seen to disrupt traditional business models in finance, trade,
and logistics. Like many earlier disruptive technologies, blockchain is merely the foundation
and enabler of novel applications.33 Alternative protocols will help to reduce the power
requirements of future blockchain applications, and many blockchain-based systems will
certainly be private, permissioned blockchains, which do not need a Proof-of-Work like
Bitcoin. Notwithstanding, our findings for the first stage of blockchain diffusion underline the
need for further research on externalities, in order to support policy-makers in setting the right
rules for the adoption of these technologies.

12
References
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14
Methods
This section provides the methodology for calculating the range of power consumption, and the
approach to derive a best-guess estimate.
(1) Lower limit
The lower limit is defined by a scenario in which all miners use the most efficient hardware.
We calculate the lower limit of the range by multiplying the required computing power –
indicated by the hash rate – by the energy efficiency of the most efficient hardware:
    , (1)
with:
-    
-     
- 
= energy efficiency of most efficient hardware

.
(2) Upper limit
The upper limit is defined by the break-even point of revenues and electricity cost. Rational
behavior would lead miners to disconnect their hardware from the network as soon as their costs
exceed their revenues from mining and validation:
 

 , (2)
with:
-    
-    
-    
-     
-    
-     .
(3) Best-guess
The best-guess estimate follows the approach of the lower limit, but includes the anticipated
energy efficiency of the network, as well as further losses from cooling and IT components:
     , (3)
with

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-    
- 
    

-        .
The realistic energy efficiency of the network can be determined using the market shares of
mining hardware producers and the energy efficiency of the hardware in operation:
  

      

   , (4)
with
-
i = mining hardware producer (1, ..., n)
- 
    

-        
- 
  
   
- 
 
   .
If some of the computing power cannot be assigned to one of the major mining hardware
producers, we assume this computing power originates from hardware, which generates zero
profit. By equalizing PLL and PBG, we derive:


 . (5)
In terms of the average losses from cooling and equipment, we differentiate between three types
of mining facilities according to size, and weight them by their share in terms of computing
power:
         ,
with
-       
-        
-             .
We derive the energy consumption by multiplying the power consumption by a respective time
period:
    ,
with
-    
-    .

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The resulting carbon footprint of the Bitcoin network depends on the carbon intensity  of the
power mix:
    ,
with
-   
-   .
In order to incorporate local differences in the carbon intensity of the power mix, we
differentiate among regions and weight them by computing power share:
       

 ,
with
-   
(1, ..., n)
-      .

17
Data availability
All data used in this analysis are included in the Supplementary Notes file [Link when
published], or publicly available online under the noted sources.
Acknowledgments
We thank Christian Catalini, Gunther Glenk, Isabel Hoekstein, Alexander Rieger, and
Antonio Teran for their valuable comments.
Author contributions
C.S. conceived of the study. All authors contributed to the design of the study and data
acquisition. L.K. and C.S. aggregated and analyzed the data. C.S. drafted the manuscript. L.K.
and U.G. reviewed several drafts, made substantial revisions, and provided additions.
Competing interests
The authors declare no competing financial or non-financial interests.