Gini Coefficients Of Cryptocurrencies

The Gini coefficient expresses a system's degree of inequality or, in the blockchain context, centralization. It therefore factors into arguments, like mine, that claims of blockchains' decentralization are bogus.

In his testimony to the US Senate Committee on Banking, Housing and Community Affairs' hearing on “Exploring the Cryptocurrency and Blockchain Ecosystem" entitled Crypto is the Mother of All Scams and (Now Busted) Bubbles While Blockchain Is The Most Over-Hyped Technology Ever, No Better than a Spreadsheet/Database, Nouriel Roubini wrote:

wealth in crypto-land is more concentrated than in North Korea where the inequality Gini coefficient is 0.86 (it is 0.41 in the quite unequal US): the Gini coefficient for Bitcoin is an astonishing 0.88.

The link is to Joe Weisenthal's How Bitcoin Is Like North Korea from nearly five years ago, which was based upon a Stack Exchange post, which in turn was based upon a post by the owner of the Bitcoinica exchange from 2011! Which didn't look at all holdings of Bitcoin, let alone the whole of crypto-land, but only at Bitcoinica's customers!

Follow me below the fold as I search for more up-to-date and comprehensive information. I'm not even questioning how Roubini knows the Gini coefficient of North Korea to two decimal places.

Most cryptocurrencies will start with a Gini coefficient of 1; Satoshi Nakamoto mined the first million Bitcoin. As adoption spreads, the Gini coefficient will decrease naturally. The question isn't whether, but how fast it will decrease.

On Steem, ckfrpark is concerned that it hasn't decreased anything like quickly enough:

Cryptocurrency as of September 2018, has not been narrowing the gap between the rich and poor but also is aggravating the inequality in our society. Based on the three major cryptocurrency wallets, Bitcoin, Ethereum and Ripple, top 1% shares the property value of the rest 99%, resulting in a drastic figure of Gini coefficient of 0.99. If we consider those who do not own a cryptocurrency wallet, it would result as radical figure of over 0.999999 Gini coefficient.
...
The greater the value of Cryptocurrency, the greater the gap between rich and poor, which governments and people will not tolerate. It is a prophecy that existing cryptocurrencies will fail.

Balaji S. Srinivasan is CTO of Coinbase, a cryptocurrency insider. In July last year, together with Leland Lee, he wrote Quantifying Decentralization, arguing for the importance of measuring decentralization:

The primary advantage of Bitcoin and Ethereum over their legacy alternatives is widely understood to be decentralization. However, despite the widely acknowledged importance of this property, most discussion on the topic lacks quantification. If we could agree upon a quantitative measure, it would allow us to:

• Measure the extent of a given system’s decentralization
• Determine how much a given system modification improves or reduces decentralization
• Design optimization algorithms and architectures to maximize decentralization

Source

Srinivasan and Lee start with an explanation of the Gini coefficient and the Lorenz curve from which it is derived. They go on to make the important point that a decentralized system is compromised if any of its decentralized subsystems is compromised, identifying six subsystems of cryptocurrencies; mining, exchanges, client, nodes, developers and ownership. Only the last has been the focus of most discussion of cryptocurrency Gini coefficients.

Source

They plot Lorenz curves for each of their six subsystems for Bitcoin and Ethereum, and derive these Gini coefficients:

Subsystem	Bitcoin	Ethereum
Mining	0.40	0.82
Client	0.92	0.92
Developer	0.79	0.91
Exchange	0.83	0.85
Node	0.84	0.85
Owner	0.65	0.76

These are rather large Gini coefficients, but in the case of the only one that Roubini and others have focused on, the distribution of wealth, it vastly underestimates the problem:

One important point: if we actually include all 7 billion people on the earth, most of whom have zero BTC or Ethereum, the Gini coefficient is essentially 0.99+. And if we just include all balances, we include many dust balances which would again put the Gini coefficient at 0.99+. Thus, we need some kind of threshold here. The imperfect threshold we picked was the Gini coefficient among accounts with ≥185 BTC per address, and ≥2477 ETH per address. So this is the distribution of ownership among the Bitcoin and Ethereum rich with >$500k as of July 2017.

In other words, even among the "whales" the distribution of wealth is extremely unequal (though not actually as unequal as North Korea). This, incidentally, explains the enthusiasm of the whalier Ethereum whales for "proof of stake" as a consensus mechanism. They could afford to control Etherum's blockchain by staking a small fraction of their wealth.

The reason why decentralization is attractive is that, if it were actually achieved in practice, it would make compromising the system very difficult. Srinivasan and Lee go on to point out that the Gini coefficient, while indicative, isn't a good measure of the vulnerability of a decentralized system to compromise. Instead, they propose:

The Nakamoto coefficient is the number of units in a subsystem you need to control 51% of that subsystem.

• It’s not clear that 51% is the number to worry about for each system, so you can pick a number and calculate it based on what you believe the critical threshold is.
• It’s also not clear which subsystems matter.

Regardless, having a measure is an essential first step and here are the Nakamoto coefficients of each subsystem:

Source

They compute the Nakamoto coefficients of Bitcoin and Ethereum, as shown in this table.

Subsystem	Bitcoin	Ethereum
Mining	5	3
Client	1	1
Developer	5	2
Exchange	5	5
Node	3	4
Owner	456	72

These are interesting numbers:

• 

  Source

  They show that Ethereum ("market cap" $21B) is significantly more vulnerable than Bitcoin ("market cap" $113B), reinforcing the observation that the Gini coefficient of the top 100 cryptocurrencies' "market cap" at 0.91 is extremely high. The smaller cryptocurrencies are very vulnerable to 51% attacks. Even Ethereum  currently suffers from the "selfish mining" attack, which has been known since 2013.
• They show the risk posed by software monocultures, driven by network effects and economies of scale. These risks were illustrated by the recent major bug in Bitcoin Core.

• 

  Ether Miners 10/10/18

  Even ignoring the fact that Bitmain:
  

  operates the world’s largest and second largest Bitcoin mining pools in terms of computing power, BTC.com and Antpool.

  so the 5 for Bitcoin mining should be 4, and that:
  

  two major mining pools, Ethpool and Ethermine, publicly reveal that they share the same admin

  they show that economies of scale mean mining pools are very concentrated. And that proving the 4 or 3 pools aren't colluding is effectively impossible.
• Only the top 456 wallets hold 51% of the Bitcoin held by the whales, and only the top 72 wallets hold 51% of the Ether held by the whales. There just aren't a lot of whales.

Gini Coefficient Based Wealth Distribution in the Bitcoin Network: A Case Study by Manas Gupta and Parth Gupta was published behind Springer's obnoxious paywall last July. Alas, the data upon which it is based is from 2013, so it despite its recent publication it is only slightly less out-of-date than the data that Roubini quoted.

An important, and much more up-to-date study of several different measures of decentralization (but that doesn't use the Gini coefficient) is Decentralization in Bitcoin and Ethereum Networks by Adem Efe Gencer, Soumya Basu, Ittay Eyal, Robbert van Renesse and Emin Gün Sirer:

in Bitcoin, the weekly mining power of a single entity has never exceeded 21% of the overall power. In contrast, the top Ethereum miner has never had less than 21% of the mining power. Moreover, the top four Bitcoin miners have more than 53% of the average mining power. On average, 61% of the weekly power was shared by only three Ethereum miners. These observations suggest a slightly more centralized mining process in Ethereum.

Although miners do change ranks over the observation period, each spot is only contested by a few miners. In particular, only two Bitcoin and three Ethereum miners ever held the top rank. The same mining pool has been at the top rank for 29% of the time in Bitcoin and 14% of the time in Ethereum. Over 50% of the mining power has exclusively been shared by eight miners in Bitcoin and five miners in Ethereum throughout the observed period. Even 90% of the mining power seems to be controlled by only 16 miners in Bitcoin and only 11 miners in Ethereum.

This shows how incredibly poor proof-of-work is at decentralization compared with conventional distributed database technology:

These results show that a Byzantine quorum system of size 20 could achieve better decentralization than proof-of-work mining at a much lower resource cost. This shows that further research is necessary to create a permissionless consensus protocol without such a high degree of centralization

Source

Raul at HowMuch.net published an analysis of the wealth distribution among Bitcoin wallets a year ago. It didn't compute a Gini coefficient but it did claim that only 118 wallets owned 17.49% of Bitcoin:

There are a couple limitations in our data. Most importantly, each address can represent more than one individual person. An obvious example would be a bitcoin exchange or wallet, which hold the currency for a lot of different people. Another limitation has to do with anonymity. If you want to remain completely anonymous, you can use something called CoinJoin, a process that allows users to group similar transactions together. This makes it seem like two people are using the same address, when in reality they are not.

BambouClub tweeted a superficially similar analysis at about the same time, again without computing a Gini coefficient,  but you had to read down into the tweet chain to discover it wasn't based on analyzing wallets at all. but on assuming that the Bitcoin distribution matched the global distribution of wealth.

Hannah Murphy's Bitcoin: Who really owns it, the whales or small fry? reports, based on data from Chainalysis, that in the December 2017 "pump and dump":

$30B Pump and Dump

longer-term holders sold at least $30 billion worth of bitcoin to new speculators over the December to April period, with half of this movement taking place in December alone.

“This was an exceptional transfer of wealth,” says Philip Gradwell, Chainalysis’ chief economist, who dubs the past six months as bitcoin’s “liquidity event”.

Echo in ICOs

Gradwell argues that this sudden injection of liquidity – the amount of bitcoin available for trading rose by close to 60 per cent over that period – has been a “fundamental driver” behind the recent price decline. At the same time, bitcoin trading volumes have now fallen in tandem with the prices, from close to $4 billion daily in December to $1 billion today.

As far as I know no-one has measured by how much this transfer of wealth from later to early adopters, and Bitcoin in the reverse direction, will have decreased the Gini coefficient. Or how much the transfer of cryptocurrency from speculators to ICO promoters will have increased it.