Before we can increase the degree of blockchain decentralization, we must first know the measure.

Decentralization is widely seen as the main advantage bitcoin and Ethereum have over their traditional counterparts. Editor’s note: Here are four hyperlinks. However, despite widespread recognition of the importance of decentralization, most discussions on the topic have not been quantified. If we can agree on a quantitative measure, we can:

  • Measure the degree of decentralization of a system

  • Determine the impact of a change to the system on the degree of decentralization (increase or decrease decentralization)

  • Design optimization algorithms and architectures to maximize decentralization

In this paper, we propose the Minimum Nakamoto coefficient as a simple quantitative measure of the degree of system decentralization, inspired by the well-known Gini coefficient and lorenz curve.

My basic idea is to (a) list the basic subsystems of a decentralized system, (b) determine how many individuals in the system need to be destroyed to control each subsystem, and (c) then use this minimum value as a measure of the effective degree of decentralization of the system. The higher the value of the minimum medium background coefficient, the higher the degree of decentralization of the system.

To better understand this definition, let’s first give some background to the concepts related to the Gini coefficient and lorentz curve, and then show some graphs and calculations based on these metrics to see the current state of decentralization of the entire crypto ecosystem. We will then discuss the concept of measuring decentralization as a comprehensive measure of the fundamental subsystems of Bitcoin and Ethereum. We conclude by defining the minimum Satoshi coefficient as a proposed measure of system-level decentralization and discussing ways to improve this coefficient.

Lorentz curve and Gini coefficient

Although the two are generally of concern across the political spectrum, there are striking similarities between the concepts of “too unfair” and “too centralized.” Specifically, we can regard “unequal distribution of wealth” as highly unfair, and “unequal distribution of power” as highly centralized.

Economists have long used two tools to measure inequality within a group: the Lorentz curve and the Gini coefficient. The basic concept of the Lorentz curve is shown below:

The Lorentz curve is shown in red in the figure above. As the cumulative distribution deviates from a straight line, the Gini coefficient (G) increases from 0 to 1. Graphic courtesy of Matthew John.

The equation for the Gini coefficient can be calculated from the Lorentz curve shown below and the so-called “Line of equality” in the following areas:

— Lorentz curve and Gini coefficient

The Gini coefficient can also be calculated from the individual share of a continuously and discretely-distributed entity (see equation here).

Intuitively, the more evenly distributed the resources, the closer the Gini coefficient is to zero. Conversely, the more resources are distributed in one direction, the closer the Gini coefficient is to 1.

This captures our intuitive concept of centralization: in a highly centralized system with G=1, it only takes one decision maker and/or one entity to break the system. Conversely, in a highly decentralized system with G=0, breaking the system requires multiple decision makers. Therefore, a small Gini coefficient means a high degree of decentralization.

Cryptocurrency: Gini coefficient and Lorenz Curve

To get an idea, let’s take a look at the Lorentz curve and Gini coefficient with a simple example: the distribution of wealth within the capital of the cryptocurrency market. To this end, we show the market capitalization distribution of the top 100 digital currencies by market capitalization as of July 15, 2017, calculate their market share ratios, and make a Lorentz curve related to the Gini coefficient:

If we measure the centralization of the market capitalization of the top 100 digital currencies, the Gini coefficient is 0.91. This is in line with our intuition, as 70% of the entire market cap has been held by the top two digital currencies since July 2017, namely Bitcoin and Ethereum.

A decentralized system is made up of subsystems

To apply this concept to the realm of public chains, we need to distinguish between decentralized systems and decentralized subsystems. Specifically, a decentralized system (such as Bitcoin) consists of a series of decentralized subsystems (such as mining, exchanges, nodes, developers, clients, and so on). Here are the six subsystems that make up bitcoin:

– We will use these six subsystems to illustrate how to measure the degree of decentralization of Bitcoin or Ethereum. Note: You can use different subsystems depending on which one you think is more important to the degree of decentralization. –

Now, one could argue that some of these decentralized subsystems may be more necessary than others; For example, mining is absolutely essential to the operation of Bitcoin, yet exchanges (though important) are not actually part of the bitcoin protocol.

However, let’s assume that some individual can identify the basic decentralized subsystems in a decentralized system. We can then stipulate that if someone can break any of the basic decentralized subsystems of a decentralized system, that person can break the decentralized system.

Quantify how decentralized Bitcoin and Ethereum are

With these definitions, we now calculate the Lorentz curve and Gini coefficient of the system for the subsystems of Bitcoin and Ethereum mining, clients, developers, exchanges, nodes, and owners. We can judge the degree of decentralization of each system according to the Gini coefficient and lorentz curve.

Here’s the bitcoin curve:

Here’s the ethereum curve:

Let’s take a look at each of these subsystems in turn, using the six panels in each of the diagrams above as a reference.

(Editor’s note: There are no separate charts in the following sections of the original text; For ease of reading, the editor added a comparison chart made from screenshots.)

Degree of decentralization of mining

As shown in the upper left panel of the chart, by measuring block rewards over the past 24 hours, we find that bitcoin mining has become surprisingly decentralized. Ethereum mining is more centralized. These values vary considerably, so we can keep track or stabilize the results by averaging over the past 7 or 30 days.

Degree of client decentralization

As the panel at the top center of each chart shows, the majority of Bitcoin users use the Bitcoin Core client, while Bitcoin Unlimited is the second most popular client. This means that bitcoin is highly centralized, as measured by the number of different client codels (Gini coefficient =0.92). For Ethereum, the majority (76%) of clients are GEth, another 16% are Parity, and the Ethereum client code base has a Gini coefficient of 0.92, which makes up the majority of the ecosystem.

Degree of developer decentralization

In the upper right panel, we can see that the Bitcoin Core client has a large number of engineers contributing code to it. While the raw number of submissions is certainly an imprecise measure of contribution, it seems to indicate that a relatively small group of engineers did most of the work for Bitcoin Core. The development of the Ethereum Geth client was even more centralized, with only two developers contributing code.

Degree of exchange decentralization

Trading volumes for Bitcoin and Ethereum vary widely from exchange to exchange, as do the corresponding Gini coefficients. However, we calculated a snapshot of the Gini coefficient over the past 24 hours in the lower-left panel for presentation purposes.

Degree of node decentralization

Another measure of decentralization (bottom middle panel) is to determine the distribution of bitcoin and Ethereum nodes in different countries.

Degree of ownership decentralization

In the bottom right panel, we take a look at the degree of decentralization of bitcoin and Ethereum ownership, measured by the distribution of addresses. It’s important to note that if we were to include the 7 billion people on the planet, most of whom don’t own Bitcoin or Ethereum, the Gini coefficient would basically be 0.99+. If we were to cover all the balances, we would cover a lot of empty balances, and again we would have a gini coefficient of 0.99+. So, we need some threshold here. The incomplete threshold we used was the Gini coefficient for all accounts over 185 BTC and over 2,477 Ether. So this is the distribution of ownership of the bitcoin and Ethereum rich (who hold tokens equivalent to $500,000 or more) before July 2017.

Under what circumstances does a deterministic measure like this make sense? Perhaps in a scenario similar to the current IRS vs. Coinbase issue: the IRS is collecting data on all account holders with balances greater than $20,000. From an attacker’s point of view, a large Gini coefficient means that the government only needs to woo a few large holders to gain a large percentage of outstanding cryptocurrencies and the ability to control prices.

To sum up, two conclusions can be drawn. The first point: when a person doesn’t want BTC or ETH the gini coefficient of precision of 1.0 (because this time, only one person owns all digital currency, then no one will help improve the motivation of the network), and in fact the case still is the wealth of a high degree of centralized and decentralized protocol compatible. Second point: as shown below, we believe that The Satoshi coefficient is better than the Gini coefficient especially in measuring the degree of holder decentralization, because it eliminates the problem of arbitrariness in the selection of thresholds.

The original link: https://news.earn.com/quantifying-decentralization-eTranslated & proofread by Balaji S. Srinivasan and Leland Lee Zhang Ling & Elisa articles: the etheric fang lovers (https://ethfans.org/posts/quantifying-decentralization-part-1)Copy the code