Notable Works in Decentralization metrics

Notable works on “Decentralization Measurements” (Historical order) :

  • "Is Bitcoin a Decentralized Currency?"

    • Source: https://www.researchgate.net/publication/270802537_Is_Bitcoin_a_Decentralized_Currency
    • Citation: Gervais, Arthur & Karame, Ghassan & Capkun, Vedran & Capkun, Srdjan. (2014).
    • Summary: This paper describes centralization bottlenecks in Bitcoin and proposes some possible improvements.
    • The authors identify different concepts which tend to centralize Bitcoin such as the role of clients/client developers and the emergence of ASICs, mining pools, and tainted coins. They also describe improvements such as more decentralized mining pools, the diversification of available services (exchanges, wallets, etc.), and transparent decision-making from developers during client maintenance and implementation.
    • Tags: consensus, bft, ethereum
  • "The Meaning of Decentralization"

    • Source: https://medium.com/@VitalikButerin/the-meaning-of-decentralization-a0c92b76a274
    • Citation: Vitalik Buterin (2017).
    • Summary: This post discusses the definition of decentralization by describing three axes of “software decentralization” (architectural, political, and logical decentralization) and applies them to the blockchain.
    • The author studies blockchains’ properties (fault tolerance, attack resistance, collusion resistance) and their relations with ‘software decentralization’ axes. He identifies centralization bottlenecks in blockchains and suggests ways to improve them (better diversity of developers and implementations, proof of stake over proof of work, disincentive various collusion models)
    • Tags: consensus, bft, proof-of-stake, proof-of-work, ethereum
  • "Quantifying Decentralization"

    • Source: Quantifying Decentralization. We must be able to measure blockchain… | by Balaji S. Srinivasan | news.earn.com
    • Citation: Balaji S. Srinivasan and Leland Lee, (2017)
    • Summary: This post introduces the Nakamoto Coefficient, a quantitative measure of the decentralization of a blockchain system.
    • The authors explain that decentralization measures can help compare blockchains, but also monitor and optimize current architectures. They propose the Nakamoto Coefficient based on tools to measure non-uniformity within a population (Gini coefficient and Lorenz curve). They identify that blockchains are generally composed of six so-called “sub-systems” (mining, client, developers, exchanges, nodes, ownership) and that if a subsystem is centralized, the system is centralized. They apply their measures to Ethereum and Bitcoin sub-systems and discuss the pertinence of the results. In this response to the post, Buterin brought clarification to some of the subsystem metrics and discussed the limitations of using Gini.
    • Tags: consensus, bft, proof-of-work, ethereum
  • "Decentralization in Bitcoin and Ethereum Networks"

    • Source: [1801.03998] Decentralization in Bitcoin and Ethereum Networks
    • Citation: Adem Efe Gencer, Soumya Basu, Ittay Eyal, Robbert van Renesse, Emin Gün Sirer (2018).
    • Summary: This paper provides a comparison of the decentralization of Bitcoin and Ethereum based on node capacities and usages. They discuss known biases and limits of their metrics and dataset before suggesting improvements.
    • The authors focus on the resource capabilities using metrics such as the structure of the network (latency/geography), provisioned bandwidth, distribution of mining power, mining power utilization (pruned/uncle blocks network ratio), and fairness (pruned/uncle blocks miner ratio). To collect a consequent amount of data as accurately as possible, the authors deployed a “probe” connected to different Ethereum and Bitcoin nodes for one year. This research was one of the first large-scale, peer-reviewed, formal studies in the field of decentralization metrics.
    • Tags: consensus, bft, proof-of-work, ethereum
  • "Measuring Blockchain Decentralization"

    • Source: Measuring Blockchain Decentralization | ConsenSys Research | ConsenSys
    • Citation: Everett Muzzy and Mally Anderson (2019)
    • Summary: This paper introduces several categories and sub-systems composing a blockchain system. They identify pertinent decentralization measures for each sub-system.
    • The authors take a step back from their previous article by concluding that, due to their specificities (notably concerning consensus algorithms) and always-evolving architectures, blockchains are difficult to compare in terms of decentralization. They focus their research on the categorization of decentralization metrics that can be used regardless of the type of consensus algorithm. They describe 19 sub-systems within four categories of metrics present among any blockchain architecture. They apply these metrics to Ethereum and discuss the results.
    • Tags: consensus, bft, proof-of-work, ethereum
  • “Taxonomy of centralization in public blockchain systems: A systematic literature review”

    • Source: Taxonomy of centralization in public blockchain systems: A systematic literature review - ScienceDirect
    • Citation: Ashish Rajendra Sai, Jim Buckley, Brian Fitzgerald, Andrew Le Gear (2019)
    • Summary: This publication provides a systematic literature review of centralization in blockchains focusing on 89 identified papers (from 2009 to 2019). They build and iterate on a taxonomy through feedback acquired from experts interviews. The taxonomy provides centralization metrics and measurements but also highlights research gaps.
    • Authors describe in-depth the methodology leading to the selection of publications, metrics, and measurements (systematic literature review, interviews, cross-validation, etc.). Their taxonomy relies on a categorization of blockchains’ layers provided in this publication and being extended by adding additional layers etc. The authors highlight the fact that centralization has distinct aspects (13 identified) and discuss the significance (or the lack) of measurements. They compare different aspects of centralization in Ethereum and Bitcoin. This publication is one of the most recent, formal, and complete studies/literature reviews on decentralization.
    • Tags: consensus, bft, ethereum
  • "Measuring Decentrality in Blockchain Based Systems"

    • Source: https://ieeexplore.ieee.org/stamp/stamp.jsp?arnumber=9205256
    • Citation: S. P. Gochhayat, S. Shetty, R. Mukkamala, P. Foytik, G. A. Kamhoua and L. Njilla (2020)
    • Summary: This paper identifies the emergence of centralization in three “layers” of blockchain systems (governance, network, storage). They identify and apply layer-specific metrics to Ethereum and Bitcoin and discuss the results.
    • The authors first provide a summary of decentralization-measurement related works. Then they describe their own categorization of metrics before applying and discussing the experimentation results. They conclude that with time BTC and ETH nodes tend to centralize.
    • Tags: consensus, bft, proof-of-work, ethereum
  • “A Coefficient of Variation Method to Measure the Extents of Decentralization for Bitcoin and Ethereum Networks”

    • Source: http://ijns.jalaxy.com.tw/contents/ijns-v22-n2/ijns-2020-v22-n2-p191-200.pdf
    • Citation: Wu, K., Peng, B., Xie, H., & Zhan, S. (2020).
    • Summary: This paper describes a quantitative method based on a coefficient of variation (relative standard deviation) to evaluate the degree of decentralization for a blockchain system.
    • The authors provide a measurement method which can be applied to any metrics to estimate distribution/variability of centralization in blockchains systems. They apply their metrics to address balances (top 100 addresses) and blocks mined (a 7-day period in October 2018) in Bitcoin and Ethereum networks before concluding that, according to the chosen samples, Bitcoin’s mining and wealth is more distributed than Ethereum’s.
    • Tags: consensus, bft, ethereum
  • "Measuring Decentralization in Bitcoin and Ethereum using Multiple Metrics and Granularities"

    • Source: [2101.10699v2] Measuring Decentralization in Bitcoin and Ethereum using Multiple Metrics and Granularities
    • Citation: Qinwei Lin, Chao Li, Xifeng Zhao, Xianhai Chen (2021)
    • Summary: This article compares Bitcoin and Ethereum decentralization using three metrics and several temporal granularities.
    • The authors use the Shanon entropy, Nakamoto coefficient, and the Gini coefficient with different time periods (days, weeks, months) on mining power distribution. They conclude that the degree of decentralization in Bitcoin is higher, while it is more stable in Ethereum.
    • Tags: consensus, bft, proof-of-work, ethereum
  • "Against overuse of the Gini coefficient"

    • Source: https://vitalik.ca/general/2021/07/29/gini.html
    • Citation: Vitalik Buterin (2021).
    • Summary: This post discusses the limits of using the Gini coefficient as a measure of inequality in the blockchain context and suggests alternatives.
    • The author highlights that inequality in an internet community can come from a lack of interest (as opposed to a lack of resources in a geographic community). He suggests alternatives (Nakamoto coefficient, Herfindahl-Hirschman index, Theil L/T index) and tries to distinguish between the concentration of power and the lack of resources in the metrics.
    • Tags: ethereum
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Sami, I’m also very interested in the subject of decentralization … in terms of technology, but also politically in the sense that large centralized organizations quickly become ungovernable and ultimately corrupt. You’ve posted a very interesting collection of materials here. I’m curious about what’s going through your mind. Would you mind sharing a few of your thoughts about where you’re going with this? What is your ultimate purpose in collecting all of this information about decentralization? Are you developing a project?

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Ralph, the purpose of performing this state of the art about decentralization metrics was to build the foundations for an original research project which aims at exploring the solutions required for blockchains to improve decentralization. The goal is to abstract all the aspects of decentralization and highlight research gaps to provide directions for researchers to improve decentralization in their field of expertise. Discussions and collaborations will be stimulated around the expansion of the taxonomy provided in

The idea would be to follow the same exploratory research approach to describe threats to decentralization, how to measure those threats, and what could be the solutions to those threats. In this vein we will try to make the already existing taxonomy more up-to-date and complete to integrate any innovations and not covered aspect of decentralization.

Anyone who wants to collaborate is free to contact me!

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@Sami_B can you tell us a little bit about why this project would be useful? Why is it useful to develop these kinds of metrics? Would this be a tool for investors or would there be an engineering use for this project?

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Such research are useful because decentralization can be considered as the core property of blockchains. However centralization emerges under numerous forms (from voluntary trade-offs to gain on scalability but also from unanticipated situations) and there is currently no consensus on the decentralization’s terminology in the context of blockchains (some consider address balances as a representative metric while others may focus on miners’ concentration).
My vision is that blockchains’ decentralization has distinct aspects which still need to be explored (to identify centralization bottlenecks, their measurements, and their potential solutions). However we do not need to compare blockchains to improve their decentralization. Therefore the project will not aim to provide a scale of comparison or an audit tool but rather aim to highlight the risks of “centralized” approaches in order to provide direction for better models and usages.
As the research in this domain is still nascent, the research approach will be an “exploratory research” to define the scope of future research.

I will present the project and provide more details soon in a discussion post.

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We have open bounties available for anyone who can suggest additions, deletions, corrections or updates to this page. Please see forum for details.

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Decentralization, while meaning different things to different people is a common concept in blockchain. This awareness is the first step on the road towards harmonizing what it is and how it can be measured. This is why this list of notable works in decentralization metrics put together by @Sami_B are vital.

On that note, here are a few suggestions for additions to the list.

Mechanism Design and Game Theory

Is Decentralisation Even Real?

  • Source: https://hackernoon.com/is-decentralisation-even-real

  • Authors: Sharmini Ravindran

  • Description: This article looks at decentralization and how it features in decentralized finance (DeFi).

  • Relevance: This work, as a balance to other research focusing on the technical aspects, examines the economics aspects.

  • Citation: Sharmini Ravindran “Is Decentralisation Even Real?” in Hackernoon, Is Decentralisation Even Real? | Hacker Noon.

  • Tags: decentralization, game theory, regulatory

Mechanism Design and Game Theory

Decentralisation in the blockchain space

Mechanism Design and Game Theory

Defining Decentralization for Law

Mechanism Design and Game Theory

Blockchain technology and decentralized governance: Is the state still necessary?

  • Source: https://www.researchgate.net/publication/315919685_Blockchain_technology_and_decentralized_governance_Is_the_state_still_necessary

  • Author: Marcella Atzori

  • Description: This paper explores the potential of blockchain technology being used to decentralize societal governance.

  • Relevance: This work is one of the earliest works that researches the use of blockchain for societal governance and concludes that while technology could decentralize societal governance, the State would not be replaced, rather technology would complement.

  • Citation: Atzori, Marcella. (2017). Blockchain technology and decentralized governance: Is the state still necessary?. Journal of Governance and Regulation. 6. 10.22495/jgr_v6_i1_p5.

  • Tags: decentralization, game theory, regulatory

From @Sami_B’s list and the new suggestions, it appears that there are three categories in which decentralization can be considered: as it relates to (1) the protocol, (2) the token economics and (3) the users. All of these raise novel legal questions and must be the reason James @jmcgirk said he is “curious about the legal reasons for wanting decentralization metrics.”

There are several legal reasons for wanting decentralization metrics as seen in addressing issues relating to liability, jurisdiction, ownership and so on. There is a reason why the US Congress can summon Mark Zukerberg to answer for Libra, but not Satoshi Nakamoto to answer for Bitcoin. It is because, one is deemed to be centralized (Libra) and the other “sufficiently decentralized”.

On the issue of liability, decentralization could mean the absence of legal personhood and thus the infeasibility of identifying who should be held liable. On the flip side, a lack of decentralization means certain individuals or entities can be identified and held liable.

On the issue of jurisdiction, decentralization could mean no single terrestrial jurisdiction can be invoked. Nevertheless, it is possible to embed decentralized justice within any decentralization category.

On the issue of ownership, in the absence of legal personhood, it would be difficult to assign intellectual property rights to no one. Generally, there is usually a resort to making all intellectual property open source.

These issues are just a tip of the ice berg. I look forward to this research making significant progress and exploring more issues that corroborates the reason why knowing what decentralization is and being able to measure it is vital.

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Thanks for the suggestions @Fizzymidas, I already had a few from your list in stock and will work to incorporate them.

It’s interesting because your addition clearly illustrates the lack of legal aspect in the 1st version of the notable works.

Concerning these legal aspects, an interesting concept is the CRC one, which proposes a framework (an evaluation grid) to determine the proximity between a token and a security (noting that this framework has no legal value). They assign a score to the tokens based on scale from 1 to 5; 5 being the closest to a security. While this score has no judicial value, it allows to start “measuring” certain metrics and provide some guidance. Framework’s methodology/measurements try to answer to the “Howey Test” (test determining if an asset is a security) which is also mentioned in this publication.

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This appears to be decentralization as it relates to tokeneconomics.

I came across CRC last year through Dr Phillip Sander, one of the CBDC panellists. Although, I have not truly studied it.

Some lawyers have argued that the Howey Test is not an appropriate litmus test for determining if tokens are securities or not. But, I am not aware of any alternative. Moreover, different laws apply in different jurisdictions.

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I would be interested to see the rationalization as to how the Howey test would not be appropriate for determining if something is a security, as that is its specific purpose. SEC has released guidelines for token sales, but obviously, their rules do not apply across the globe.

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As a compilation of resources on “measuring decentralization” in blockchains (mostly Bitcoin + Ethereum), it is interesting how little scholarship is captured on this, and how most of it comes out of the blockchain community (Buterin, Balaji, Gun Sirer, etc).

Also, do people have more thoughts on the relative conclusions (i.e. "tends to centralize, or decentralized vis a vis’ more stable)?

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Yes many articles are not academic but the trend is reversing, as it has been with blockchains in general for some years. I think this pattern appears when the concepts are still immature, we see this in many innovations like DeFi or NFTs for example.

Concerning your question about conclusions, Ethereum and Bitcoin are mainly used as 2 references to execute such comparisons. Without taking any position, most publications show that Bitcoin is more “decentralized” than Ethereum on most of the used metrics. I will try to summarize some of the findings from the Notable Works list:

This article concludes that over time, ETH and BTC nodes tend to centralize, they also provide some comparison such as :

Mining pools

Extents of decentralization

This research concludes that Bitcoin is 27.3% more decentralized than Ethereum concerning block mined (and 16.5% concerning address balance).

In this one they conclude that ‘the degree of decentralization in Bitcoin is higher, while the degree of decentralization in Ethereum is more stable’ according to their multiple metrics and granularities:

  • ‘Compared with Bitcoin, Ethereum tends to be more stable but less decentralized in terms of the measurements of the Shannon entropy.’
  • ‘Compared with Bitcoin, Ethereum tends to be less decentralized, as revealed by the results of the Nakamoto coefficient.’
  • ‘Compared with Bitcoin, Ethereum tends to be significantly less decentralized in terms of the measurements of the Gini coefficient, which might be affected by the huge difference of the block production rates between Bitcoin and Ethereum.’

They conclude that, according to their metrics and data from 2016/2017:

  • ‘Bitcoin has a higher capacity network than Ethereum,but with more clustered nodes likely in datacenters’ , ‘Ethereum nodes are geographically further apart than Bitcoin’.
  • ‘In Ethereum, the block rewards have less variance than Bitcoin’s.’
  • ‘Ethereum has a lower mining power utilization than Bitcoin, likely due to the high block frequency.’ There are more pruned blocks in Ethereum which means the power is, in a sense, less efficiently used than in Bitcoin (but they recognize that their data may be incomplete).



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