Quantifying Decentralization

Quantifying Decentralization
We must be able to measure blockchain decentralization before we can improve it.
By Balaji S. Srinivasan and Leland Lee
Jul 27 2017

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

In this post we propose the minimum Nakamoto coefficient as a simple, quantitative measure of a system’s decentralization, motivated by the well-known Gini coefficient and Lorenz curve.

The basic idea is to (a) enumerate the essential subsystems of a decentralized system, (b) determine how many entities one would need to be compromised to control each subsystem, and (c) then use the minimum of these as a measure of the effective decentralization of the system. The higher the value of this minimum Nakamoto coefficient, the more decentralized the system is.

To motivate this definition, we begin by giving some background on the related concepts of the Gini coefficient and Lorenz curve, and then display some graphs and calculations to look at the current state of centralization in the cryptocurrency ecosystem as a whole according to these measures. We then discuss the concept of measuring decentralization as an aggregate measure over the essential subsystems of Bitcoin and Ethereum. We conclude by defining the minimum Nakamoto coefficient as a proposed measure of system-wide decentralization, and discuss ways to improve this coefficient.

The Lorenz Curve and the Gini Coefficient

Even though they are typically concerns of different political factions, there are striking similarities between the concepts of “too much inequality” and “too much centralization”. Specifically, we can think of a non-uniform distribution of wealth as highly unequal and a non-uniform distribution of power as highly centralized.

Economists have long employed two tools for measuring non-uniformity within a population: the Lorenz curve and the Gini coefficient. The basic concept of the Lorenz curve is illustrated in the figure below:



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