Decentralization
Defining a quantitative Decentralization Index for a Blockchain network running on Proof of Stake (PoS) consensus is not simple: a precise and rigorous definition of such a metric could easily fit as subject of an academic research (which is not the intent of this project).
So, how can we quantify PPoS decentralization?
Here is a proposal.
Consenus Protocol as Blockchain "engine"
To facilitate the presentation of our arguments for the definition of a Decentralization Index, let’s use an example that relies on the comparison of blockchain networks, running on PoS Consensus Protocols, with engines, exploring the concept of efficiency of a machine.
When mathematicians search for equations' solutions or when physicists do not know how to measure physical properties, they usually start investigating if such a solutions or properties have upper or lower bounds.
In 1842 the French physicist Nicolas Léonard Sadi Carnot discovered that the efficiency of any classical thermodynamic engine, that converts heat into work (or vice versa), must be lower than a theoretical upper bound represented by the efficiency of a purely ideal machine, named Carnot engine after him. Such a "perfect" engine is just a purely theoretical construct and cannot be built in practice.
This is probably the most elegant and general result in Classical Physics: it implies that any system undergoing any kind of thermodynamic cycle can only tend to the efficiency of a Carnot engine operating under the same conditions, never reach it, no matter how cleverly that system has been designed.
In the same way we try here to define an equivalent of a “Carnot engine” for PoS consensus decentralization.
Does such a theoretical decentralization upper bound even exist?
When should we say that a Blockchain running on PoS consensus is completely decentralized?
Decentralization factors
In order to reach a common understanding of what measuring decentralization even means, we should agree on some definitions.
We consider three different factors of decentralization that concur to define a Decentralization Index (\(DEX\)) of PoS networks:
- Nodes Hardware Decentralization (\(d_N\))
- Network Topology Decentralization (\(d_T\))
- Stake Decentralization (\(d_S\))
We have to quantify each of these three factors as bounded per-unit metrics so that the Decentralization Index can express "how far" a PoS Blockchain network is with respect to the “purely theoretical decentralization”.
The index can range from 0 (completely centralized) to 1 (completely decentralized):
\[ DEX = d_N \cdot d_T \cdot d_S \]
Let's try first to define an ideal theoretical condition of decentralization for each of those three per-unit factors. Then, everything deviating from those conditions will make a PoS Blockchain more real and far from platonic ideality.