Today I saw
http://bytemaster.bitshares.org/article/2015/01/13/Decentralization-of-Nxt-vs-BitShares/ and became interested by the title enough to spend some time on reading. The article is related to
http://bytemaster.bitshares.org/article/2015/01/07/The-Most-Decentralized-Proof-of-Stake-System/ and the both analyze the same phenomenon (decentralization), so I will treat them as a single article.
I'd like to comment some things mentioned in the articles.
Today the numbers are in for Nxt with data from their very own block explorer. These numbers show that 60% of all blocks are produced by just 15 people.
I believe "people" means "accounts", we don't know how many people behind these accounts. There can be only 4 of them, or 400 (yes, one of the accounts can be controlled by a company which has its own hierarchy).
...I found enough block producers that were above 1% and less than 2% that I can safely conclude that after 720 blocks less than 101 unique block signers have confirmed the block.
I see a reference to the 101 delegates. I'd like to point that 101 is not a big number, someone could successfully control 10 such delegates or 20 delegates could collude. I can safely bet that the 101 delegates distribution follows Pareto's Principle that states that "80 delegates are controlled by 20 entities" (numbers may vary). The point of "101 is not a big number" is that order of magnitude of this number (let's write it as 99 + 2) is roughly the same as deviation caused by external factors. When a measured value has the same order of magnitude as errors of measurement scientists trash such measurements. The comparison of number of forgers and number of delegates in a 720-block window doesn't make sense to me because of this very reason.
What is even more interesting is the overall speed of the network. The Nxt blockchain aims for 1 minute blocks, but on average gets only one block every two minutes. You can see this on their blocks-per-day chart.
It's a long story why we have 2-minute blocks now, it doesn't influence distribution of forgers among forged blocks though and should be discarded.
Our delegates are far more reliable with near 100% participation compared to Nxt forgers at about 50% participation.
A number would be much better. One could argue that it's not "far more" but rather "a little bit more".
For Nxt to have a block confirmed by 101 unique individuals would require 7 hours best case.
This is an incorrect statement. Block generation and block confirmation are different things. All nodes confirm every single block indirectly by agreeing to propagate it over the network. All merchants confirm every single block indirectly by accepting money sent to them recently. All users confirm every single block indirectly by including the reference to a block generated 20 minutes back in their transactions.
If BitShares were to lose 50% of its delegates all at once due to a government crackdown the remaining 50 delegates would still be producing a more secure, decentralized, and distributed ledger with greater decentralization per minute than every other blockchain on the market.
I see a violation of CAP theorem there (if BitShares are decentralized). How do you know that a blockchain generated by remaining 50 delegates is legit while a blockchain generated by other 50 delegates is not?
For the sake of this article, I am going to define decentralization as the total number of unique individuals participating in the validation process such that no one individual is responsible for a disproportionate amount of blocks.
You have the right to define decentralization in such the way, but practical usefulness of this definition is quite low. It assumes that all individuals are equal in their power and their intentions to save the current state of things. One person who is able to protect blockchain against a reorg is more valuable than 100 others who are unable to do it.
If you want to have a million users participate in the consensus process then you will require a million computers all connected to the internet and consuming bandwidth.
No, we will not. Imagine that one of the nodes is a computer controlled by 1000 people (a company). In Nxt users without computers take part in the consensus too, via Economic Clustering (though it's almost not used now).
Each additional validator provides less and less value to the network despite costing the network the same.
It's true only for a system with a bad architecture. O(N) should be replaced by O(log N). I'm almost sure that Bitcoin, BitShares and Nxt networks are all follow O(log N) because nodes send packets to a fixed number of peers.
To cover operating expenses a crypto currency network must charge transaction fees.
Why? If usage of a cryptocurrency network generates extra profit itself then fees can be as small as it's enough for fighting spam. Hashcash could be used to remove fees completely.
These early proof of stake systems claim that they have greater decentralization than BitShares.
These systems can claim nothing. Only
some of their users can.
I skipped the rest of the article because there are already so much disagreements that the rest of the math from the article is worthless.
PS: It would be great to see comments on comments...
Read through the rest of that thread and you will find these blogs are written by a developer who hasn't implemented solutions to issues that have already been understood and solved (Byantine Generals problem). Right now, Come-from-Beyond's modelling sshows the bloggers crypto is vulnerable to attack from just 22 nodes (he voluntarily admits he doesn't know the theory behind cryptos, another referred to theory as 'ivory tower' development). Bitcoin only needs a handful of pool operators to collude.
While all crypto is bootstrapping, I think it would be wise not to throw stones when we all live in glass houses.
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. The facts are that people like Nxt and people use it. The blockchain data and the standard 100+ people online at nxtforum.org supports this. Open your eyes 
