Theorem: the control over the resources in every consensus ordering system will be power-law distributed. No counter example will be discovered.
In the real world, there might be
inertia acting in the system, such as the middle class has
income, which is the counter-force to their getting poorer. In Kansanmarkka in particular, all classes receive the same amount of income, greatly resisting the (natural and often beneficial) tendency to power law distribution.
Hence, wealth tends to follow power law in the top-3% only.
Source: Pietilä, 2013 & al
Coincidentally I am writing about that point also in a non-published section of my white paper:
Satoshi's Proof-of-Work
1. Permissionless free market to stand up a consensus ordering (i.e. mining) node.
2. Power-law mining distribution is unstable trending toward winner-take-all devolution.
3. Transaction fees are not a free market because of the block size, regardless whether block size is fixed or variable.
4. No parallelization scaling. Only the node that produces the next block may add transactions during the block period.
5. 51% attack on minority blocks can't be objectively observed.
6. Orphans blocks. High transaction confirmation latency. Confirmation only probabilistic, never final.
7. Wasteful and inefficient.
1. Satoshi's design enables anyone to stand up a mining node without any permission required from the system. In practice due to variance, most miners need to pool their hashrate[Meni2011]; and due to the winner-take-all issue pools could potentially become a choke point requiring permission in the future. To generate an economic return, proof-of-work mining requires the purchase of ASIC mining equipment which can't be generally repurposed.
2. A normal system in nature is small things grow exponentially faster than large things. Most small things don't grow large enough to become stable large things, e.g. the competing saplings in the forest, because they have more competition and friction, e.g. a higher portion of a lower income is budgeted for food instead of savings and investment. A stable power-law distribution appears to be one where large things peak and decay, which retains competition and renewal.
Satoshi's design appears to be a power vacuum which can only reach equilibrium at winner-take-all on mining, thus appears to be incongruent with a long-term stable power-law distribution. Examples include the selfish mining attack and propagation delays, all of which accrue more than proportional rewards (thus accumulating ever more hashrate) to those with more hashrate due to wasted mining of the others¹. Also there is variance[Meni2011] and the cost of verifying a disproportionate volume of transactions. These factors force miners into pools and ostensibly eventually the winner-take-all pool. We can't presume that a multitude of pools aren't all controlled by the same entity behind the scenes, i.e. a Sybil attack on objective decentralization of the network hashrate.
As explained in the Power-law Distribution Control section, the long-term stabilty of the power-law distribution is not the same as the Nash equilibrium of the game theory of the protocol.
Perhaps I can somehow add a few words about external income, but I am trying to keep the white paper concise enough.
Risto I think you are happiest doing mental work and being around people who are positive.
I hope you can set up a good environment for such. I don't think it is reasonable to expect the best of such people to travel to your castle. I mean it is probably a wonderful place to visit, but you know people have conflicting priorities and preferences (for example in my case the #1 priority is to get to Singapore in January and to not disrupt the work I am doing every day until then, albeit at a slower pace due to my health problem, and Estonia
in the winter wouldn't be compatible with my athletics and love of warm, sunny climate ... although the Philippines is too hot and humid).
Also until I get cured, I won't be much of conversational companion, not like I was before. I mean especially not at your level of intellect/bandwidth. I can often not speak clearly and can't sustain a dialogue for too long before running out of energy. I somewhat slur my words and/or weak/crackling voice now because of this illness. Some days I do better. It varies.
