[pa7x1]

What pushes towards centralization are two factors; economies of scale and barriers of entry. For those mathematically inclined you can imagine plotting economic reward (y-axis) vs economic input (x-axis). Economies of scale determine the shape and growth of the curve while barriers of entry determine the cut with the y-axis. Obviously, the greater the barriers of entry or the higher the reward as your economic scale grows the bigger the push towards centralization. In the first case because you forbid small actors to participate in the game, in the second case because you reward bigger actors more generously.

So how does this graph look for Ethereum? Pretty simple, if you have more than 32 ETH it's basically flat. You get the same APY irrespectively of your size. And if you have less than 32 ETH? Well, you can then stake with RocketPool (a decentralized staking pool) in which case your APY is 0.85 the full APY. So the graph for Ethereum is:

- 0.85 * APY between [0 ETH, 32 ETH)

- APY between [32 ETH, infty ETH)

Where APY is the yield returned by the network which depends on total amount staked in the network and network fee revenues.

This is a remarkably flat curve, which highlights that there are almost non-existent economies of scale in PoS as designed in Ethereum. If you do the same analysis for PoW you will find it requires significant investment in specialized HW (either top of the line GPU or ASICS), and there are significant economies of scale in the form of access to cheap or unusable sources of energy.

[ruuda]

> You get the same APY irrespectively of your size

On-chain, yes. But there is an off-chain cost to operating the validators, and there is economy of scale there. You can run many 32-ETH validators on a single machine using almost the same resources as running a single one, so the amortized cost of the hardware goes down. And when you do need to expand to multiple machines, the same applies; you don’t need 10× the people to manage 10× the machines. Of course, you can pay somebody to operate the validator for you, and those parties benefit from economy of scale.

[pa7x1]

Indeed. So let me flesh it out a bit more. You can run a validator using 100W (conservative figure) of energy and an Intel NUC with 2 TiB SSD (you can even run it on a Raspberry Pi but no need to be too greedy in HW resources).

That's 876 kWh in a year and 1000 $ in HW. Energy costs vary from place to place but let's pick 0,2 $ / kWh. Which results in 175 $/year in energy. The computer can easily last you 5 years if not more, so 200 $ per year. Let's add internet costs too. 30$ x 12 = 360 $ / year.

Those are the operational costs. Once you have 32 ETH this is pretty negligible.

[ruuda]

There is also the people cost. If you’re a hobbyist you could argue those are zero or there is only some opportunity cost. But for a professional validator, SRE salaries dwarf the hardware cost.

[pa7x1]

True, but these are costs that affect large scale operators so they are not a barrier to entry. If anything they highlight that in some ways a small hobbyist is positioned to be as profitable as a large scale operator.

[ruuda]

Yeah, that's true.

[Yizahi]

You don't take into account the social factors. People having a ton of tokens can easily freeze majority of them in the stake. People having a small amount of tokens won't be able to do so - first because they need them for a living expenses, second because they will be hit by transfer fees much more that people moving big amounts. This is all fine, but the system is deflatory, so this discrepancy will only increase and rate of it will also increase over time (accelerate). Basically big holders at the moment of the PoS switch will be the only big owners forever in the human history, and no new big holders can appear ever again.

[anonymousDan]

Interesting. Do you have any references to resources describing the theory of how economies of scale/barriers to entry interact?

[Hbruz0]

So if the graph is flat above 32eth, why not reduce that amount to lower the barrier of entry ?

[pa7x1]

Great question. You can check here how the 32 ETH came to be: https://github.com/ethereum/annotated-spec/blob/master/phase...

[jlokier]

A short technical answer is the beacon chain network wouldn't function properly if it had too many nodes (unless other parameters were also changed undesirably), so the number is limited.

32ETH was calculated to be approximately the sweet spot, optimising various parameters.

When this decision was made, back in 2018, it cost very much less than it does now.

There are secondary mechanisms for staking with less (RocketPool) but in these, below a certain threshold you don't participate in the beacon chain directly. Instead your stake is combined with others to allow someone to run a beacon chain node on your behalf collectively, with the rewards shared back to you, and a small cut taken off. The cut is why the graph changes below 32ETH.

[c0mptonFP]

> the beacon chain network wouldn't function properly if it had too many nodes

The fact that a decentralized P2P blockchain can have "too many nodes" is such a massive failure of engineering. It's honestly mind-blowing.

[jlokier]

It's probably not an engineering failure given current-day knowledge, because (as far as I know) nobody knows how to engineer a network that scales arbitrarily to any number of nodes while achieving total consensus (agreement) on all state every few seconds in a fair-decentralised and consistent manner.

The Ethereum blockchain does scale to more nodes and use scalable P2P networking algorithms. It is only the active beacon chain nodes which are constrained. Just as many users with "full nodes" in the current PoW network do not run a mining operation, not everyone needs to run a beacon chain validator to participate in a decentralised way in the PoS network.

You may think it sounds easy or natural to scale, but actually there are some difficult trade-offs when coordinating global consensus over all state at once. Because communication grows faster than O(n) for n nodes in a flat structure, one of the solutions to that is an uneven power-law network (like a hierarchy), or communication latency rising (along with costs), but both of those are undesirable factors when optimising for fair decentralisation with reasonable latency and costs.

These issues don't arise on other P2P applications such as file sharing and VPN onion routing. That's because they don't need to provide a real-time global consensus of all state on a fixed time scale.

Some blockchains offer low latency local-only consensus, or optimistic consensus which might be rolled back, but those are also a negative for some purposes.

There are some techniques for arbitrary scaling while keeping all the other desirable properties, but they are still open research problems. Some of the most promising techniques use zero-knowledge proofs, but those are mathematically very compute intensive and the current techniques can't run something as complex as Ethereum in real-time yet on an ordinary high-end PC.

Even the PoS beacon chain being readied for the Ethereum merge depends on fairly advanced mathematical cryptography to work.

It really isn't as simple as you imagine.