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(Mis)Understanding Economies of Scale and Centralisation in Proof of Stake


For background

I own both Ether and Bitcoin. I write this because I am concerned with what I see as a misunderstanding of centralising forces in Ethereum and the risks they pose. This piece looks specifically at what kind of economies of scale are present in proof of stake and how that leads to centralisation.

The argument from this week’s Bankless Podcast

On this week’s Bankless podcast (see 1 hour 15 mins in), David Hoffman makes a few points. He sees centralisation in Proof of Stake as a code orange, not a code red, issue. Notably, his view is that proof of stake is less centralising than proof of work because, amongst other arguments:

The core argument being made is that, because there are higher economies of scale in Bitcoin mining and higher returns, this results in stronger centralisation.

While I see point 1 above as plausible and point 2 as correct, I think the framing of what causes centralisation in Proof of Stake is wrong.

Framing centralising forces in Proof of Stake

The Bankless assessment finds low economies of scale in Ethereum staking because they consider stakers that put their own funds at stake. Yes, in specific case, to get a higher amount (absolute, not percentage) of staking rewards, you need to put a proportionally higher amount of capital at stake.

However, this is not what has happened to date with Ethereum proof of stake. Rather, a majority of Ether is staked through centralised providers, the largest being LIDO. Lido doesn’t stake its own funds — it stakes other people’s capital and takes a small revenue share. Lido domination is well covered at 20 mins and 50 seconds in the latest Bankless podcast.

So, in looking at economies of scale in Proof of Stake, one has to consider not the economies of scale of participants staking their own funds, but rather the economies of scale of centralised staking providers like Lido.

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Economies of scale of staking providers like Lido

What protocols or companies like Lido do is operate servers and code. That is their capital cost, which has some level of associated operating cost. Staking capital (Ether) itself is not a capital cost for Lido.

The returns, for Lido, come in the form of a share of staking rewards (10%).

So, Lido (and Coinbase and anyone else providing staking as a service) has:

For every added unit of Ether staked with Lido, there is negligible increased cost to Lido, but a linear increase in rewards share. Mathematically, the marginal cost of revenue is near-zero and the economy of scale is near-infinite (ok, infinite is an exaggeration, but the economy of scale is extremely large).

Economies of scale in Bitcoin

Again, I’m not here to bash proof of work or proof of stake. I own both Eth and Bitcoin and appreciate the innovation in each, but I hope we can come up with an even better form of security. I don’t think proof of work or proof of stake are the best we can do.

Bitcoin (proof of work) also has centralising forces in mining, but it is much more along the lines of typical industrial company economies of scale whereby there are savings on building bigger and bigger factories or mining rigs. I’ve run and sold a process engineering business with technology involving high energy consumption, and the rule of thumb is an economy of scale of 2/3rds. As an example, if you want to tenfold (10X) output (think hashpower/revenue), you need to multiply by five (5X) your capital invested in mining equipment (The scaling of cost is 10⁰.66). This is a much weaker economy of scale than for Lido, who can cater for much larger amounts of staked Ether (and thus income via rewards sharing) with very little marginal cost.

The economies of scale for mining are already visible in Bitcoin, with a relatively small number of mining pools dominating a majority of total hashpower. Still, there are some natural/geography based limits on how big a miner (and, less so, a mining pool) can become because of constraints on how much energy can be generated in any one location — whether that be hydro, coal or gas. So, there is perhaps some constraint on having just one large Bitcoin mining pool controlling a majority of hashpower, although I don’t rule out the possibility.

Yes, in Ethereum Proof of Stake, more servers in different locations might be needed to scale a staking provider like Lido, but the marginal costs of servers are very low compared to the marginal costs of power generation. The key point is that, because Lido doesn’t have to front the capital for Ether staked on its platform, it gets a massive economy of scale on its business model.

Solutions from here:

I think Vitalik understands well the risks above. In my opinion, these risks motivated his article End Game, which looks at how centralisation risks might be averted. One argument presented by Vitalik is that staking may become very centralised, but perhaps there can be sufficient independent altruistic non-validating nodes to hold the validators accountable and protect against double spends. I’m not so optimistic and fear that — for coordination reasons — leverage will rest with the staking providers, not non-validating nodes (even if there are always sufficient altruistic non-validating nodes on the network).

A better solution than Proof of Work or Proof of Stake is not obvious (some ideas here), but acknowledging the risks seems an important step that has not yet widely been taken.

For me, centralisation risks in Ethereum should be code red, but I see this not as the end of Ethereum, but as an opportunity to invent something better, within Ethereum or beyond.

Side-note: A rough analogy (shared with me by Cambridge Cryptographic) is to think of staking providers like banks. A banks holds deposits that it doesn’t itself own. It has roughly fixed costs (branches + servers + security) that increase only slowly as its deposits increase. At the same time, a bank earns a small percentage interest (the spread between what it lends at and what it borrows at) on deposits. So, the marginal cost of a bank’s revenue is quite low. This is a big part of the reason why banking is centralised and why most US dollars are held in a small number of banks in New York. Further, physical branches are perhaps one of the least scalable parts of banking in terms of costs — and there are no branches required to be a staking provider!

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