> Not sure if this is what you meant but there's no actual "yield boundary," it's a continuous function. The table just gives examples of the function outputs.

Yes, I see that now. Thanks again for the clarification (honestly, I wish they just put out a graph like literally everyone else does). Let me see if I can formulate my point now with their continuous function:

You had said up-thread:

> And while having fewer validators gives you a somewhat higher reward per validator, it's still that case that all validators get the same reward in any given block. Everyone is equally competitive. Someone who reinvests will get higher absolute rewards than they got before, but they pay the price of locking up more capital.

First, I think you meant "it's still the case that all staked coins get the same reward in a given block" (emphasis mine). The system doesn't know how many distinct validators exist, since a single entity can just simulate a bunch of entities.

Second, the fundamental issue here is that you have to do something that's at least as profitable (in ETH) as re-staking your coins to remain competitive with other stakers. Because staking ETH is intrinsically tied to block production, this has an impact on the system's overall resiliency with respect to how quickly new honest block producers can be brought online: honest block producers need to buy their way in. The higher the yield on ETH, the higher the barrier to entry for new block producers -- the equivalent to "difficulty adjustments" in PoW would be the price and yield of ETH crashing.

From a resiliency perspective, that's pretty bad -- the only way for new honest block producers to be able to afford to enter the system is to either (1) wait for the system to shit itself so badly that the market devalues it to the point where they can afford to join, or (2) amass enough wealth that they can buy the coins. Part (2) is problematic because this wealth threshold can easily be higher than the wealth threshold required to attack the network itself. For example, it could be cheaper to just steal coins, or bribe other people to cause competing block producers to get slashed.

Which brings me to your point here:

> Also, while losing over 1/3 results in a loss of finality, we'd be losing something that doesn't exist in PoW networks in the first place. The network continues to run[1], with a nonzero but low chance of reverted blocks, while the quadratic inactivity leak burns away stake until 2/3 of remaining stake is active again.

First, "loss of finality" here is the same as a liveness failure. A distributed system that implements a consensus algorithm using decisions made by fewer than 2/3 of the decision-making participants (staked coins in this case) cannot be BFT, by definition. You can't put a probability on finality here either (i.e. "low chance of reverted blocks" is a nonsensical statement), because if over 1/3 of the staked coins are malicious and under the control of an adaptive adversary, then the adversary always has a way to stop the remaining 2/3 from ever reaching agreement. Your only recourse here is to declare out-of-band that these coins are bad, manually and permanently slash them via a code patch, and restart the network by decree (at which point, what's the point of having a blockchain?)

Second, this means that there does not exist a BFT agreement algorithm that removes votes from the system with less than 2/3 of the original votes. Like, how do nodes even agree in a BFT way on who to slash? How do they even agree in a BFT way that it's been long enough for them to carry out a slashing? Again, because the over-1/3 of the coins are not participating honestly, and because the system must be BFT, this means that there's always a way for that over-1/3 coins to prevent the under-2/3 coins from deciding these things.

Now, it doesn't have to be this way. The problem of recovering from BFT liveness failures has been investigated before [2], even before Bitcoin existed, and one approach to recovery is to cause the system to permanently split into two systems (i.e. fork), with 2/3 votes on one side and 1/3 on the other. Maybe this is what Ethereum 2.0 will do? But if so, that kinda breaks the promise of finality -- it's up to each use to choose which fork represents the fork that did _not_ get compromised, and without PoW, it's really one validator set's word against another's (of course, both forks' sets will insist up and down that the other is the corrupted fork -- they're financially incentivized to do so).

> DDoS that knocked out over a third of the network, running on ISPs and hosting services all over the world on various independently-developed clients, would be quite a feat, and not likely to be sustained for very long.

Maybe this data is out of date by now, but as of September 2019 over half of ETH nodes run in datacenters (and of those datacenters, most run in Amazon) [1]. If these datacenter operators kill VMs or delay their network traffic (and to be clear, accidental outages do happen), then the coins staked on these VMs will get slashed. Also, the question to ask here what the distribution of distinct network paths that exist between staked coins looks like. If there are not many distinct network paths between staked coins -- i.e. if there are a few "choke points" in the network -- then these become the points of failure in the entire system. A BGP prefix hijack or a cut cable can lead to liveness failures, and whatever slashing behavior takes place from that.

> Since there will likely be plenty of non-staking ETH, more stake will be deposited after the attack, bringing the network back to the equilibrium of satisfactory returns.

If over 1/3 of the staked coins go offline, there's no way for the network to agree in a BFT manner on anything. That includes deciding to admit new ETH to staking.

> Or, if the attack were so severe it scared people off, then the price of ETH would also be affected, reducing the value of the attacker's stake.

If the attacker only cares about causing a liveness failure, the value of the ETH is presumably unimportant. The goal has been met.

[1] https://thenextweb.com/news/ethereum-nodes-cloud-services-am...

[2] https://www.usenix.org/conference/nsdi-07/beyond-one-third-f...