1. merkle proofs more efficient in mixers using append only to store latest state

Layer 2: Leaders as temporary monopoly holders.

In layer 2 protocols like zkrollup we can only select a single entity to create blocks. We can cycle this responsibility. But in each block a single person has the monopoly to include/exclude any transactions.

Therefore we need to select a leader in such a way that minimizes the power of monopolys.

Proof of Stake

https://en.wikipedia.org/wiki/Proof-of-stake

Basically we randomly select someone to create a block. Where you chances of being selected is proportional to how much stake they have.

Proof of Burn

https://ethresear.ch/t/spam-resistant-block-creator-selection-via-burn-auction/5851

Basically we select the person who is willing to burn the most amount of ether in order to be allowed create that block. The idea being that a single honest person will bid the amount that they can get paid in fees while an attacker needs to out bid them imposing a cost on their attack.

Eth interest rates

On ethereum their are ways that users can deploy their capital to earn interest. Therefore any proof of stake system has to be competitive with their rewards. An indication of these kinds of rewards is 0.5% on chain 3.2 % per year on exchange (loanscan.io at the time of writing)

That means that total fees from transactions needs to be >= 0.5% of the stake in order to pay a compeditive reward.

Proof of Stake Censorship

If a staker can control 99% of the stake in a POS system it means that they can censor 99% of the through put. In such a case they have a huge power over the users of the system. They can basically prevent all transactions from being included.

Opertuntiy cost of ETH

Another thing that is important that in proof of stake stakers are paying a fee in order to be allowed to create the next block. That fee is the opertunity cost of their eth. The problem with paying in oppertunity cost is that someone who is holding eth is able to

Random number generation

In order to do proof of stake you need to do random number generation which adds alot of compeixty to the protocol including slashing users who do not reveal their randomness. This could be a huge incentive for miners not to include transactions from coordintaors.

Conclusion

I have laid out the case against proof of stake. I hope that someone can do the same for proof of burn. Also please let me know if any of my claims are incorrect. I hope to start a dialog here.