I’ve made this table, to make things more visual. (Because I’m not sure everyone sees my point, according to the post you wrote above)
(1) The author admits their formula is not 100% fair: "With respect to Sibyl attacks and the ‘rich get richer’ problem, in our scheme, increasing Sibyl-resilience affects inverse proportionally egalitarianism.”
(2) I’ve set this in orange because even though a0 introduces some incentives to have pledge which lessens the possibility of Sybil attacks, there are serious drawbacks:
a-“Sibyl-resilience affects inverse proportionally egalitarianism”, so there is a need for a compromise, we cannot push unfairness too far off, so we cannot push Sibyl-resilience too far-off
b-We can only guess that the chosen value of a0 will give sufficient incentives to prevent someone creating many large pools without sufficient pledge level, but we cannot be sure of it (contrary to the formula I propose).
c-At the same time Introduction of a0 and variable RoS also impact negatively Sybill-resilience on an other side, because it incentize users to delegate according to RoS, so it discourages the natural tendency of users to delegate to someone or some organization they know directly and trust. This latter behavior is a very powerfull brakes on Sybill attacks.
(3) I mean by cartel attacks, a situation where a certain number of pools take a dominant position, and where a newcomer willing to replace one of them, would need to invest way more than any of the pool in the cartel did in the past in order to have a chance to replace them. Having such a cartel implies high risks of corruption. I’ve shown the proposed formula leads almost certainly to this cartel problem.
(4) The formula I propose is simple to understand because it can be summed up in one short sentence: “The reward and ability to create blocks of your pool is proportional to the stake of your pool, but the stake taken into account is limited to 10 times your pledge, and the stake taken into account cannot exceed 1/100th of the global stake”. You’re welcome to try and do the same thing with the other formula. (Values b0=10 and k=100 have been chosen randomly).