Thank’s a lot, but I don’t want to pretend or imply what is not true. I’ve not followed either all the formal proofs especially the ones corresponding to what seemed to me as obvious or intuitively true. I’ve also read the paper focusing on finding the motivation for choosing their formula and the advantage in comparison to other possibilities, and I’ve skipped sections that seemed irrelevant to that like numerical simulations.
So the problem is how to have a high enough Pledge to prevent Sibyl attacks, but not such a high pledge that small pool operators aren’t discouraged from participating, and that diversity is created amongst pools and within pools.
Rewards are therefore capped once the Pool reaches a certain amount of delegated stake (the saturation point)
In their formula ( and mine as well ) saturation when reaching 1/k, is not to prevent Sybill attacks , but to avoid the natural tendency to centralization, in order to share operating costs across only one pool.
Purely for the sake of an example, I will assume a Pool’s reward is capped at 10 ADA. If only 1 ADA is staked in that pool, the reward will be 10 per ADA. If there are 2 ADA, the reward will be 5 per ADA. If there are 10 ADA, the reward for each ADA is 1. After that point, any additional Stake will reduce everyone’s reward.
I’m not following you here, if we forget a0 and focus only on saturation point. It is stake that is limited not rewards. If Pool’s stake is capped at 10ADA and for 1ADA staked in that pool the reward is 10 per ADA, If there are 2 ADA it will also be 10 per ADA, If there are 10 ADA it will also be 10 per ADA, If there are 20 ADA it will also be 5 per ADA, If there are 100 ADA it will also be 1 per ADA.
But if the above mechanism were the end of the story, there would be no prevention against sybil attacks.
Yes indeed as mentioned above the saturation mechanism is not here to prevent Sybill attacks.
So a certain amount of pledge is required. The amount of the pledge works in tandem with the cost and the margin variables in the desirability rankings that wallets will publish. The higher the amount of pledge, the higher up in the rankings the pool will be.
However, the lower the costs and the lower the margin, the more desirable the pool will be, and the higher up in the wallet rankings it will appear. So a pool operator with high costs can compensate by having a higher pledge, and vice versa.
Yes to some extend a pool operator will be able to compensate low pledge with low costs. But only to some extend of course, if a0 is high enough, 0 fees may not be able to compensate for 0 pledge. But this is the purpose of all this, to force having some pledge.
The “strange factor” changes the importance of pledge compared to cost in the calculations of reward.
The strange factor removes any positive influence of pledge ratio for small pools. From what I understand, the authors did it intentional, for that purpose, because they feared a small pool ( or pools at “early stages” ) could very easily get a high pledge percentage and therefore get high RoS which would be an unfair advantage. Which as I said above I don’t think is an advantage at all. ( And on the contrary the strange factor does introduce actual unfair advantages )
A higher A0 value means that pools with higher pledge amounts can earn higher returns, because the final capped value of rewards for that pool will be higher. That pool with a high pledge amount should therefore be more attractive to delegators and appear higher in the rankings. An A0 value of 0 means the amount of the pledge has no influence, and pools will have the same returns regardless of pledge amount.
While IOHK is doing everything possible to strike the right balance when setting the initial value of A0
Unfortunatly it would appear IOHK is not, for now, doing everything possible, to make an informed choice about the reward scheme, after reviewing and discussing all possibilities (even though I agree this topic comes a bit late). I hope this can change. Please IOHK team, come here and let’s discuss!
the community later sees that the value is pushing things too far in one direction, the community can decide to change the value.
Yes the community can change the value of a0 but can the community decide to change the formula? To my mind there is no good value of a0. Too high is too unfair, too low is too insecure against Sybill attacks. The authors admit it “With respect to Sibyl attacks and the ‘rich get richer’ problem, in our scheme, increasing Sibyl-resilience affects inverse proportionally egalitarianism.”. But it is possible, (until I’m proven wrong) to have a solution that is both strongly secured against Sybill attacks and fair (and also decentralized): f(σ,λ)= R* min ( σ , 1/k , b0 * λ )
At the risk of annoying you with one more suggestion of something to look at, I liked the graphs in this article: https://iohk.io/en/blog/posts/2018/10/29/preventing-sybil-attacks/ as I finally could see the impact of the A0 value.
I’ve allready read this article before I opened this thread.
Someone how my notifications were turned off previously. So if you do decide to respond, I should be able to reply immediately I have enjoyed these exchanges and hope that all is well with you!
Thank’s a lot for your kindness, I really do appreciate very much .
I have to admit that I’ve been some times a bit too much on the defensive, being a bit “alone against all of them” is never easy.