Just to make sure we understand ourselves, I noted that higher pledge ratio ( s/σ ) was necessary in order to prevent Sybil attacks, not absolute value. Do you agree on that?
Yes, I do.
But I don’t see at all how this is a flaw of my proposal, or how this is relative to my proposal at all, and even less how this justifies to further disadvantage small pools in the official scheme.
With our proposal, attractive small pools will grow to saturation (if people behave rationally), in yours they won’t.
We are aiming for stake being roughly distributed equally among the k most attractive pools. Your proposal won’t achieve that. Your small-pledge pools would be unattractive, so people would instead delegate to pools that already have 1/k stake, so those pools would grow even bigger, which is exactly the centralization we want to avoid.
Note that the motivations of a small pool may not only be short term profitability. Some will want to start small and grow progressively, some might want to take a position foreseeing ADA price increases, and some might simply want to participate in securing the network, not trusting it if they don’t participate to it directly.
They can do this under our scheme as well. The pledge-influence factor is quite low and won’t have a big effect on profits anyway.
I do understand, and I do understand that after such a large amount of work, it can be hard to reconsider, although It might be best to do, at least to think about it.
Certainly. We are always willing to improve if something better comes along. The point is that even if some idea sounds good, it needs to be analyzed very carefully before it can be put into effect. We know our scheme may not be perfect, but we at least understand the mathematics and know it has the desired properties.
It has the properties that you saw as the desired properties at that time, but it might not have all the desired properties that we did not necessarily think about yet. For example the cartel problem I showed above could not be analyzed with game theory and Nash equilibrium (on the contrary), and yet is obviously a very big problem.
We want the system to have the following desired properties: Lead to an equilibrium with k pools of equal size (roughly), be as fair as possible while at the same time being secure against Sybil attacks. I think those properties are very desirable indeed.
I don’t agree with what you call the “cartel” problem, I think you misunderstand the way “desirability” of pools is calculated: We use so-called “non-myopic” desirability to calculate pool ranking, which roughly means we look at potential rewards, not actual rewards. So in your hypothetical scenario, where we already have k saturated pools, and a new pool comes along, that new pool can be ranked very highly from the very beginning, no matter how big it is. It won’t need higher pledge than existing pools in order to be competitive. As long as its combination of pledge, costs, performance and margin is good, it will be highly ranked and attract delegation.
Furthermore, things like your “cartel problem” can certainly be analyzed with game theory. We haven’t done this in our existing paper, but it can certainly be done.
Overall I feel that you did not yet answer my questions for now, especially it could be usefull for everyone to have an answer point by point to the flaws I saw in your scheme ( Cartel attack, partial protection against Sybill Attacks, unnecessary unfairness and complicated), and to show me any flaw really specific to the reward scheme I propose.
I’m sorry about that. Here we go:
- cartel attack: based on a misunderstanding of how pool ranking works (see above).
- unnecessary unfairness: We believe that unfairness is a price you have to pay for Sybil protection. It’s a trade off, and the Community will ultimately decide how important one is in comparison to the other. As I tried to explain above, your suggestion is unfair in exactly the same way by making pools with higher pledge more attractive to users. Your proposal has the additional problem that it doesn’t prevent centralization.
- unnecessary complicated: It was the easiest scheme we could think of that had the desired properties of leading to an equilibrium with k pools of equal size while offering Sybil protection. If anybody can suggest a simpler scheme with the same properties, we’ll certainly be happy to consider it. The formula may be complicated, but the ideas are actually quite simple: Cap rewards at saturation to enforce decentralization, and make pledge matter to prevent Sybil attacks.
So we can deepen things if you wish. (Or, because I don’t want to be a burden leading an endless discussion, if you wish I can also leave you alone, and leave the community, while benevolently alerting you that from my point of view, I don’t see how keeping this rewards scheme will not lead to severe problems in the future.)
I’m indeed busy, as you can imagine, but I’m nevertheless happy to discuss, as long as we keep it rational and respectful. This is clearly a topic of great importance to the system, so we should try to explain it as well as possible.
We believe the scheme will work, but in the unlikely event that it doesn’t, we can always improve it.
by
. Nothing else. Nothing fancy, No further change needed for this switch to make sense. (let’s forget about changing the probability formula for now and suppose we leave as you did: the probability to validate block is strictly proportional to the real stake)