An Alternative to a0 and k

You are correct, in that, as I alluded, I see it that both systems do not incentivize decentralization directly. I would argue that a good metric for decentralization is not as straightforward as the number of pools or even the number of SPOs. To me, a better metric would be the average number of unique block producers per epoch. Even this can be somewhat skewed though. This proposed solution is meant to be more of an iterative improvement on the current method, as a “best” solution (in my mind at least) is likely to require re-examining PoS entirely. I hope that the current solution is both more equitable and would lead to an easier analysis of the state of the network (i.e. as there is no/less incentive to split pools the number of pools more closely relates to the degree of decentralization than in the current system).

To answer if I think an artificial k is still a better option, I would say no, not in its current form. I would say that it is worse because it can lead to a false sense of security in the network. We could have k=1000 pools, but if 80% of the blocks were to be produced by the same entity, we’d be no more decentralized than when Shelley first released. Aside from the decentralization aspect, I find the current optimal rewards function overly-complicated by seemingly coupling with the monetary expansion term. Note: It would be great if someone could verify that this is the case, as I haven’t compared the true expansion with the intended expansion. Or if someone can link me to the reserves, T-T, (between Shelley launch and epoch 234) I could run the numbers myself.

That being said, the incentive for “real” decentralization with this solution is the same as in the current system, free market competition for resources. If a person thinks that they can provide a better stake pool service, then are free to compete with the rest of the market (on what I would consider a more level playing field with this proposal). On the flip side, a truly free market (no regulation) allows those on top to engage in anti-competitive behavior. Of course, if we go much further, the question becomes one about what behaviors a protocol can incentivize/enforce and what is outside of the domain of the protocol.

Thank you for the link, I hadn’t seen the other CIP! It looks similar to where I started with this proposal and think it could be an improvement. However, I also think that it muddies an already complicated optimal reward function by adding two more parameters. After a certain point, you might as well ditch an explanation of all of the parameters and just use the curve itself (lookup table). I went through and found CIP: change the reward formula which has a similar approach, but still puts a 1/k saturation limit (though I don’t necessarily share the proposers viewpoint on the subject, in general).

Edit: @danny_cryptofay linked me to some circulation/reserve data he has. I’m a bit confused about the drop at epoch 209, but if I’m interpreting it correctly it appears that the current optimal rewards function does indeed interfere with monetary expansion. The effective expansion coefficient appears to be closer to 0.0015 which is about 68% of the expected expansion coefficient of 0.0022 (see slopes in plot). I realize that I’m fitting a linear curve to an exponential decay, but at short time scales such as this, it’s a close approximation.
ADA Reserves

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