In the sub-title the minFee = 30. I also show a case where minFee = 0 in the next chart.
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min fee is 30
The IOG plot does have “stake saturation” as the x-axis, but yours is “stake fraction”. I am looking forward to your updated document. Thanks!
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True! Also ‘modified behavior’ includes things like the SundaeSwap ISO or other ISO’s, smart contract staking, custodial wealth management pledging/staking, and exchange staking.
I’m in no rush. Cardano is stable and secure. The draft is maturing and there are still a few charts of data which are necessary for the “Motivation” (Histogram of Stake vs Pledge across the entire network by group). Based on the questions and feedback I’m also enhancing the technical communication of the core ideas.
This proposal is not based on game theory forecasts. The information presented is based on the benefit of more than a year of game-theory game-reality hindsight.
A re-name may be in order… “Shelley’s Basho Voltaire decentralization update”.
While waiting for your updated document, I have more questions in the meantime. Note that my knowledge about the ecosystem is very limited. Hence, the question(s). My question is related to the K-effective, and I am showing the figure on here again for convenience (and please correct me if I’m wrong with my interpretation).
My intuition as to why the K-effective is plateauing as the number of pools increases is perhaps because small pools as well as new pools (particularly SPOs) are not getting any delegation. In other words, the stake delegation becomes static because delegators have no incentive to move from large pools to small pools. Hence, the small pools’ contribution to (group stake / total stake)^2 is practically small. Therefore, SUM (group stake / total stake)^2 remains practically constant. The term SUM(group stake / total stake)^2 should keep decreasing as the number of pools increases, and this only happens if delegations are incentivized or disincentivized so that they’d move to small pools. I just read from twitter today that a single pool is retiring because for the whole year that he operated, he did not get any block.
Question: How does your CIP affect K-effective? If the reward is practically ~5-6% across the board, there is no incentive for delegators to move from large pools to small pools because delegators get the same reward anyway, and especially that some of these large pools offer lucrative rewards, i.e., Binance offers 17% but practically its only about 8%. But this is still better than 5-6% that your CIP offers.
I plan to revise the Rationale section of my CIP to reflect on how my CIP increases K-effective as the number of pools increases. Your CIP actually helped me better understand how rewards are distributed and how decentralization is parameterized. So, thank you for that. Cheers.
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Open Question:
I have found the original paper and reference for the current reward equation, but I haven’t been able to find any information on alternative reward equations tested or the logic/rationale behind why R/(1+a0)*( … a0…) was selected in the context of Sybil protection.
I think v2 of the RSS paper has a more detailed explanation of the rationale for the final formula:
Or maybe not… the content is reorganised. What was the Introduction in v2 is now in section: 4 A Sybil Resilient Reward Sharing Scheme
The beginning of section 4 explains how the final form of the rewards formula is achieved.
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- It forces pool operators to provide adequate pledge (since saturation is proportional to pledge). Even Binance will then have to provide adequate pledge to its pools. There is a cost to locking up pledge because they can’t access the pledge as easily as if they just staked. This is why Binance currently runs their pools with minimal pledge. Maybe they will find it “cheaper” to just stake to community pools???
- It removes the incentive for whales to run full pledge saturated pools to get extra yield. If they can’t earn this extra yield, at least some will simply delegate instead. Why not, if the yield is the same? It is certainly easier than running a pool.
- It removes the disincentive to stake to small pools (so long as min fee is reduced to 30). Small pools are currently at a disadvantage with min fee 340 because a higher percentage of rewards is taken by the min fee.
One additional disincentive for small pools is that they produce hit/miss rewards depending on their luck with slot leadership lottery. However, a whale can split his wallet and stake to multiple small pools to achieve the same average rewards. - For those people that place a value on decentralisation they will want to increase this by spreading their stake across multiple pools. Whales likely understand this more than others. So long as there is not a yield disadvantage then these whales will seek to increase decentralisation (everything else being equal). (Currently there is a disincentive because you earn more yield by staking to nearly saturated pools.)
- There is a slight advantage to small pools when slot battles and single block forks (due to propagation delays) occur since these are resolved by VRF scores which the smaller pool usually wins. Thus if fees are similar (after min fee reduced to 30) then the smaller pools may actually slightly do better. Whales that understand this may slightly preference small pools that are well run.
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Indeed!
I believe the intellectual disconnect is not realizing that 1 pool does not equal 1 actor. One actor could operate 0 to N numbers of pools.
If I was a reviewer I would have recommended to the authors:
Create N actors for each simulation.
Each epoch:
sample block production (rewards) per pool from a normal distribution
Each actor may choose to:
create/retire 1 or more pools
adjust the fee/margin structure of their pool(s)
delegate to the pool of a different actor
Then I would recommend to the authors to repeat the analysis suite for many possible equations, not just one. A nakamoto coefficient, ‘k-effective’ coefficient (actor/group based metric equivalent), and ‘sybil coefficient’ should be computed each (equation, (simulation, (and epoch))).
- Current Equation, Brünjes, Kiayias, Koutsoupias, Stouka
- Curve Pledge CIP7, @shawnim
- CIP-45?, @jcamp
- Tobias Francee’s CIP-draft, @TobiasFancee
- MJL’s CIP-draft, @Michael.Liesenfelt
- …
- …
For each actor I would also recommend that the authors incorporate historical behavior of exchanges, liquidity pools, ISO’s, custodial wealth management, greedy MPO operators, and single pool operators into randomly created agent profiles. Also, I would recommend that the initial state of the network be seeded from the existing stake distribution of Cardano in addition to ‘ideal/uniform’ stake initial conditions.
Hey @7.4d4 ,
- It forces pool operators to provide adequate pledge (since saturation is proportional to pledge). Even Binance will then have to provide adequate pledge to its pools. There is a cost to locking up pledge because they can’t access the pledge as easily as if they just staked. This is why Binance currently runs their pools with minimal pledge. Maybe they will find it “cheaper” to just stake to community pools???
Interesting because the pledge is only between 0.00 - 1.00% which is more relaxed than the current implementation. But maybe I am not fully understanding everything here. Initially, the graphs were plotted with “stake fraction” as the x-axis. Just recently, I saw it was changed to “stake saturation” and the plots look a bit similar. So, I am eagerly waiting for the equation. We can discuss more when the document gets updated.
Granting that it really does force a pool to pledge, and granting that the recent graph is “reward vs stake saturation”. What happens when ADA gets expensive so that small pools can no longer afford the 1% pledge or even the 0.02%? At $10 ADA, a 0.02% pledge is already $136,000 (68Mx0.0002x10, correct me if my calculation is wrong). In this situation, the growth in the number of validators will probably stagnate as Cardano grows. Also, a $10, 20, 30, or even $100 ADA is not impossible to achieve. Do we then constantly redefine the equation? In the CIP that I proposed, there is only one parameter that needs network consensus. That paramater determines the optimal pledge so that it becomes affordable to middle income SPOs. Also, the optimal pledge becomes cheaper as the number of validators increases.
As an ADA holder, I am all for earning >5%, and I want this CIP to succeed. That is why I try to find possible weaknesses in it so that they could be fixed. BTW, my CIP will probably not get merged into the repository until I present it in a CIP Editors’ meeting. I plan to delay the presentation and wait on the fate of this CIP.
- It removes the incentive for whales to run full pledge saturated pools to get extra yield. If they can’t earn this extra yield, at least some will simply delegate instead. Why not, if the yield is the same? It is certainly easier than running a pool.
Hey, if I am an ADA whale, you will not find me anywhere else but in the Caribbean. 
- It removes the disincentive to stake to small pools (so long as min fee is reduced to 30). Small pools are currently at a disadvantage with min fee 340 because a higher percentage of rewards is taken by the min fee.
One additional disincentive for small pools is that they produce hit/miss rewards depending on their luck with slot leadership lottery. However, a whale can split his wallet and stake to multiple small pools to achieve the same average rewards.
I believe the 30 min fee was already proposed prior to this CIP.
- For those people that place a value on decentralisation they will want to increase this by spreading their stake across multiple pools. Whales likely understand this more than others. So long as there is not a yield disadvantage then these whales will seek to increase decentralisation (everything else being equal). (Currently there is a disincentive because you earn more yield by staking to nearly saturated pools.)
Lest we forget the ecosystem also has minnows, shrimps, sharks, etc, and these people will always seek greener pastures.
- There is a slight advantage to small pools when slot battles and single block forks (due to propagation delays) occur since these are resolved by VRF scores which the smaller pool usually wins. Thus if fees are similar (after min fee reduced to 30) then the smaller pools may actually slightly do better. Whales that understand this may slightly preference small pools that are well run.
Apologies, I just don’t have the technical knowledge to comment on this.
A further question for @Michael.Liesenfelt: How does a reward that’s >5% ADA affect the reserve?
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Here is the original equation and my proposed equation in the same terms:
It is elegantly compact. Originally I considered using the product of two exponential equations, however it wouldn’t have resulted in a flat yield ceiling (egalitarian principle) with easy to understand effects.
That was my mistake. I wasn’t being clear enough.
The payout of the reserve is governed by the parameter rho. Recommending a change to the rho or tau parameters are outside the scope of this CIP.
FYI:
Thank you @Michael.Liesenfelt,
Okay, it is only a slight modification of the original equation.
Here are my concerns:
- The CIP is less resistant to price fluctuation.
a) In the IOG equation, the reward (r) does not go to zero even if pool pledge (λ)
is zero. The pool can still mint blocks and get rewards so long as it gets
delegation.
b) The CIP formula is very restrictive because when pledge (λ) is zero, reward is
automatically zero. The problem here is that when ADA becomes expensive,
potential SPOs may no longer be able to afford the pledge. In fact, when ADA
is $10, a pledge of 0.02% is already $136,000. Small pools may not be able to
prosper under this CIP. This is not a problem for MPOs (the exchanges)
because they have full control of ADA delegated to them. In fact, a 1% pledge
for Binance is only 0.02% of the total ADA they control.
c) Given the situation in “b”, the would-be protocol from this CIP needs constant updating either by new CIP submission or network consensus. Both are probably not ideal because determining a suitable pledge range needs careful examination and therefore slow, but as we know cryptocurrencies are very volatile.
A further weakness in this CIP is its effect either on the reserve or treasury. Currently, delegators are getting 4.5% in stake reward. This CIP will provide an extra 1% which is about 230M annually (0.01*23B). If rho is maintained, the reserve will not get affected, but the excess 1% reward would need to get sourced from the treasury. This is a sum of money that Cardano projects that are dependent on the treasury may potentially lose.
My gut feeling here is that re-structuring the reward calculation to solve decentralization is probably not going to do it. The reason for this is that exchanges just have the upper hand when it comes to resources. They are unlikely to struggle compared to SPOs because these exchanges have full control of the ADA delegated to them.
This property enables Sybil behavior. I’m not a fan of Sybil behavior.
That ‘restrictive’ property makes pledge mandatory instead of a slightly optional incentive. I included an example at a0=100 where 5k pledge can support a delegation up to 5k*100 = 500k would yield on average >5% psychologically and economically competitive returns. Any pool which is successful enough to grow a delegation close to their maximum would be a very attractive business partner.
1% pledge for Binance would be 1% of the ADA they control.
Rho governs payout from the reserve and Tau governs contributions to the Treasury. Both of those parameters contributing to R remain the same for the current equation and my proposed equation as I showed above. Adjusting Rho and Tau is is beyond the scope of this CIP. If the reserve is dropping too fast, another CIP can propose the monetary policy adjustment for the Rho parameter.
By not automatically returning 23% of rewards to the reserve for the vast majority of the Cardano community yields become egalitarian and fair without >50% pledge fractions.
Going on gut feelings instead of quantifiable independent metrics has yielded the current decentralization result. I’m providing the justifications, data, methods, metrics, and a path to implementation which doesn’t include gut feelings or emotions.
Blockquote
This property enables Sybil behavior. I’m not a fan of Sybil behavior.
The paper passed a peer-review process.
That ‘restrictive’ property makes pledge mandatory instead of a slightly optional incentive. I included an example at a0=100 where 5k pledge can support a delegation up to 5k*100 = 500k would yield on average >5% psychologically and economically competitive returns. Any pool which is successful enough to grow a delegation close to their maximum would be a very attractive business partner.
True. But here’s the thing: ADA is not moving from large pools because these pools offer better rewards (Binance is 8%). So, to go from a higher yield to a lower yield is against human psychology. Therefore, getting a “500K delegation” is quite a challenge for new SPOs because delegations are entrenched in large pools. Re-structuring reward is probably not going to do it because if we try to be better than 8%, Cardano is going to go broke. We need a different mechanism that will force the movement of delegation from large pools to small pools.
Also, 5k ADA now is ~$5k. Next time it could be $50k, after that $500k.
1% pledge for Binance would be 1% of the ADA they control.
Correct me if I’m wrong, 1% of 68M is 680,000. This number is only 0.02% of the 2.9B ADA that Binance currently controls.
Rho governs payout from the reserve and Tau governs contributions to the Treasury. Both of those parameters contributing to R remain the same for the current equation and my proposed equation as I showed above. Adjusting Rho and Tau is is beyond the scope of this CIP. If the reserve is dropping too fast, another CIP can propose the monetary policy adjustment for the Rho parameter.
Something’s got to give to support the >5%. Cardano is still young so it needs to tighten its belt until it becomes profitable, and delegators appear to be happy with 4.5% reward.
Going on gut feelings instead of quantifiable independent metrics has yielded the current decentralization result. I’m providing the justifications, data, methods, metrics, and a path to implementation which doesn’t include gut feelings or emotions.
Apologies if I’m making it difficult for you. But there is a reason why we have this forum. We debate to improve CIPs.
Best of luck!
I’m a professor, of course I love difficult! You haven’t found anything difficult yet.
If I was a reviewer I would have forced them to abandon the assumption that 1 pool is equal to 1 independent actor. In the real world 1 actor can delegate, operate one pool, or operate many pools. The paper passed a peer-review process with that paradigm flaw intact. Go back and analyze my reply to Carlos a day ago with the original RSS paper open side-by-side.
I love this community and the principles so I got my shovel and I’m here to fix decentralization. I’m still drafting important sections of the draft CIP (histogram of stake vs pledge, Methods and paradigms for equation validation).
Binance is earning ~4.25% yield from the stake pools using 0 pledge. I want to treat Binance fairly.
That’s not in my proposal. R remains the same.
I’m here to balance the equations and free them from bias by treating everybody fairly and equally, it’s one of my principles. Your CIP may be founded upon different principles and paradigms.
My proposal with a0=100 would require Binance to pledge at least 28.900M across 62 pools to support 2890.0M in stake.
I’m proposing that the average member of the community should not be returning 23% of rewards to the reserve.
Keep the review comments coming! Re-read the google doc because I’m often adding content or enhancing my technical communication.
I think everyone has equal rights in this forum. I have a Ph.D. as well in the physical sciences and now a postdoc. So you being a professor (a research assistant professor - let’s include that qualification) does not impress me. I know a lot of professors who are just too dumb, but I keep those impressions to myself. I like to stay anonymous. I don’t brag, and I try not to get any attention.
Seriously, best of luck. Please find humility in your heart. Ciao!
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Remember that sometimes text on a bulletin board can seem pointed or a bit short when the message was not necessarily intended to be antagonistic by the writer. All the facial expression queues present in normal face to face conversation are missing.
I love the first principles rigour you are taking to this challenge.
Furthermore, despite your mathematical expertise, you have chosen to simplify the formula which is quite different to many other proposals for change that I have seen.
Another thing worth pointing out is that a lot of people seem to be approaching this problem with an attitude that they deserve to be able to earn something from the protocol if they put effort in to spin up a stake pool. The reality is that with Cardano’s design, a stake pool will need to have 1M Ada total stake in order to produce regular blocks. As the price of Ada increases this fact will not change.
No doubt stake pool operators will be able to build viable businesses, borrow money to fund pledge and provide services to attract delegation. As the price of Ada increases, the amounts of money required will likewise increase. There is no point complaining that the cost to fund pledge will be massive when the price of Ada is $10 US, this won’t change the facts and it won’t change the consensus mechanism.
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I cannot deny this. People make mistakes, professors included. Hubris and ego get in the way of being wrong.
Your criticisms and attempts at a ‘gotcha’ flaw are making this proposal better! When you attempt to catch me on treasury/reserve balance, chart labeling, current formula function, or proposed formula clarity it really means is that my technical communication of core concepts have failed and it’s my responsibility to continue to improve my technical communication before draft submission. You may not be finding structural flaws (the equation is very simple and R, rewards, is the exact same), but you are exposing my communication weaknesses.
I have to be public to support this CIP and if/when I make mistakes I have to publicly admit fault and correct them. I may be wrong about the original RSS paper simulating 1 actor as 1 pool without considering multipool actors. Am I?
This is a fantastic point so I’ve added a Conflict of Interest Declaration section.
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Community,
I’ve continued incorporating private and public comments. @KryptoKing previously asked about determining initial values for (a0,k) and until now I haven’t created a decent visualization. Here is something decent!
Note, the largest bubble at 5.1B stake is the Single Pool Operator Alliance with an average leverage ratio of ~21 and an average stake pool size of 2.2M.
Question: In your opinion where is the secure to Sybil transition zone as a function of stake distribution and leverage?
I’m now starting to wonder about an initial value of a leverage limiting a0 parameter.
I’ve also added to:
- The Intent of (a0,k)
- Current Reward Formula
- The economic motivations of large stakeholders and collective pools
- Methods and paradigms for equation validation
- Conflict of Interest Declaration
I updated all of the charts to include a red dotted line for the current maximum rewards R * sigma.
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