Gordian Knot of Cardano | Desired number of pools and pledge stake influence factor

Hi everyone,

Finding the K factor and a0 is the Gordian knot of Cardano. It requires purposeful integration that will make or break the token economics of Cardano staking. Just as you need to work towards building a robust protocol, it’s essential that you reward operators who put their money where their mouth is. Prioritize the token economics and you’ll have a robust ecosystem of solid staking pools. More pools = more longterm volatility.



interesting points, will be responding to this in a better informed way in due course.

created a post:
( Equilibrium ⇌ A0/k (or) pledge/cost proportionate to number of pools )

Hi Philippe!

Really? Maybe you meant “viability”?

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Can someone link to a documentation with exact definition of k and a0 so that we can talk, while being sure to know what talk about?

Edit: Here are the definitions page 38 https://hydra.iohk.io/build/790053/download/1/delegation_design_spec.pdf

I meant volatility. My theory is that the greater number of pools will reduce additional rewards and lead to increase selling pressure as price increases. Less pools = greater rewards = greater incentive to stay put as price increases.

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Sorry, I should have watched the vid.

I think there is in this video a use of the word “decentralized” which does not correspond to my vision of it.

Decentralized is not only about how many pools there are ( 20? 100? 500? 1000? 2000?). But it is also about the fact that anyone should have the potentiality to participate directly to the network in proportion to their means, no more, no less. One way to progressively go centralized is to allow only big actors to participate, or to advantage them over small ones (giving more power to those who already have much, and giving less to those who already have a little).

True decentralization, gives then added trust because anyone feels that he can/could participate directly in security of the network, even in a small proportion.

Good points. Based on your definition of decentralized, anyone should be able to run a stake pool. K factor should very high which would increase the chance of a Sybil attack.

@ philpa See my other post were I propose an other formula , and ask why the current one is better (because it is probably since mine is found in 5 minutes of thinking):


(Basically it is about limiting the pool size proportionally to the stake directly owned by the pool, pretty much like we limit it with k)

It seems to me that with this formula you can have k pretty high without risking sybill attack.

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Also note that one thing that helps sybill attacks is to push on the fact that different stake-pools should have structurally very different RoS (including according to their size, and proportion of directly owned stake). It pushes users to delegate randomly to the most efficient pool, even if they don’t know it at all, and even if there are another pool operator that they know directly and trust, but have a lower RoS (e.g because smaller).

On the contrary if all stake-pools had basically the same expected RoS, then users would be encouraged to have for sole criteria, the fact that they know and trust (or even are thankfull to) the pool operator, which would make Sybil attacks harder.

I strongly disagree with the PoV expressed in this video

If we follow the numbers, what emerges ?

IOHK 2.4B, EMURGO ~2B, BINANCE~1.5B (worst case). That is already almost 6B ada.

There won’t be 100% of circulating supply staked, so let’s be positive and take Tezos for a reference with their 75% staked. That gives 23B staked ada at cruise speed. These 6B represent 25% of the staked ada, and I believe these three entities won’t forget to do their job and stake.

That means at least 25 private pools, not even accounting yet for the delegator attraction a big exchange might trigger by putting a 0% fee. So with a optimum pool number of a 100, anywhere between 25 to 30 will be private pools, maxing out their returns. The rest is left to 70-75 players, a perfect set up for further consolidation. Once only a few actors are in place, and enough people left the pool operator ecosystem, their pledge will go down. No one has any interest in locking up that much assets. Up to the point where figuring out the differences between an army of exogenous ASICs miner and the implementation of PoS will be a uncomfortable discussion to have.

I fear that gatekeeping the pool operator role with such parameters for Cardano is a call for well funded mercenaries. That leads to another important point : community interests might decay. In that case, who is then relaying, spending time to read, discuss and help forging a set of divergent opinions regarding governance. A small set of actors is much more likely to have a convergent point of view, and the means to preach them.

Finally, at the end of ITN, it is clear that a group of ~300 pools could come up with a near perfect network efficiency, so this point does not even hold.

It is my opinion that a little bit more permissive barrier than what is proposed here won’t hurt.