Proof of stake, decentralization, and network parameters

TLDR: PoS is a capitalistic system and therefore has the same problems with centralization of wealth (monopolies). Because a proof of stake system benefits those with stake, it incentivizes the accumulation (centralization) of stake and therefore power. Parameter changes alter the reward structure, but such incentives don’t enforce decentralization on the whole.

The current formula for the distribution of rewards appears to be working as intended (there are roughly k pools which might be considered “sustainable”), but there are a number of consequences of the parameters which are beginning to rear their heads, even early on. Primarily, there is the dispute as to what k should be. Having a low k with so many eager stake pool operators (SPOs) has put a bit of pressure on IOG to increase k, in hopes of thereby putting pressure on larger pools to drive their delegators to smaller ones. In response, larger pools simply engage in pool splitting and request their delegators redirect their delegation to another pool owned by the same them.

The other side of the coin is the parameter a0, for which higher values incentivize SPOs to pledge more by increasing the payout for pools with higher pledge. Currently, a0 is very low and so there is very little additional benefit except for extremely large amounts of pledge, on the order of tens of millions of ADA, or currently above $1 million USD.

Two other parameters exist, rho, the monetary expansion parameter and tau, the percentage of rewards sent to the treasury. rho was chosen so that the total remaining ADA decreases by half roughly every 4-5 years. This is somewhat analogous to Bitcoin’s monetary expansion, except that the change in the rate of funds created is more of a continuous process with Cardano rather than occurring in discreet “halving” events as with Bitcoin.

Going through the Hydra delegation design specifications (, I found the current pool rewards formula to be a bit overcomplicated. I set out to simplify it and come up with, what I thought would be, a better distribution curve. This involved ditching a0 and k in lieu of a new parameter which I called the ‘leverage ratio,’ L. Essentially, a pools saturation would be dependent on some multiple L of the amount of their pledge staked (and therefore reduce or eliminate the incentive for pool splitting. For more details, see An Alternative to a0 and k). When trying to determine if this new method was better overall than the current method, I ran into a more fundamental issue.

At its core, the fundamental problem is not with Cardano’s parameters at all, it is the fact that Cardano is a proof of stake (PoS) network. PoS ensures that those who are invested in the network play a role in maintaining its security. This should not be misconstrued as to imply that the system will trend towards decentralization. It has been made abundantly clear by historical example that wealth accumulates, whether by force, monopolization, the passage of laws, economies of scale, or other means. Since Cardano’s network security is centered around the wealth of its native asset, it too is inherently susceptible to the same means of centralization unless other measures are taken to counterbalance this.

Now centralization and decentralization are not binary terms, there is a spectrum from one end to the other. What those participating in the Cardano network need to reconcile amongst ourselves is the question of how much centralization is acceptable? Essentially, changing incentive parameters is just a way to pick our poison by choosing what means we will allow the network to become more centralized (i.e. pool splitting or large pools).

Taking a step back, let’s consider a few thought experiments. We have a system that distributes rewards to SPOs (and delegators) and we wish to define how large these rewards are as a function of the amount of pledge by the SPO. On one end of the spectrum there are the ‘poor’ SPOs that have a small amount of ADA to pledge and on the other end there are ‘wealthy’ SPOs with large amounts of ADA to pledge. We will, for the moment, ignore the fact that this pledge doesn’t necessarily need to be ‘owned’ by the SPO, it just needs to be in their custody (i.e. it could be ‘lent’ by another individual). Returning to the question at hand, the pledge-reward distribution curve could be anything we choose. For the sake of simplicity, we will limit our values to between 0 and 1 where 0 is no pledge benefit and 1 is maximum pledge benefit. A few examples are in the figures below. The simplest case is a horizontal line, which implies that adding any amount of pledge provides the same returns (the case when a0 = 0). This is the ‘most equitable’ scenario in which no SPO has any advantage over another; however, it also makes the system vulnerable to a Sybil attack (a scenario in which a SPO creates a very large number of pools in order to gain a disproportionately large number of delegates to control or influence the network) as there is a negligible cost to setting up each additional stake pool. A downward sloping line skews benefits to pools with lower pledge (‘poor’ SPOs) while an upward sloping line benefits pools with a higher pledge (‘wealthy’ SPOs) greater.

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Running through the various options, it becomes apparent that every scenario has its shortcomings. Any upward sloping line effectively puts an entry fee to operating a stake pool as there is now a minimum pledge (soft limit) necessary to stay competitive. If we really want to pursue the idea that a “single mother could operate a [viable] stake pool” then this implies shifting the benefit towards lower pledge amounts (or neutral benefit), which leaves the system vulnerable to a Sybil attack. Furthermore, due to the relatively low overhead of setting up additional pools, ‘wealthy’ SPOs will always have the ability to engage in pool splitting to take advantage of features intended to aid ‘poor’ SPOs or decentralization. For this same reason, saturation limits for pools (and the notion of k implying a degree of decentralization) have largely become a moot point as evidenced by the fact that nearly every large pool has resorted to pool splitting in an attempt to circumvent this limit and maintain “their” delegates. Better curves exist, such as having one or multiple peaks to create optimal pledge amounts, but entry costs and pool splitting appear unavoidable without additional oversight and regulation.

Regulation becomes another issue, especially if votes for network parameters are determined by stake. Whales and large players are incentivized to vote for parameters that give them a larger proportion of rewards and, therefore, voting power in the network. This is analogous to the way that corporations lobby for legislation that either benefits them directly or puts up roadblocks for competitors. On the other hand, increasing adoption of Cardano means bringing in institutions (ex: exchanges) which bring with them large influence on the network. Even if we want to increase regulation (such as limiting SPOs to 1-3 pools per operator), this requires identity solutions that have not yet been released as well as general discussions about the tradeoffs that regulation impose, such as privacy rights and ability to enforce.

At the end of the day, there is already a good amount of competition between stake pools and this will only increase as adoption grows. I just don’t want those participating to be deluded into thinking that just the right tweaking of parameters will prevent centralization or even make running a stake pool with a small amount of capital viable in the long term without either charity delegators or additional regulation. PoS brings some benefits over PoW, but this does not insulate from the effects of great economic disparity.


Great analysis! I’ll be very disappointed if this doesn’t stimulate a lot of deep discussion.

Just as a side note, here’s a nice way to view the larger issue: cybernetics. All stable self-regulating systems necessarily involve one or more negative feedback loops so that, as any factor tends towards an extreme value, others automatically come into play to bring it back into line. But the accumulation of resources involves the opposite, a positive feedback loop, because generally speaking owning more resources means more ability to accumulate yet more resources: it is not self regulating, so unstable. To maintain equilibrium, such systems require “artificial” constraints. This is the fundamental reason for market regulation.

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Ha, thanks, but don’t hold your breath. I don’t think I could have timed the post much worse than right before Thanksgiving and in the middle of a crypto market flash crash.

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Correction: “correction”. :smile:

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