In the previous article, we identified the objectives of the reward scheme in Cardano, and we gave general guidelines regarding engaging with the system.

Taking a more high-level view, we will examine from first principles, the general problem of reward sharing in blockchain systems. To recall, the two overarching objectives of any resource-based consensus system is to incentivize the following.

High engagement. Resource-based consensus protocols are more secure the more resources are engaged with protocol maintenance. The problem, of course, is that the underlying resources are useful for a wide variety of other things too (e.g., electricity and computational power in the case of proof of work, or stake for engaging in decentralized apps in the case of proof of stake), so resource holders should be incentivized to commit resources for protocol maintenance.

Low leverage: leverage relates to decentralization. Take a group of 10 people; if there is a leader and the group follows the leader’s wishes all the time, the leader’s leverage is 10 while everyone else’s is zero. If, on the other hand, everyone’s opinion matters the same, everyone’s leverage is 1. These are two extremes, but it should be fairly obvious what types of leverage align better with decentralization. From an economic viewpoint, however, a “benevolent dictatorship” is always more efficient; as a result, decentralization will come at a cost (exactly as democracy does), and hence it has to be also properly incentivized.

Given the above objectives, let us now examine some approaches that have been considered in consensus systems and systematize them in terms of how they address the above objectives. An important first categorization we will introduce is between unimodal and multimodal reward schemes.

Unimodal

In a unimodal scheme, there is only one way to engage in the consensus protocol with your resources. We examine two sub-categories of unimodal schemes.

1. Linear Unimodal

This is the simplest approach and is followed by many systems, notably Bitcoin; the original proof-of-work based Ethereum, as well as Algorand. The idea is simple: if an entity commands x% resources, then the system will attempt to provide x% of the rewards – at least in expectation. This might seem fair—until one observes the serious downsides that come with it.

First, consider that someone has x% of resources and that x% of the rewards in expectation are below their individual cost to operate as a node. Then, they will either not engage (lowering the engagement rate of the system), or, more likely, actively seek others to combine resources and create a node. Even if there are two resource holders with x% of resources each and a viable individual cost c when running as separate nodes, they will fare better by combining resources into a single node of 2x% resources because the resulting cost will be typically less than 2c. This can result in a strong trend to centralize, and lead to high leverage since the combined pool of resources will be (typically) run by one entity.

In practice, a single dictatorially operated node is unlikely to emerge. This is due to various reasons such as friction in coordination between parties, fear of the potential drop in the exchange rate of the system’s underlying token if the centralization trend becomes noticeable, as well as the occasional use of complex protocols to jointly run pools. Even so, it is clear that unimodal linear rewards can hurt decentralization.

One does not need to go much further than looking at Bitcoin and its current, fairly centralized, mining pool lineup. It is worth noting that if stake (rather than hashing power) is used as a resource, the centralization pressure will be less – since the expenditure to operate a node is smaller. But the same problems apply in principle.

An additional disadvantage of the above setting is that the ensuing “off-chain” resource pooling that occurs will be completely opaque from the ledger perspective, and hence more difficult for the community to monitor and react to. In summary, the linear unimodal approach has the advantage of being simple, but is precarious, both in terms of increasing engagement and for keeping leverage low.

2. Quantized Linear Unimodal

This approach is the same as the linear rewards approach, but it quantizes the underlying resource. I.e., if your resources are below a certain threshold, you may be completely unable to participate; you can only participate in fixed quanta. Notably, this approach is taken in ETH2.0, where 32 Ether should be pledged in order to acquire a validator identity. It should be clear that this quantized approach shares the same problems with the linear unimodal approach in terms of participation and leverage. Despite this, it has been considered for two primary reasons. First, using the quantized approach enables one to retrofit traditional BFT-style protocol design elements (e.g. that require counting identities) in a resource-based consensus setting. The resulting system is less elegant than true resource-based consensus but this is unavoidable since traditional BFT-style protocols do not work very well when there are more than a few hundred nodes involved. The second reason, specific to the proof-of-stake setting, is seeking to impose penalties on participants as a means of ensuring compliance with the protocol. Imposing quantized collateral pledges makes penalties for protocol infractions more substantial and painful.

Multimodal

We next turn to multimodal schemes. This broad category includes Cosmos, Tezos, Polkadot & EOS. It also includes Cardano. In a multimodal scheme, a resource holder may take different roles in the protocol; being a fully active node in the consensus protocol is just one of the options. The advantage of a multimodal scheme is that offering multiple ways to engage (with correspondingly different rates of return) within the protocol itself can accommodate a higher engagement, as well as limit off-chain resource pooling. For instance, if the potential rewards received by an individual when they engage with all their resources sit below their operational cost of running a node, they can still choose to engage by a different mode in the protocol. In this way, the tendency to combine resources off-chain is eased and the system – if designed properly – may translate this higher engagement to increased resilience.

We will distinguish between a number of different multimodal schemes.

• Representative bimodal without leverage control. The representative approach is inspired by representative democracy: the system is run by a number of elected operators. The approach is bimodal as it enables parties to (1) advertise themselves as operators in the ledger and/or (2) “vote” for operators with their resources. The set of representative operators has a fixed size and is updated on a rolling basis typically with fixed terms using some election function that selects representatives based on the votes they received. Rewards are distributed evenly between representatives, possibly taking into account performance data and adjusting accordingly. Allowing rewards to flow to voters using a smart contract can incentivize higher engagement in voting since resource holders get paid for voting for good representatives (note that this is not necessarily followed by all schemes in this category). The disadvantage of this approach is the lack of leverage control, beyond, possibly, the existence of a very large upper bound, which suggests that the system may end up with a set of very highly leveraged operators. This is the approach that is broadly followed by Cosmos, EOS, and Polkadot.

A different approach to the representative approach is the delegative approach. In general, this approach is closer to direct democracy as it allows resource holders the option to engage directly with the protocol with the resources they have. However, they are free to also delegate their resources to others as in liquid (or delegative) democracy (where the term delegative is derived from). This results in a community-selected operator configuration that does not have a predetermined number of representatives. As in the representative approach, user engagement is bimodal. Resource holders can advertise themselves as operators and/or delegate their resources to existing operators. The rewards provided are proportional to the amount of delegated resources and delegates can be paid via an on-chain smart contract, perhaps at various different rates. Within the delegative approach we will further distinguish two subcategories.

• Delegative bimodal with pledge-based capped rewards. What typifies this particular delegative approach is that the resource pool’s rewards have a bound that is determined by the amount of pledge that is committed to the pool by its operator. In this way, the total leverage of an operator can be controlled and fixed to a constant. Unfortunately, this leverage control feature has the negative side effect of implicitly imposing the same bound to all, small and large resource holders. So, on the one hand, in a population of small resource holders, engagement will be constrained by the little pledge that operators are able to commit. On the other hand, a few large whale resource holders may end up influencing the consensus protocol in a very significant manner, possibly even beyond its security threshold bound. In terms of leverage control, it should be clear that one size does not fit all! From existing systems, this is the approach that is (in essence) followed by Tezos.

It is worth noting that all the specific approaches we have seen so far come with downsides – either in terms of maximizing engagement, controlling leverage, or both. With this in mind, let us now fit into our systematization, the approach of the reward-sharing scheme that we are using in Cardano.

• Delegative bimodal with capped rewards and incentivized pledging. In this delegative system (introduced in our reward-sharing scheme paper), the rewards that are provided to each pool follow a piecewise function on the pool’s size. The function is initially monotonically increasing and then becomes constant at a certain “cap” level which is a configurable system parameter (in Cardano this is determined by the parameter k). This cap limits the incentives to grow individual resource pools. At the same time, pledging resources to a pool is incentivized with higher pledged pools receiving more rewards. As a result, lowering one’s leverage becomes incentive-driven: resource pools have bounded size and operators have an incentive to pledge all the resources they can afford into the smallest number of pools possible. In particular, whale resource holders are incentivized to keep their leverage low. The benefit of the approach is that high engagement is reinforced, while leverage is kept in control by incentivizing the community to (i) pledge as much as possible, (ii) use all the remaining unpledged resources as part of a crowdsourced filtering mechanism. This translates stake to voting power and supports exactly those operators that materially contribute to the system’s goals the most.

The above systematization puts into perspective the choices that we have made in the design of the reward-sharing scheme used in Cardano vis-a-vis other systems. In summary, what the Cardano reward system achieves is to materially promote with incentives and community stake-based voting the best possible outcome: low leverage and high engagement. And this is accomplished, while still allowing for a very high degree of heterogeneity in terms of input behavior from the stakeholders.

As a final point, it is important to stress that while considerable progress has been made since the introduction of the Bitcoin blockchain, research in reward sharing for collaborative projects is still an extremely active and growing domain. Our team continuously evaluates various aspects of reward-sharing schemes and actively explores the whole design space in a first-principles manner. In this way, we can ensure that any research advances will be disseminated widely for the benefit of the whole community.

I am grateful to Christian Badertscher, Sandro Coretti-Drayton, Matthias Fitzi, and Peter Gaži, for their help in the review of other systems and their placement in the systematization of this article.