Chain Quality (CQ) is a core attribute of blockchain. In simple terms, it means:

If you hold 3% of the staked stake, then on average over time, you can control 3% of the block space.

For early blockchains with low throughput, chain quality was sufficient. But modern blockchains have much greater bandwidth, with a single block capable of containing a large number of transactions.

This leads to a stronger and more refined concept. It not only focuses on the proportion of block space averaged over time but also looks at the division of block space within each individual block. We call this Strong Chain Quality (SCQ):

If you hold 3% of the staked stake, then in every block, you control 3% of the block space.

Essentially, this property allows stakeholders a "virtual lane" within a high-throughput blockchain, ensuring their transactions can be included.

Chain Quality in Blockchain

One of Bitcoin's key innovations—now present in almost every blockchain—is the built-in reward mechanism for block proposers within the protocol: the party that successfully appends a block to the state machine can receive newly minted tokens as well as transaction fees. These rewards are stipulated by the state transition function and are ultimately reflected in the system state.

In traditional distributed computing models, participants are divided into honest and malicious parties. There is no need to reward honest behavior, as it is the default assumption in the model.

In cryptoeconomic models, participants are viewed as rational actors with potentially unknown utility functions. The goal is to design incentives so that these participants, in pursuing their own profit maximization, naturally align with the successful operation of the protocol. Combining the internal reward mechanism of the protocol, we can derive the following idealized definition of chain quality:

Chain Quality (CQ): A coalition holding X% of the total staked stake has an X% probability of being the proposer of each block that enters the chain after the Global Stabilization Time (GST).

If a chain deviates from chain quality requirements, it may allow certain coalitions to obtain a share of rewards beyond their normal proportion, thereby weakening the incentive for honest behavior and threatening the security of the protocol.

Many blockchains satisfy or strive to satisfy this property through mechanisms like "random leader rotation based on staking weight."

Typical current challenges include: Bitcoin's "selfish mining" problem; Monad's tail forking resistance issue; and problems in Ethereum's LMD GHOST protocol.

The Origin of "Strong Chain Quality"

When block space is sufficiently abundant, we don't have to hand over the entire content of a single block to a single proposer's monopoly. Instead, the block space of the same block can be divided among multiple participants. The cryptoeconomic definition of Strong Chain Quality expresses precisely this idea:

Strong Chain Quality (SCQ): A coalition holding X% of the total staked stake can control X% of the block space in every block after the Global Stabilization Time (GST).

This idealized property implicitly introduces the abstraction of a "virtual lane." That is, the coalition effectively controls a certain proportion of dedicated block space in every block.

From an economic perspective, owning a virtual lane is equivalent to holding a productive asset that can generate returns, which may come from transaction fees or MEV (Maximal Extractable Value). External entities will compete for staking rights to acquire and maintain these lanes, creating sustained demand for the underlying L1 token. The greater the economic value a lane can generate, the stronger the motivation for parties to compete for staking rights, and the higher the value that the L1 staking rights controlling access to this block space can accumulate. Through this abstraction, we can translate stronger censorship resistance into the SCQ validity property within the protocol.

Strong Chain Quality and Censorship Resistance

Recent research has shown that censorship-resistant protocols are very important. Such protocols must not only ensure that honest inputs are eventually included but also that they are included immediately. Strong Chain Quality (SCQ) can be seen as an extension of this property under conditions of limited block capacity.

In practical scenarios, if the volume of transactions awaiting inclusion exceeds the available block space, no protocol can satisfy the notion of ideal censorship resistance. SCQ addresses this limitation with a more pragmatic approach: it does not insist that all honest transactions must always be included, but rather allocates a "budget" to each staking node, ensuring that its transactions can be included within this budget.

The MCP protocol was proposed as a component on top of existing Practical Byzantine Fault Tolerance (PBFT)-style consensus protocols to make them censorship-resistant. This protocol also satisfies the requirements of SCQ—it allocates block space to proposers according to their proportion of staked stake. Existing Directed Acyclic Graph (DAG)-based BFT protocols offer a way to implement a multi-writer mempool and also provide a degree of censorship resistance.

Standard implementations of these protocols often fail to strictly satisfy SCQ because they allow leaders to selectively delay certain subsets of transactions. However, with minor modifications to these protocols, it might be possible to re-establish SCQ. A related direction is "forced transaction inclusion," used to reduce censorship behavior.

MCP also demonstrates how to achieve a stronger hidden property. With this property, stakeholders can create virtual private lanes, the contents of which are only revealed when the entire block is made public. We will elaborate on this point in a subsequent article.

How to Achieve Strong Chain Quality

The key to achieving Strong Chain Quality after the Global Stabilization Time (GST) is to ensure that proposers cannot arbitrarily censor stakeholder inputs. This can be achieved through a two-round protocol. With just two small modifications to almost any view-based BFT protocol:

First Round: Each participant sends its certified input to all other participants.

Second Round: If a participant receives a certified input from participant i, it adds i to its inclusion list. Then, the participant sends its inclusion list to the leader. This operation is equivalent to a commitment: it will only accept blocks that include all the inputs in this list.

BFT Proposal: After receiving these messages, the leader includes the union of all received inclusion lists in the block.

BFT Vote: A participant will only vote in favor of a block if that block includes all the inputs from its own inclusion list.

It is not difficult to see that a complete protocol can be constructed from this protocol sketch. This protocol can satisfy Strong Chain Quality after GST, provide censorship resistance, and maintain liveness when the leader is honest. To achieve SCQ before GST, it would also be necessary to wait for a sufficient number (a quorum) of values or lists in each round. We will detail this protocol and its extensions in a subsequent article.

Recent research indicates that achieving Strong Chain Quality and censorship resistance requires adding two additional rounds (as shown in the protocol sketch above) on top of the regular voting rounds of a BFT protocol. We will also detail this result in a subsequent article.

While Strong Chain Quality (SCQ) specifies the proportion of block space a coalition can control, it does not fully dictate the ordering of transactions within the block. SCQ can be understood as: reserving space for each staking node, but making no guarantees about the order of transactions within that space.

This opens up a rich space for research into transaction ordering mechanisms. A good ordering mechanism has the potential to further enhance fairness and efficiency within the blockchain ecosystem. One noteworthy direction is ordering transactions based on priority fees.