Tackling the Challenge of Wealth Concentration in PoS Blockchains

While Proof of Stake (PoS) systems are often praised for their scalability and energy efficiency, centralisation concerns have drawn criticism to the system. Beyond centralisation, there are other issues to be concerned about, such as the possibility of wealth concentration and self-censorship. These can seriously jeopardise the fundamental principles of blockchain if not appropriately addressed. The recent transition of DarkFi from the PoS-based Ouroboros Crypsinous protocol due to wealth concentration findings motivated us at Nomos to investigate the matter. Before looking into our research a bit deeper, examining a few crucial terms is necessary.

Why Wealth Concentration Matters

The possibility of wealth concentration in proof-of-stake blockchains is particularly concerning. It can undercut the democratic ethos of blockchain by giving disproportionate control and influence to the wealthiest stakeholders due to the amount they can stake. This distorts decision-making procedures and raises the possibility of manipulation and integrity-related assaults on the network.

Simply put, a concentration of money can result in a concentration of power, converting decentralised networks into oligarchies in which a few validators hold all the control. However, it's crucial to remember that many PoS systems have safeguards to allay these worries. Our research is among the many studies that have demonstrated that PoS systems do not inevitably result in the concentration of wealth.

Ouroboros Protocols:
Enhancing Security and Fairness

Ouroboros is the first provably secure proof-of-stake system and the first blockchain protocol based on peer-reviewed research. It employs advanced cryptography techniques, combinatorial mathematics, and game theory ideas to secure the blockchain's integrity, durability, and operational efficiency.

The core of Ouroboros is its unique transaction processing mechanism, which divides the blockchain into epochs and further divides it into discrete time slots. Within this architecture, each time slot is allocated a slot leader, who is responsible for adding a new block to the blockchain.

The leader election function in Ouroboros Praos operates based on verifiable random functions (VRFs), which distribute the possibility of being chosen to build a new block evenly across all network participants depending on the relative stake. Using VRFs guarantees that generating new blocks is fair, unpredictable, and open to participant verification.

When we focus on the Ouroboros Crypsinous' leadership lottery function, we find the factor used to compute the relative stake is, in reality, unknown to the protocol due to privacy constraints. Additionally, Crypsinous' leadership lottery function distinguishes between old coins, those eligible for leadership proofs, and young coins, ineligible due to recent movement. This differentiation further affects the leader election function by reducing the potential for stake manipulation.

DarkFi's Departure from Ouroboros Crypsinous

The recent shift of DarkFi from the PoS Ouroboros Crypsinous to the RandomX proof-of-work (PoW) mining algorithm caught our interest. This switch was based on their conclusion that the Ouroboros system, without a protracted predistribution of DRK tokens, would lead towards centralisation over time and cause wealth concentration.

We were surprised by their decision for two main reasons: first, the issue of initial centralisation in PoS protocols is widely recognised (because the team behind the protocol needs to create the native tokens before the genesis block of a blockchain), and second, there has been considerable research that PoS systems like Ethereum do not result in wealth concentration. Even though Praos has a different leader election function than Ethereum, our research demonstrates that PoS systems, in general, do not inherently result in wealth concentration, more specifically:

• The absence of wealth concentration also holds in Praos.
• The absence of wealth concentration also holds in Crypsinous when we use an algorithm to learn the total stake.

Crypsinous' Leader Election Function: Insights from Nomos' Simulations

Driven by DarkFi's results and its accompanying pivot, we decided to look into the complexities of the Crypsinous Leader Election Function and its implications for wealth concentration in PoS systems. Our research focused on identifying the conditions under which PoS may avoid the issues of wealth concentration.

We found that wealth concentration does not emerge as an inherent property of PoS if certain conditions are met, even when we introduce a modified stake relativisation algorithm with an adjusted learning rate and recalculated total stake estimates.

One of the above-mentioned conditions is the selection of a fork-choice rule. Further studies are still required to understand whether these selection mechanisms can be gamified, given that the protocol can't enforce (through penalisation, for example) that a node will follow the appropriate fork-choice rule.

Nomos' Contribution to the Ecosystem

Like any innovation, proof-of-Stake (PoS) protocols have advantages and disadvantages. Nevertheless, our research reveals that the concentration of wealth is not one of the drawbacks. We believe blockchain technology can build a more fair, less corrupt, and freer society. However, achieving this goal requires more research and collective efforts.

At Nomos, we are creating a highly resilient network which is robust and resistant to corruption and malicious actors. Only in this way can blockchain technology truly reach its transformative potential. For more details on this research, check out our leader election simulations and stake relativisation analysis, or read our article on network privacy in PoS systems.