Quadratic Proof of Stake (qPoS)

Quadratic Proof of Stake (qPos)

This discussion is highly conceptual and encourages the collective effort of the community. We formulise two quadratic-based consensus mechanisms that extend concepts related to Liberal Radicalism. Firstly, we define a more robust qPoS algorithm called Reputed Quadratic Delegated Proof of Stake (RQD-PoS), then, a more rudimentary algorithm is defined.

Introduction to Reputed Quadratic Delegated Proof of Stake (RQD-PoS)

Participants in the consensus have a reputation, whereby, their reputation grows the longer they participate in consensus decisions. Each participant stakes a certain amount of coins into the system and this will allow them to start generating reputation in the system. This reputation function is based on a sigmoid function that ensures that reputation is easily gained at the start, then progressively increases, which finally reaches an asymptotical plateau. This ensures that there is a balance in reputation, whereby, veteran community members do not have complete control over the system.

The reputation in the system acts as a mechanism to allocate voting power to each participant.

Now let’s formally define voting power in the system.

Voting Power of A Participant = Participant Reputation / Total Reputation in the system

Block Reward Mechanism

Block rewards that are generated are placed in a self-governed account that issues out the rewards in cycles (a cycle refers to an arbitrary period of time).

At each cycle, each participant in the consensus will be allocated a certain amount of voting power based on their reputation. They are then allowed to use this voting power to delegate votes based on concepts related to Quadratic Voting. This ensures that the n’th vote has a cost of n. This means that even with a strong reputation, participants still have to pay a significant amount of votes to influence block reward allocation. Then, at the end of the cycle, the block rewards and fees are rewarded to the participants based on the votes allocated to each participant.

This would allow us to leverage the benefits provided by quadratic voting and reputation by ensuring that new users must gain reputation before being able to vote in consensus decisions.

Important Caveats

  1. This is highly conceptual to encourage discussion from the community. It focuses on concepts related to Liberal Radicalism to figure out methods to construct consensus algorithms.
  2. Proves for Proof-Of-Reputation (Section 6.2), however, it’s important to note that the paper discusses computational power based reputation instead of actual stake.
  3. However, a quadratic-based consensus is still subjected to plutocracy, while, in theory, it is still more expensive than dPoS. This is a benefit provided by Quadratic Voting which ensures that n’th vote cost $n.

Additional Scheme: Quadratic Delegated Proof of Stake

It’s also possible to construct the same scheme without utilising reputation as a solution to gain voting power, also known as Quadratic Delegated Proof-Of-Stake (QD-PoS).

Related Concepts

Some essential reads that are related to Liberal Radicalism and Proof of Reputation.

  1. Quadratic Payments: A Primer by Vitalik Buterin
  2. Developer incentivization: in-protocol contract author fee rebates by Vitalik Buterin
  3. RepuCoin: Your Reputation is Your Power by Jiangshan Yu, David Kozhaya, Jeremie Decouchant and Paulo Esteves-Verissimo


This section is an open discussion to encourage the collective community to solve issues related to Proof-Of-Stake based consensus.

  1. How do we solve plutocracy?
    - Can enforce a wealth tax for the rich reputed miners to reduce economic disparity?
    - What happens if there is a Universal Dividend from the reward pool?


I would love to chat with as many people as I can on solving/proposing a more robust and secure consensus mechanism, so don’t be afraid to drop me a message.

Email: jeevan.pillay8@gmail.com
Telegram: lpfloyd

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1 - You made the claim that reputation systems solve plutocracy problems by raising the floor, I’m not familiar with that result; could you cite a specific place that result is stated? Intuitively, it seems that a reputation system would only be a short-term fix to plutocracy, while acting as a mechanism towards increasing network conservatism. ie. over the long term, veteran community members, who are most likely to be conservative, relative to new joiners, would have a dominant reputation over the network. Somewhat related, this seems to be partly why Buterin has been trying to take a step back from being Ethereum’s public face, to avoid acting as a veteran with outsized reputation to change the network.

2 - Sort of a joke, sort of not, is there an upper character limit in ABP—Acronym Best Practice? If not, I might suggest any acronym longer than 4 letters deserves a nickname.


1- the reputation function used by PoR is based on a sigmoid function which ensures that overtime the reputation will stabilize for all miners in the system to a certain threshold.

Here’s is a quote from the OC:

The formula defining the progression (resp. regression) of reputation, f(x) above, is a sigmoid function. It ensures that miners, at the start, can only increase their reputation slowly, even if having a strong computing power. A miner needs to stay in the system and behave honestly for a long enough period, to progressively increase its reputation up to the turning point, where it is trusted enough to be incentivized to make it grow more quickly, to more inter- esting levels. And finally, the curve inflects again, so that the reputation does not grow forever, but asymptotically reaches a plateau that promotes a balance of power amongst miners.

This doesn’t actually solve plutocracy, instead, it ensures that reputation must be gained first before being able to attack the system. That’s is why I mentioned that the lower bound of plutocracy is much higher in RQD-PoS, as there is an additional factor of ensuring that reputation must be gained first before colluding with other adversaries. It’s not a fix to plutocracy, but it does help increase the threshold for an adversary to attack the system.

Moreover, another important caveat about PoR is that the parameters of the reputation function are based on the fact that miners have “integrated power” which is calculated based on the regularity of creating blocks. This helps ensure that miners that haven’t proposed new blocks will start losing their power meaning that only miners that continually do good in the system will have a reputation.

2- Also, any recommendations on an acronym? Haha

P.S Feel free to drop me a message so we can chat about this further. Also, opened up a section in the original post on issues and possible solutions. Let’s discuss this together and figure this out.