# Quad-linear Voting (QLV)

- Channel: [ETHBerlin](https://streameth.org/ethberlin)
- Date: 2025-06-19
- Duration: 17:19
- Watch: https://streameth.org/watch/6854208190bd41297b4cedf9

## Description

Quad-linear voting (QLV) is a progressive plutoratic voting model, that aims align the interests of an organisation with its participants and make power dynamics explicit, rather than opaque, to complement a more strategic and nuanced governance process.

## Transcript

Hello. My name is Samuel, and I'm here today to talk about game theory and voting games. And that's simply it. So I'm sure a lot of you are familiar with plutocracy, or many call it linear voting, or share-weighted voting, token-weighted voting. It goes by many names. I've dealt with it myself personally as a contributor to decentralised governance, and it can be empowering, but also disenfranchising. It is effective at what it does, though, as it gives efficiency to an organisation and economic robustness through its market evaluation. And capital directly translates into immediate power, which can be quite contentious, as you might have seen yourself, through many governance attacks or, let's say, disenfranchising the smaller contributors in these organisations. It sacrifices broader representation for the sense of efficiency's sake, and it is the go-to model for organisational governance, wherever you go. And then we go on to conviction voting and the VE token model. These are time-weighted voting models that have shown some potential, but also some flaws. They use linear time as a multiplier to represent voting power. And conviction voting focuses more on commitment for independent proposals. And VE token is more around locking shares for a select amount of time in order for a multiplier or a boost in voting power. And we'll give credit to Curve Finance for the VE token model. But when it comes down to the origin of conviction voting, I can't quite pinpoint it. It was either made in Paris in 2019, or there were some claims by the Commons Act. Still an interesting method for voting. And to summarise conviction voting a bit better, I seem to fade that. It's about individual proposals where you can stake your voting power or to showcase your commitment or conviction to an individual, let's say, proposition or proposal in an organisation. Now, why do both of these methods fall short? Conviction voting creates voting inertia simply through fragmenting governance, but then also stagnating the process. That's why Ruthocracy is really desirable. It's agile, it's effective, and it's robust. It's agile. That's why it's usually the go-to choice. Conviction voting also fragments governance because you have to individually stake your shares or tokens into individual proposals. So you can imagine this affects quorums, it affects participation. And if you really care about a proposal, you're not going to redact your voting weight for a new proposal that was just proposed last week. And why do VE escrows and the token model, the VE token model, fall short also? It's because it creates governance qualification and entrenchment, essentially creating a hierarchy in the governance demographic, which has some pretty prevailing effects afterwards, and obviously contributes to voter apathy, as we see in plutocrats, plutocratic systems. And so then we get on to quadratic voting, probably one of the biggest innovations in this industry into governance and game theory, even though it has existed for some time. It's been advocated by Whale, Lally, and Posner, and it's a voting method to reference signaling across multiple choice ballots using a square root voting cost. And ultimately, it empowers the sum of parts and not the sum of a whole. But why it lacks, I'd argue, a lot of practical usage. It's more applicable to democratic systems. And time and time again, it's been advocated as a method for public spending and government, let's say, authorization and policies, you could say. And so it's very good for empowering the minority stakeholders in any voting demographic. But with this, it heavily relies on identity assurances to prevent civil attacks. And that's probably its biggest downfall in terms of practical implementation and adoption. And secondly, it's not quite applicable to organizational governance, which is more binary, through refusing or confirming or abstaining a proposal. And so what are the takeaways from each of these voting models? Time weighting is being used to represent commitment. Quadratic weighting can help to normalize larger concentrated influences. And linear weighting is really effective for agile decision making and economic robustness. So that brings us to ULV, Quad Linear Voting. And it's a progressive, bureaucratic voting model that aims to make power dynamics explicit rather than opaque, like in plutocracy, and adding friction to the governance process. How it does this is using a combination of quadratic and linear weighting that temporally transitions over time. And we'll start with one of the first parameters is the effective time weight. And so this is the duration of which the stakeholder has held their token or shares. It's a time average sum relative to the deposit or holding amount. You might see this method in a lot of solidity contracts. It's just an easier way to model systems into our contracts as a reward rate. Some people might call it. And it's important about this formula is that additional increments actually dilute a stakeholder's time weight. And this is to prevent gamification, but also entrenchment. It makes the governance dynamics competitive. And it's important to note the second equation is not here. And you'll find out about that later. But time weight is preserved on balance reductions to not compromise commitment. Now we're going to get into power levels. This is the P in our formula. We started with P. And power levels are discrete bands or tranches across the voting power curve and to create nuance and normalize voting demographics into distinct stages or tiers. And simply put, you could have your new median and mature demographics. And why is this interesting? Why is this beneficial? Well, it makes a case for more contentious decision making and requires more, say, cross-pollination, cross-coalition building and cross-consensus for decision making in the governance process. And here's the P cumulative formula. So, these are actually not our P values. Our P values are simply 0 to 1. And you can define the tranches or discrete power bands through those decimal values. I'll explain in the next slide or second slide why we use the cumulative value. And now we're going to go to the power ratio, which is the real magic here. And it's the ratio which derives the quadratic and linear weighting of voting power, where alpha equals 1 equals the fully linear weighting. And then alpha equals to 0 would be fully quadratic weighting. And we also have OR-min and OR-max. I found so far in my studies an ideal value for OR-min is 0.2. So, that would give you 20% linear weighting and 80% quadratic to start. And as time evolves, it will eventually converge towards purely linear weighting. Important to note here also, T is the time limiting factor. It's literally OR-max over log time. And T-max would be your duration of convergence. And so far, I'm kind of settled on 720 days, so around two years to fully translate as a mature voter. And now we get into our final time weight formula. So, we use our cumulative power level P formula that we previously talked about. And we do this basically to solve the problem of doing a sum for our power levels on each time we went to compute voting power. So, in order to have 0-1 time complexity, we use the cumulative P values. Just a little hack, right? This is the main place where this is aimed to be integrated. And how does this all come together? And forgive me for my charts at this time. They're a work in progress. As you can see here, this is the voting power curve under QLD. And underneath this distribution, we're going to assume that 40% of the tokens or the shares are allocated to the team. And then 40% is allocated to a community distributed, not proportionally, but among that allocation. And what this chart is supposed to visualize is basically that even though both demographics have the equivalent amount of voting shares, they have different voting power due to how the asset is distributed amongst those stakeholders. So, you can see that the community is not completely overpowering, but it has a significant influence over the team. And this could be catered to a buffer in terms of when you are implementing this voting model. You could have a buffer for the team that locks the tokens one month or two months ahead of the public. And so, when we look at this from a game theory standpoint with everything that has been discussed, we can identify three main strategies. The first is a singleton strategy. It's a single denomination state with no reductions or changes in your balance. It's effective for absolute power accumulation at the cost of flexibility. Then we have sequential, which is more of a realistic, healthy strategy that changes over time, where you progressively dilute your time waste incrementally, but not substantially. And it's a balanced state of power accumulation. And finally, we have the splitting attack or splitting strategy. So, this is our civil attack, if you may call it that. And it's a fragmented stake that is separated into different accounts to take advantage of the earlier quadratic weighting in this voting model. And it's the fastest power accumulation. But what does that really look like when we map it all out? And as you can see, some interesting results. The splitting strategy shows some potential in the early stages of CLV, but ultimately, it reduces up to 50% in your potential voting power because of the lack of the time multiplier. And this is that P value or main is at 0.2. So, the more you increase that initial value, the less prevalent this effect will have with the splitting attack because of the mix of linear voting or linear weighting. And we can see that the singleton strategy is actually the dominant strategy here. And as we said, it does come at a cost of flexibility. But overall, you get the most absolute power accumulation. And then finally, sequential is actually our equilibrium strategy. It just comes right underneath the singleton strategy. And it's one of the more realistic behavioral mechanics in a voting or an organization. I think in human decision making, and you will often not put all your eggs in one basket, you put them in slowly, bit by bit. And I call the splitting strategy suboptimal here because it is dominant in the early phases. But ultimately, it's transient. And that actually completely decapitates your voting power towards convergence to linear weighting. And so, not only does this method, this model make it a high execution cost for splitting attacks, but it's also a high opportunity cost. And sometimes that's invaluable, especially when you're trying to execute a governance attack. And so, QLD and endowment is a model to quantify commitment or loyalty in linear voting and on-chain governance or organizational governance. And larger actors' influence is normalized while smaller actors are empowered over time. It creates byproducts to a scale not yet seen in capital-weighted voting systems, including delegation markets, graduated proposals, and coalition building. It adds friction to the governance process and translates governance attacks from capital problems into coordination problems, exponentially increasing the cost of such actions. And you can find an early draft for this paper under a new collective I'm forming called Focal, focusing pretty much on mechanism design, game theory, and all that good stuff. And thank you very much. Thank you so much, Amirul. We have a couple of questions here, so I'll pass it over to you in a second. First of all, we have, whether quadratic or quad-linear, what incentives do large stakeholders have against splitting up the voting balance into multiple accounts to improve their weight? And you touched a little bit upon it in the results, but maybe you can elaborate. So, ultimately, if, let's say, a large venture capital firm wants to try to game the system, as they do with plutocracy all of the time through the short-sighted governance that they propel, in QLD, if they wanted to take this effectively, as previously mentioned, there's a high execution cost to execute the strategy. You've got to operate multiple wallets. You've got to pay for gas. But then also, at that point in time, you need to have the highest convergence of voting power, additional to the fact that there isn't mature voters in the system to contend with. So, while there may be potential or opportunities for large financial actors to game the system, it essentially comes down to the distribution of power in that organization, and that's probably another area in relation to delegation markets that we're about to answer. Excellent. Thank you, Samuel. The second question was more of a comment to the first question. So, that marks the end of the questions, unless there are any last-minute questions. Okay. Otherwise, you can always catch Samuel right now, right after the talk.