Emergent Outcomes of the veToken Model

Summary

Decentralised organisations use blockchains as a basis for governance: they use on-chain transactions to allocate voting weight, publish proposals, cast votes, and enact the results. However, blockchain-based governance structures have challenges, most notably, the need to align the short-term outlook of pseudonymous voters with the long-term growth and success of the decentralised organisation. The Vote-Escrowed Token (veToken) model attempts to resolve this tension by requiring voters to escrow or lock tokens of value for an extended period in exchange for voting weight.

In this paper, the authors describe the veToken model and analyse its emergent outcomes. They show that voting behaviour follows bribes set by higher-level protocols, and that the cost per vote varies depending on how it is acquired. They describe the implementation of the veToken model by Curve Finance, a popular automated market maker for stablecoins, and the ecosystem of protocols that has arisen on top of this implementation. They show that voting markets such as Votium largely determine the outcome of fortnightly votes held by Convex Finance, and they show that Frax Finance, a stablecoin issuer, plays a central role in the ecosystem even though they directly lock relatively few tokens with Curve. Instead, they indirectly lock tokens through yield aggregators such as Convex Finance and purchase voting weight through voting markets such as Votium. Although the veToken model in isolation is straight-forward and easily explained, it leads to many complex and emergent outcomes. Decentralised organisations should consider these outcomes before adopting the model.

The veToken model was proposed and implemented by Michael Egorov as part of Curve Finance, an automated market maker that specialises in stablecoin trading. The model was implemented using smart contracts that extend Aragon, a DAO governance framework. The critical difference between it and previous systems was that it replaced the one-token one-vote model with a voting weight proportional to lock time. Users need to lock or escrow tokens for a fixed period in exchange for voting weight. The longer the period, the more voting weight is granted. For Curve Finance, the token is known as CRV and the corresponding locked tokens or voting weight is known as veCRV. During the lockup period, the locked tokens are non-transferrable, i.e., CRV is transferrable but veCRV is not. Voting weight, w, for a user can be calculated using: w = a · (t / tmax), where a is the number of tokens (e.g., CRV), t is the desired lockup period, and tmax is the maximum lockup period. In Curve Finance, the minimum lockup period is one week and the maximum is four years. Consequently, a user who locks up their tokens for one week would need to lockup 208 times the number of tokens compared to a user who locks for the maximum lockup period of four years to get the same voting weight. The intention is to align the, potentially short-term, interest of the voters with the long-term goals of the decentralised organisation by having users commit to a lockup period to become voters with their voting weight being proportional to the duration of the lockup.

There is another aspect to the veToken model that warrants discussion. In general, decentralised organisations suffer from poor voter turnout and voting weight alone might not be incentive enough for users to lock tokens for extended periods. Therefore, the veToken model includes an additional economic incentive: the allocation of new tokens (CRV tokens in the case of Curve Finance) is directed via voting using a mechanism known as gauges. Curve Finance is a platform for stablecoin trading. It uses gauges to measure the amount of liquidity provided by users to the various liquidity pools. Each gauge is assigned a weight and those weights determine the daily emission of new CRV tokens. The weights are set every week at Thursday midnight UTC after a gauge proposal vote. Therefore, users with voting weight decide on the allocation of new CRV tokens to liquidity providers. In fact, the voters may be liquidity providers and they can choose to direct the new tokens to themselves. This incentivises the lockup of tokens for extended periods.

Curve has spawned several higher-level protocols and strategies. For example, yield aggregators such as Convex Finance, Yearn Finance, and Stake DAO provide smart contracts that hold and lock CRV on behalf of users. This allows users to lock tokens for the maximum lockup period, to trade tokenised claims on those locked tokens, and to amortise gas costs. Voting markets such as Votium allows anyone to incentivise particular Curve gauges by rewarding votes with bribes. Frax Finance is a stablecoin issuer that interacts with many of these protocols. For example, they use Curve to lock CRV for veCRV, they hold tokenised veCRV via Convex, and they incentivise Curve gauges using Votium.

The authors collected on-chain and off-chain data from three primary sources within the Curve ecosystem. Firstly, they gathered transaction data from the Ethereum blockchain relating to Curve: transactions involving the CRV token contract, the veCRV token contract, and the Gauge Controller contract. Curve executes its governance entirely on-chain. Their data for Curve covers the period from the deployment of the CRV token on 12th August 2020 until 17th March 2023. Secondly, they gathered transaction data from the Ethereum blockchain relating to Convex: transactions involving the CVX token contract, the vlCVX token contract, and the cvxCRV token contract. CVX is Convex’s governance token; vlCVX is a locked version of CVX — it works in a manner similar to CRV and veCRV except that the maximum lockup period is much shorter (16 weeks) and the voting weight per vlCVX is determined by the amount of veCRV the Convex protocol owns. Users that lock CVX to get vlCVX receive voting weight on Convex, and in turn, voting weight from the veCRV held by Convex. Their data for Convex covers the period from the deployment of the CVX token on 17th May 2021 until 17th March 2023. Additionally, they collected the details of all Convex proposals via Snapshot using their GraphQL API. Thirdly, they gathered transaction data from the Ethereum blockchain relating to Votium: transactions involving the bribing contracts for the gauges. Their data for Votium covers the period from the deployment of the Voting bribing contracts on 12th September 2021 until 17th March 2023. They mapped the bribes in the Votium contracts to their associated gauge in the Curve Gauge Controller contract.

The authors begin with results relating to Curve’s implementation of the veToken model. These can be considered first-order results, in that, they relate directly to CRV and veCRV. Firstly, they analysed participation in the weekly gauge proposals and the non-gauge proposals. The former are economically incentivised through bribes and CRV emissions whereas the latter are not. They found 9551 unique addresses that lock their CRV tokens to get veCRV, with 2555 (27%) voting in the fortnightly gauge proposals. However, participation in the non-gauge proposals is significantly lower. For example, ‘ownership proposals’ that seek the community’s decision on adding new gauges, receive votes from an average of 24 unique addresses. This mirrors the low participation found in other decentralised organisations and shows that the economically incentivised gauge proposals have better turnout, but this turnout does not carry-over to the non-gauge proposals. Secondly, they considered the quantity of CRV tokens that are locked for veCRV: there are 644 million CRV (46%) locked for veCRV, leaving 770 million CRV in circulation. The tokens are locked with an average remaining lockup period of 181 weeks, or 3.5 years. This duration indicates a high level of commitment by the token holders to the ecosystem and a long-term outlook on the value of the protocol. Arguably, these numbers show the veToken model is working as expected: users are incentivised to lockup their CRV tokens for extended periods in order to gain voting weight. They use that voting weight to vote on the gauge proposals and direct the emissions of CRV to liquidity providers. However, the participation in non-gauge proposals remains low with just 24 addresses voting on an average non Gauge Proposal.

The authors then turn their attention to the higher-level protocols. Convex participates in the Curve ecosystem as one of nine whitelisted contract accounts that can lock CRV for veCRV. In fact, 290 million (45%) of all locked CRV belongs to Convex, making them the entity with the largest voting weight in Curve. However, Convex’s voting weight is itself governed by its own token, CVX. There are 71 million CVX, of which 78% is locked for vlCVX to gain voting weight. This is higher than the equivalent number for Curve. Voting on Convex is conducted off-chain via Snapshot with the results relating to Curve proposals posted on-chain. As with Curve, the fortnightly gauge proposals attract the most interest: 1124 unique addresses and 95% of all vlCVX vote in the gauge proposals. The number of unique addresses might be higher except for delegation where a single address can vote using voting weight delegated to it from many other addresses. There is less interest in non-gauge proposals which receive votes from an average of 77 unique addresses. All of this voting activity appears as a single address when analysing Curve in isolation.

Votium operates at a higher level than Convex. It gathers and distributes bribes to holders of veCRV and vlCVX in return for them voting a particular way in the gauge proposals. The total USD value of those bribes for each fortnightly vote is highly dependent on broader market conditions: the peaks in late 2021 and early 2022 coincide with peaks across cryptocurrency markets. At the time of writing, the total value of Votium bribes to date is USD 248 million and the value for the most recent fortnight period is over 3 million. The authors divide the data into a bootstrapping phase and a mature phase. The bootstrapping phase includes the first eight gauge proposals; the mature phase includes all subsequent gauge proposals and continues to the present day. In the bootstrapping phase the correlation coefficient between the percentage of bribes attracted and the percentage of votes received is 0.88. In the mature phase the correlation coefficient is 0.99. There were few outliers in the mature phase. Of the 691 dots in the figure, only one represented a gauge that received a percentage of votes less than 0.8 of its relative bribe in a given fortnight. In other words, votes follow bribes. Conversely, there were 91 instances where a gauge received a percentage of votes more than 1.2 times its relative bribe. However, this can be explained due to two overlapping factors. Firstly, 71 received a vote that was less than 1% of the total number of votes for a given fortnight — the bribes and votes associated with the gauges were too small to be meaningful. Secondly, 79 involved Frax gauges: since Frax owns vlCVX and is a major briber to Votium, it is to be expected that they would vote for their own lesser-bribed gauges. This analysis shows that bribes have a significant impact on the outcome of gauge proposals, and, specifically, that votes follow bribes. All of the percentage point differences between the bribes directed to and the votes received by a Curve gauge for a single instance of a fortnightly vote are within the −6%–2% range.

The authors then consider the cost of votes. Frax is a central player in the Curve ecosystem. They participate at the three levels already mentioned: they lock CRV for veCRV, they lock CVX for vlCVX, and they make bribes via Votium. The Frax/USDC pool has the second-highest total value locked (TVL) across all Curve pools, trailing only to the Eth/Staked ETH pool. At the Curve level, Frax began locking CRV for veCRV in July 2022 after a successful governance proposal whitelisted the Frax staking contract. As of February 2023, Frax has locked 697 114 CRV for veCRV, or just 0.01% of all locked veCRV. The authors determined the USD value of the locked CRV by the price at which it traded when it was locked. This resulted in a total locked value of USD 618 830. Frax used this voting weight to exercise a total of 17.3 million votes. This yielded a cost per vote of USD 0.051. It is important to note that the cost per vote decreases over time as the upfront cost of the token is amortised. Additionally, these tokens do have the potential to be traded once the lockup period has expired. At the Convex level, Frax plays a more influential role. Using the same metric as above, they found that, as of February 2023, Frax has locked USD 64.74 million worth of CVX for vlCVX. To determine their voting weight at the Curve level, they examined the amount of veCRV tokens held by Convex during each fortnightly period and the percentage of voting weight held by Frax. This showed that Frax exercised a total of 2.88 billion votes which yields a cost per vote of USD 0.022. Finally, they analysed Frax’s bribes via Votium. Frax is the largest contributor to bribes, accounting for 41% of all bribes to vlCVX, or USD 103.69 million. Based on the correlations in Sect. 5.1, they estimate that these bribes resulted in 6.72 billion votes at the Curve level. As of February 2023, Votium bribes for Frax cost USD 0.015 per vote, making it the most cost-efficient option for Frax. However, it is important to note that, unlike the previously described levels, the value of bribes is realised immediately, whereas locking tokens still provides Frax with a claim to the asset once the lock reaches maturity.

The veToken model creates a system where voting weight can be acquired through different mechanisms. In the most direct method, users can lock tokens, say CRV for veCRV, and receive the corresponding voting weight. At another level, users can have a claim to locked tokens and their corresponding voting weight through an intermediary, say CVX locked for vlCVX. At yet another level, users can bribe the holders of locked tokens, say veCRV or vlCVX, to vote a particular way. The authors calculate a cost per vote for each of these levels.

In conclusion, the authors describe the veToken model and its implementation within the Curve ecosystem. They analysed its usage by looking at locking rates, lockup durations, voting participation rates, and financial incentives. They showed that, while the mechanism is simple in isolation, the outcomes are complex. They showed that votes follow bribes. In other words, the voting behaviour of users can be directed through bribes from higher-level protocols. This has a significant impact on the outcome of the gauge proposals. In fact, the distribution of the bribes largely determines the outcome. They also showed that the cost per vote depends on how the vote is acquired. It can be acquired at the base level by locking, but also at intermediary levels using yield aggregators which lock indirectly, or by paying bribes to voting markets. Their findings show a difference in participation between gauge proposals and non-gauge proposals. For non-gauge proposals, voter participation is low, which mirrors many other decentralised organisations. However, for gauge proposals, voter participation is significantly higher. This affirms the design of the veToken model: users commit to locking tokens for extended durations in exchange for voting weight. In turn, this creates greater participation. However, participation in gauge proposals is economically incentivised. Voters use their voting weight to direct emissions of CRV. Higher-level protocols including yield aggregators like Convex and voting markets like Votium have emerged to maximise the return for users. Convex’s 45% share of all locked CRV and Votium’s USD 248 million worth of bribes have a major influence on outcomes: Since January 2022, when Votium began to gain recognition, they observed a 0.99 correlation between voting percentages and the percentage of bribes distributed to each gauge. This is in contrast to existing decentralised organisations where voting coalitions and influential leaders play a more significant role. One entity that participates in Votium bribes and has influence at all levels of the Curve ecosystem is Frax, a stablecoin issuer. They hold less than 0.1% of all veCRV, yet wield significant influence at other levels. They have spent more than USD 100 million in bribes using Votium. In this way, Frax can impact the outcome of gauge proposals without having to lock tokens for extended periods. The maximum lockup period for Convex is just sixteen weeks whereas the maximum lockup period for Curve is four years. Votium does not have any lockup requirement. One might expect such votes to cost more on a per-vote basis, i.e., there might be a premium to acquiring votes without the requirement to lock for an extended period. However, the cost per vote acquired through Convex is currently lower than the cost of votes acquired through Curve, and the cost per vote acquired through Votium is currently lower than the cost of votes acquired through Convex. In conclusion, the study shows the dynamic interplay between the various levels of the Curve ecosystem, and, more generally, the veToken model. While the token locking mechanism is straight-forward to understand, it results in higher-level protocols that have complex outcomes. The model was developed to address the limitations of the one-token one-vote model. In doing so it has spawned additional protocols that try to capitalise on its behaviour. In the case of Decentralised Finance (DeFi), this is viewed as a positive (i.e., “money legos”). However, for governance, it means that higher-level protocols can have surprising and, perhaps, undue influence on lower-level ones.

Based on the paper, here are specific improvements to AI systems and what the improved systems can do:

1. Predictive Governance Outcome Model

• Improvement: Train a model on the observed 0.99 correlation between bribe distribution and vote outcomes (Fig. 2, mature phase). Use gauge-level bribe amounts, historical vote percentages, and protocol-level features (e.g., Frax ownership of vlCVX) as inputs.

• Capability: The AI can forecast the exact vote share for each gauge in an upcoming fortnightly proposal with <1% error, given the bribe allocation. This enables DAO treasuries to simulate what-if bribe scenarios before committing funds, optimizing their spend per vote.

2. Dynamic Vote Acquisition Cost Optimizer

• Improvement: Implement a multi-level cost model (Curve veCRV, Convex vlCVX, Votium bribes) that ingests real-time lock durations, token prices, and bribe amounts. Use the paper’s finding that cost per vote decreases from 0.051 (Curve) to 0.022 (Convex) to 0.015 (Votium) as of Feb 2023, but adjust for lock expiry and market volatility.

• Capability: The AI recommends the cheapest avenue to acquire voting weight for a target proposal, automatically switching between direct locking, indirect locking via Convex, or Votium bribes based on live data. It also flags when a lockup’s amortized cost becomes cheaper than bribes (e.g., after 2 years of a 4-year lock).

3. Bribe-Vote Anomaly Detector

• Improvement: Build a classifier that flags gauges where vote share deviates from bribe share by >20% (the 91 outliers in Fig. 2). Features include gauge age, liquidity depth, Frax involvement, and voter concentration.

• Capability: The AI detects when a protocol is over-voting (e.g., Frax voting for its own lesser-bribed gauges) or when bribes are ineffective due to low liquidity. This alerts governance participants to potential vote-buying manipulation or inefficiencies, enabling counter-strategies.

4. Lockup Commitment Forecaster

• Improvement: Use the paper’s data on 644M CRV locked (46%) with average remaining lockup of 181 weeks to train a time-series model predicting future lockup behavior. Inputs: historical lock/unlock events, token price, gauge emission rates, and Convex’s 45% share.

• Capability: The AI forecasts the percentage of CRV that will remain locked over the next 6–12 months, allowing DAOs to estimate future voting power concentration and plan for potential governance attacks (e.g., if lockups drop below 30%, the system alerts to increased bribe susceptibility).

5. Cross-Protocol Influence Mapper

• Improvement: Create a graph neural network that models the multi-level influence chain (CRV → veCRV → Convex → vlCVX → Votium → bribes → votes), using the paper’s finding that Frax holds <0.1% of veCRV but 41% of all Votium bribes.

• Capability: The AI maps which entities control effective voting power at each level, even when they hold minimal direct tokens. It can simulate how a change in one protocol (e.g., Convex reducing its lockup period) would shift influence across the ecosystem, helping regulators and DAOs identify hidden concentration risks.

6. Governance Participation Incentive Optimizer

• Improvement: Apply the paper’s finding that gauge proposals attract 27% voter turnout vs. 24 addresses for non-gauge proposals. Train a reinforcement learning agent to design incentive structures (e.g., emission boosts, bribe matching) that maximize participation in non-gauge proposals.

• Capability: The AI generates optimal reward schedules for non-gauge votes (e.g., ownership proposals), increasing turnout from 24 to >1000 addresses without requiring token locks, by mimicking the economic incentives that drive gauge participation.

7. Real-Time Bribe-Effectiveness Dashboard

• Improvement: Integrate the correlation model (0.88 bootstrapping, 0.99 mature) into a live monitoring system that ingests Votium bribe data and on-chain vote results every block.

• Capability: The dashboard shows, for each active gauge, the marginal cost per additional vote (based on current bribe levels) and predicts whether a new bribe will shift the outcome. It alerts users when a bribe is 80% effective (i.e., vote share ≈ bribe share) versus when it’s saturated, preventing wasted capital.

8. Lockup Period Risk Assessor

• Improvement: Use the paper’s cost-per-vote decay curves (Fig. 5) to build a risk model that quantifies the opportunity cost of locking tokens vs. using bribes, factoring in token price volatility and lockup duration (1 week to 4 years).

• Capability: The AI advises DAO treasuries on whether to lock tokens for 4 years (lower cost per vote over time but illiquid) or use short-term bribes (higher immediate cost but flexible), based on their risk tolerance and expected governance needs. It also flags when a lockup’s remaining time is <1 year, suggesting a switch to bribes to avoid holding illiquid assets.

These improvements directly operationalize the paper’s empirical findings, turning them into actionable AI tools for governance participants, DAO treasuries, and regulators.