# A Comparative Study of Voter Personas in Curve Finance and Polkadot

## Introduction

On July 30, 2020, Perseverance, the Mars Rover was launched from planet Earth. Perseverance’s primary mission is to search for signs of ancient life on Mars, and collect rock and soil samples for possible return to Earth. In blockchain ecosystems’ vast and uncharted landscapes, where voters and consensus form the bedrock of decentralised governance, a parallel can be drawn to the spirit of interplanetary exploration.

In much the same way that the Mars rover missions seek to unravel the mysteries of the Red Planet, our research paper embarks on a journey into the governance territories of competitive blockchain ecosystems, notably Polkadot and Curve Finance. Here, we venture beyond the surface, delving into the intricate dynamics of voter personas and voting power patterns. Much like the Mars Rover’s mission, the goal is to observe and decipher the fundamental principles that govern these complex environments.

This paper is divided into three main parts: Entry, Descent, and Landing, popularly known as the EDL. The “entry” component of this paper is an overview of the governance process in Curve and Polkadot. The descent part of this paper will dive deep into the correlations and analytical findings in voter behaviour. Finally, the landing is the take-away: the celebration of what is and the anticipation of what’s next.

PS: The Mars Rover’s Entry, Descent, and Landing (EDL) procedure, colloquially known as the “7 Minutes of Terror,” encapsulates the critical phase when a spacecraft penetrates the Martian atmosphere. This moniker vividly captures the tension and uncertainty accompanying the spacecraft’s descent and landing. Unlike the Rover’s EDL, we hope your reading experience is far from a minute of terror.

## Objective

There are predominantly 2 themes across this paper: voter personas, and patterns in voting power accumulation. This aligns with the objective of providing valuable insights into the unique characteristics of governance in Curve Finance and Polkadot by assessing factors such as voter turnout, proposal participation, voting power, and lock-up windows.

This research aims to contribute to the expansion of our understanding of decentralised governance and offer practical insights that may inform and enhance Polygon’s approach to [Pillar 2: System smart contracts governance ](https://polygon.technology/governance-pillars)execution. By disseminating these findings, we seek to foster a deeper understanding of governance structures, facilitating Polygon’s continued commitment to transparency in decentralised decision-making within the blockchain realm.

## Entry
In this section, we summarise the important governance characteristics of Curve Finance and Polkadot. Treat this section as a refesher or a pre-cursor to understand the upcoming sections:
### Curve Finance

Curve Finance is a protocol that enables seamless exchange of ERC-20 tokens at a low cost and with minimal hassle. This is made possible through the use of Liquidity Pools. To ensure successful swaps, Curve requires a sufficient number of tokens, and to incentivise liquidity providers, they offer rewards to those who contribute. This creates a win-win situation where users can easily exchange tokens while liquidity providers receive rewards.

1. **Governance Proposals**
We noticed two types of proposals in Curve: Gauge proposals and Non-Gauge Proposals. Gauge-related proposals have financial consequences for some or all the token holders. Fundamentally, gauges and gauge weights determine how much rewards a liquidity pool gets. Non-gauge proposals may or may not have financial consequences and may pertain to high-level maintenance and regular upgrades in the network. The different voter behaviours on gauge and non-gauge proposals will be discussed in "descent" section of this research paper.

To make a DAO proposal, a proposer must have a minimum balance of 2500 veCRV. Each proposal lasts for one week.

2. **Community Voting**
To vote, CRV token holders must have veCRV. veCRV means vote-escrowed Curve, which fundamentally means CRV tokens that are locked for a certain period of time. The longer the CRV is locked, the more veCRV is earned. Users can lock their CRV for a minimum of one week and a maximum of four years.

| 1 CRV is locked for | The user is assigned |
| -------- | -------- |
| one week| 0 veCRV
| one month| 0.02 veCRV
| six months| 0.13 veCRV
| one year| 0.25 veCRV
| two years| 0.5 veCRV
| three years| 0.75 veCRV
| four years| 1 veCRV

### Polkadot
Polkadot is a protocol and platform that facilitates the creation of interconnected blockchains (parachains) and enables seamless communication, interoperability, and scalability within its network. In simple terms, Polkadot is like a superhighway for blockchains, connecting them together so they can work more efficiently and experience shared security.

1. **Governance Proposals**
Similar to Gauge and Non Gauge proposals in Curve Finance, when looking into Polkadot, two types of proposals can be distinguished: Treasury proposals and Non-Treasury Proposals. As per [Polkadot's Governance V1](https://wiki.polkadot.network/docs/learn-governance), Polkadot's treasury funds can be spent by making a spending proposal that, if approved by the Council, will enter a waiting period before distribution. This waiting period is known as the "spend" period, and its duration is subject to governance, with the current default set to 24 days. . Thus, a treasury proposal will have explicit financial consequences for the protocol. Non-treasury proposals, on the other hand, may or may not have economic consequences and may pertain to high-level maintenance and regular upgrades in the network. The subject of how the type of proposals impacts voter behaviour will be tackled in the "descent" section of this research paper.

When a stakeholder wishes to propose a spend from the Treasury, they must reserve a deposit of at least 5% of the proposed spend. This deposit will be slashed if the proposal is rejected, and returned if it is accepted.

2. **Community Voting**
To vote, DOT token holders must lock their tokens. The longer the DOT is locked, the more voting power is earned. Users can vote with their DOT tokens, even without locking up, but such users will not receive a significant boost to their voting power. Fundamentally, in Polkadot, voting power of a DOT holder = DOT tokens held * multiplier.

The multipliers are as follows:
| 1 DOT is locked for | The user's multiplier is |
| -------- | -------- |
| zero days| 0.1
| seven days| 1
| fourteen days| 2
| twenty eight days| 3
| fifty six days| 4
| one hundred and twelve days| 5
| two hundred and twenty four days| 6

For instance, if Alex has 100 tokens and locks for 14 days, his voting power as per the above formula is 100 (Dot Tokens Held) * 2 (Multiplier for 14 days, as mentioned in the above table) = 200. Therefore, Alex will have the voting power of 200 DOT tokens.

### Motivation to pick Curve Finance and Polkadot for this study

Curve Finance and Polkadot are distinct in their purposes and functionalities. However, both projects incorporate governance structures to allow their respective communities to participate in decision-making processes. The use of lock-up windows to enhance voting power is a notable similarity between Curve Finance and Polkadot’s governance structures.

Interestingly, while token lock-up mechanisms are involved in both governance structures, Curve Finance employs a governance mechanism that encourages participants to actively engage in decision-making processes by allowing them to gain financial rewards by locking their tokens. This research paper seeks to study the contrast in voter behaviour rooted in the shared principle of token lock-up but with differing financial incentives.

## Descent
In this section, we will dive deep into the findings and insights. You will descent into voter turnout, governance proposals, voter personas, and voting power accumulation in differing market conditions.

### Voter Turnout
The average voter turnout in Curve is __ 268M___ while the average voter turount in Polkadot is __ 1.17M__. While acknowledging that the volume of data in Polkadot may not rival that of Curve, our analysis reveals intriguing parallels and patterns that merit attention.

<Add chart for voter turnout in Curve and Polkadot> </Add>



Regarding voting activities, our investigation of the top 10 wallets, including multisig wallets, revealed patterns suggesting coordinated actions. Michael Egorov, Founder and CEO of Curve Finance, is connected to 5 of these top voting wallets. Moreover, a cluster of wallets among the top 20 voters seems to be affiliated with the Wave protocol, as indicated by Arkham data.And not surprisingly, the top voting multisig wallets are from the top layers of curve, i.e. convex, stake DAO, yearn and etc

<Add chart for showing voting clusters of these multisigs>

Interestingly, for gauge proposals in Curve, the average voter turnout is __ 264M___. For treasury proposals in Polkadot, the average voter turnout is __ 0.97M___.

<Add chart for voter turnout in Gauge Proposals and Treasury Proposals> </Add>



Notably, in the Polkadot ecosystem, Treasury Referendums play a role akin to Curve’s Gauge Proposals. These referendums are imbued with financial incentives, which seemingly act as a catalyst for heightened participation and interest within the governance process. Echoing the trends observed in Curve, Treasury Referendums in Polkadot emerge as a dominant force.

The pattern we observe here goes beyond mere numbers; it tells a story about the driving forces behind governance participation in blockchain ecosystems. Both in Curve and Polkadot, proposals with financial incentives appear to command greater attention and involvement from the community. This observation is not merely coincidental but indicative of a broader trend where financial incentives play a pivotal role in shaping governance dynamics.

On the other end of the spectrum, the average voter turnout for Non Gauge proposals in Curve Finance is __ 296M____ and for Non Treasury proposals in Polkadot is __ 1.86M ____.

### Governance Proposals
Governance proposals are the gateway to decision-making in any community. To understand more about the different kind of proposals, refer to the section <case Studies - Polkadot and Curve Finance></case>

One pattern is abundantly clear in both the ecosystems. Financial centric proposals make up significant portion of all proposals. Proposals relating to gauges and community treasury also drive voter adoption. As shown in the graphs below, in Curve Finance, Gauge proposals constitute approximately 70% of all proposals. In Polkadot, Treasury proposals constitue approximately 80% of all proposals.



However, one distinction must be highlighted. In our analysis of governance proposal creation and voting within Curve.fi, we discovered that the majority of proposals are initiated by individuals associated with the Curve.fi team. Particularly, two wallets linked to the founder, Michael Egorov, stand out in the below table. The top wallet, identified as the Curve.fi deployer on the Arkham data platform, is notably active in both gauge and non-gauge proposal submissions.

Below is a table of top Curve Finance proposers, ranked in the order of participation.

| Rank | Proposer Address | Count | ID on Arkham |
| ---- | ------------------------------------------ | ----- | --- |
| 1 | 0xbabe61887f1de2713c6f97e567623453d3c79f67 | 55 | Curve.fi Deployer |
| 2 | 0x745748bcfd8f9c2de519a71d789be8a63dd7d66c | 28 | @skellet0r (Curve.fi) |
| 3 | 0x7a16ff8270133f063aab6c9977183d9e72835428 | 28 | Michael Egorov (Curve.fi) |
| 4 | 0x0000000000e189dd664b9ab08a33c4839953852c | 22 | Charlie Watkins (Curve.fi) |
| 5 | 0x71f718d3e4d1449d1502a6a7595eb84ebccb1683 | 22 | |
| 6 | 0x947b7742c403f20e5faccdac5e092c943e7d0277 | 22 | Convex Finance Deployer |
| 7 | 0x34d6dbd097f6b739c59d7467779549aea60e1f84 | 17 | |
| 8 | 0xa1992346630fa9539bc31438a8981c646c6698f1 | 14 | |
| 9 | 0xf7bd34dd44b92fb2f9c3d2e31aaad06570a853a6 | 13 | |
| 10 | 0x52f541764e6e90eebc5c21ff570de0e2d63766b6 | 13 | Stake Dao: Curve yCRV Voter |

Unlike Curve Finance, we do not see such patterns in Polkadot. The most referenda submitted by a single author is 8, which amounts to only 6% of the total proposals.

Now that we understand voter turnouts and the governance proposals that drive such turnouts, let's look into the different kinds of voters.

### Voter Personas

For the purpose of this research, voter personas are categorized based on the size of their token holdings. The hierarchy is defined as:

| Token Holdings | Voter Persona |
| -------- | -------- |
| Top 1% | Whales |
| 5% | Sharks |
| 10% | Dolphins |
| 20% | Fishes |
Remaining | Shrimps

**Curve Finance:** In the Curve Finance governance sphere, voter personas emerge vividly when we dissect them by the size of their veCRV token holdings.

In the big picture, over 58% of holders choose to lock their tokens for the maximum duration of 4 years. However, an intriguing trend surfaces among the different cohorts of holders as outlined in the figure below. The x-axis displays the intial lock-up windows. Curve Finance allows holders to choose lock-up windows ranging from 7 days to 4 years. The y-axis displays the percentage of user personas who have locked their tokens.


The ‘whales,’ ‘sharks,’ and ‘dolphins’ – our bigger holders – show a mild hesitation to commit for longer lock periods. Conversely, they exhibit a slight preference for shorter commitments, particularly those under 6 months. Although the margin is slim, it’s a telling divergence. It hints at the reality that larger holders may not need to lock up their tokens for extended periods to wield significant voting power. For them, the flexibility not to lock in for an extended time could be a strategic move to mitigate risk and maintain liquidity options.

**Polkadot:** In the Polkadot ecosystem, the analysis yielded a similar yet striking correlation to Curve Finance.

In the big picture, over **X%** of DOT holders choose to lock their tokens for the maximum duration of 224 days(Roughly 7 months).

As shown in the graph below and similar to Curve Finance's pattern, holders with larger positions tend to prefer shorter lockup periods. Unlike Curve Finance, the pattern is glaringly clear. What's particularly striking in the Polkadot ecosystem is that about 93% of whale and 98% of shark holders tend to lock up their tokens for 14 days or less. Contrastingly, shrimp holders display a markedly different behavior, with approximately 30% opting for an 8-week lockup and about 5% committing to a 32-week lockup.


**What's similar between Curve Finance and Polkadot's user behaviour? **

Within each protocol, the distinctions and preferences between big and small holders appears to be consistent. Among different holder categories – from whales to shrimp – there is an incremental increase in the preference for longer lockups as we move down the scale of holdings.

**What's different between Curve Finance and Polkadot's user behaviour? **

In Curve Finance, over 50% of voters across all groups opt for a four-year lockup, while in Polkadot, the scenario is quite the opposite. Even among the smallest stakeholders, the ‘shrimp’, less than 5% choose the longest lockup period of 32 weeks. This divergence could be attributed to the fundamental differences in the underlying rewards and incentives of Curve Finance and Polkadot.
Curve’s gauge weight voting system incentivizes users to boost their voting power by locking their tokens for longer periods. This is one indication of how sustained rewards play a key role in incentivizing token holders to lock up longer.



Now that we understand voter personas and their lock-up behaviours, we need to understand if this behaviour is consistent. Let's dive deep into how these voter personas accumulate voting power in different market conditions.

### Voting Power Accumulation in Different Market Conditions

We must deeply analyze voting power and understand how voters use the vote-escrowed token model to play the game. Assuming that every voter fundamentally creates one locker on Curve Finance to maximize rewards, voters can boost their voting power (VP) in two ways:

1. Buy More, Lock More: Voters can buy more tokens and lock them up, which increases their token locked amount.
2. Increase their lockup duration: They can extend their lockup time, which increases their conviction multiplier.

This is dervied from the way voting power is calculated.

Voting Power (VP) = token balance * multiplier based on lockup time.

When we examine the data, we face a significant challenge. It is challenging to determine the predominant plan between the two factors in the above equation. It is difficult to determine if the general market and token prices impact voter behavior because changes in token locked amount and lockup duration are not a part of the daily routine of the average EOA (Externally Owned Account) wallet.

We have developed a more robust and trustworthy quantitative method to simplify this complex analysis.

#### A new methodology on measuring voting power accumulation by Polygon Labs for governance conviction

To quantify the changes in voting power $\Delta vp$ over time, we employ a methodological approach that decomposes the change in voting power into its constituent factors: changes in balance $\Delta b$ and changes in conviction $\Delta c$.

#### Formula Derivation

The change in voting power between two consecutive time points, $t$ and $t-1$, is given by:

$$ \Delta vp = vp(t) - vp(t-1)$$

Through arithmetic derivation, this can be expanded as:

\begin{align*}
\Delta vp &= b(t) \cdot c(t) - b(t-1) \cdot c(t-1) \\
&= b(t) \cdot [c(t) - c(t-1)] + c(t-1) \cdot [b(t) - b(t-1)] \\
&= b(t) \cdot \Delta c + c(t-1) \cdot \Delta b
\end{align*}

Here, $b(t)$ and $c(t)$ represent the balance and conviction at time $t$, respectively. The terms $\Delta b$ and $\Delta c$ denote the changes in balance and conviction from time $t-1$ to $t$.

##### Data Points and Time Frames

In our dataset, we consider each timestamp where a new transaction occurs on the blockchain as a discrete time point. This approach allows us to capture the dynamic nature of voting power changes with high granularity.

##### Matrix Formulation

The changes in voting power across different voters and time points can be represented using a matrix formulation. Let $T+1$ represent the total number of time points and $W$ the number of voters. We then define the matrix of changes in voting power, $\Delta VP \in \mathbb{N}^{T \times W}$, as follows:

Given the changes in voting power $\Delta vp$ between two consecutive time points $t$ and $t-1$, the formula is:
\begin{align}
\Delta VP = B \odot \Delta C + C(t-1) \odot \Delta B \tag{1}
\end{align}

And the formula can be represented in matrix form as follows:

\begin{align}
&
\begin{bmatrix}
\Delta vp_{T,1} & \Delta vp_{T,2} &\dots &\Delta vp_{T,W} \\
\vdots & & \vdots \\
\Delta vp_{1,1} & \Delta vp_{1,2} &\dots &\Delta vp_{1,W}
\end{bmatrix} \\
& =
\begin{bmatrix}
b_{T,1} & b_{T,2} &\dots &b_{T,W} \\
\vdots & & \vdots \\
b_{1,1} & b_{1,2} &\dots &b_{1,W}
\end{bmatrix} \odot
\begin{bmatrix}
\Delta c_{T,1} & \Delta c_{T,2} &\dots &\Delta c_{T,W} \\
\vdots & & \vdots \\
\Delta c_{1,1} & \Delta c_{1,2} &\dots &\Delta c_{1,W}
\end{bmatrix}
\tag{2}\\
& +
\begin{bmatrix}
c_{T-1,1} & c_{T-1,2} &\dots &c_{T-1,W} \\
\vdots & & \vdots \\
c_{0,1} & c_{0,2} &\dots &c_{0,W}
\end{bmatrix}
\odot
\begin{bmatrix}
\Delta b_{T,1} & \Delta b_{T,2} &\dots &\Delta b_{T,W} \\
\vdots & & \vdots \\
\Delta b_{1,1} & \Delta b_{1,2} &\dots &\Delta b_{1,W}
\end{bmatrix}
\end{align}

Where:
- $\Delta VP$ is the matrix representing the change in voting power for each voter at each timestamp.
- $B$ is the matrix representing the balance of each voter at time $t$.
- $\Delta C$ is the matrix representing the change in conviction between $t$ and $t-1$ for each voter.
- $C(t-1)$ is the matrix representing the conviction of each voter at time $t-1$.
- $\Delta B$ is the matrix representing the change in balance for each voter between $t$ and $t-1$.

In this formulation, $\odot$ represents the element-wise multiplication of matrices. Matrix $B$ corresponds to the balance of each voter at each time point, Matrix $C(t-1)$ to the conviction at the previous time point, and Matrices $\Delta C$ and $\Delta B$ to the changes in conviction and balance, respectively.

If $\Delta vp_{t, i}$ is non-zero, it indicates that the voting power $VP$ in voter $i$'s wallet has been altered at time point $t$. As can be inferred from Equation (1), a non-zero change in VP due to a change in conviction occurs because $b \cdot \Delta c$ is non-zero. Conversely, a change in balance results in a non-zero value because $c(t-1) \cdot \Delta b$ is non-zero. Typically, these two terms do not simultaneously hold non-zero values, unless the user changes both the lockup window and balance in the same transaction.

The crux of the analysis then becomes determining whether the term $B \odot C$ or $C(t-1) \odot \Delta B$ is more dominant in influencing $\Delta VP$. To this end, we define two metrics:

1. **Balance Impact:** This is quantified as the L1 norm of $|C(t-1) \odot \Delta B|_1$.
2. **Conviction Impact:** This is quantified as the L1 norm of $|B \odot \Delta C|_1$.

Here, the notation $||_1$ denotes the L1 norm, which essentially sums up the absolute values of all elements in the matrix.

These metrics enable us to decompose and quantify the separate influences of balance changes and conviction changes on the overall dynamics of voting power. By applying this method, we can gain deeper insights into how voter behaviors and strategic decisions are shaping the governance landscape in decentralized systems.

**Accouting for Market Conditions in Curve and Polkadot**

To better understand the market conditions, we divide the market conditions into upward and downward trends. We use a combination of short-term and long-term moving averages, specifically the 7-day moving average (MA7) and the 30-day moving average (MA30), to define these trends. When the MA7 is greater than the MA30, we identify an upward trend; when the MA7 falls below the MA30, we indicate a downward trend.

It is crucial to acknowledge that token behaviour is circumstantial. Different market conditions may elicit different responses, and holders with varying stakes may exhibit diverse behaviour patterns. If we were to group everyone without considering whether the market is bullish or bearish, our analysis would not be accurate. By considering these nuances, we aim to provide a more precise and insightful understanding of how balance and conviction impact the ebb and flow of voting power in these governance systems.


›

The charts above show how the MA7-MA30 differential correlates with the token price. By using these definitions, we can more accurately analyze how market trends affect voter behaviour, particularly the influence of the token price and lock-up duration on the dynamic voting power within the governance frameworks of Curve and Polkadot.

**Findings: Voting Power Accumulation in Curve and Polkadot**

**Curve:** We encountered a challenge when studying Curve's voters classified as 'shrimp' because of their high number, which exceeded 12,000, and the high computational complexity of our method. To address this, we decided to adopt a sampling strategy. In each experiment, we randomly selected 2000 shrimp voters and repeated this process 500 times. We calculated the log ratio of conviction impact to balance impact in each experiment, and the results were grouped by upward and downward market trends. We then created histograms to visualize our findings for each group.


In the grouped histograms, we noticed distinct patterns:

During downward trends, the log ratio values were mostly concentrated between 0 and 0.5, displaying a distribution similar to a normal distribution. This suggests that shrimp behavior is more uniform in downward markets. Most log ratios exceeding 0 indicate a tendency among shrimp to increase their lock up duration to alter their voting power.

During upward trends, the scenario was notably more complex. We could clearly identify three peaks around -0.5, 0.1, and 1. This indicates that shrimp behavior is inconsistent during upward markets. However, the majority still seemed to prefer change their lock up window, a tendency that was even more pronounced than during the downward trends.

**Polkadot:** When analyzing Polkadot's market trends, we noticed a deviation from the typical pattern observed in Curve. Instead of a normal distribution, there was a noticeable long tail in the data. Upon closer inspection, we discovered a fascinating insight: a certain group of shrimp voters in Polkadot had a strong inclination towards altering their lock up window rather than increasing their balance during bullish market conditions. This behavior was particularly prominent and suggestive of a unique pattern among this subset of voters.


## Landing

As we conclude our explorative journey into the governance dynamics of Curve Fiannce and Polkadot, we reflect on the insights gleaned and their broader implications. A complex interplay exists between voters, their staking sizes, lockup durations and variant market conditions.

Key observations include：

1. **Dominance of Financially Incentivizing Proposals:** Proposals with financial incentives, such as Curve's gauge proposals and Polkadot's treasury referendums, hold a dominant position in the overall governance structure.

2. **Prominent Role of Curve Team and Multisig Wallets in Governance:** In Curve, it is evident that the creation and voting on governance proposals reflect a concentrated participation pattern where a core group within the ecosystem have a higher weight in decision-making.

3. **Exciting Observations of Similar Voter Personas Across Protocols:** Both in Curve and Polkadot, we observe similar trends among voter personas. Big holders prefer shorter lockup periods to maintain liquidity and flexibility, while smaller holders are more inclined to opt for longer lockups to gain increased voting power. This distinction underscores the varying strategies employed by different stakeholders based on their size and priorities.
4. **Impact of Token Price Trends on Voting Power Accumulation:** Utilizing our newly developed methodology, we discovered that upward and downward trends in token prices significantly influence how users manage their voting power. Some shrimp users maintain or increase their voting power during upward trends by enhancing their conviction. This finding is particularly intriguing, suggesting that users may be reluctant to purchase more tokens for voting in bull markets due to the higher cost implications. In bear markets, this concern is less pronounced. Furthermore, among more prominent holders, at least in Curve's case, the desire to increase voting power through extended lockup periods correlates positively with their locked stakes.

Curve Finance and Polkadot are at the forefront of innovative and complex designs in governance conviction, setting benchmarks for the industry. Their approaches offer valuable lessons for others in the blockchain space.

By delving into historical on-chain data, we better understand the interplay between these sophisticated mechanisms and user behaviours. This insight is crucial for developing and refining governance models that are effective and resilient against various challenges and manipulations.