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title: 'Final Research Draft: '

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# Trends in Voter Behaviour and Voting Power: A Comparative Study in Curve Finance and Polkadot

## Abstract
This research examines the impact of financial incentives on voter behavior in two significant blockchain ecosystems, Curve Finance and Polkadot, through a user behavior study of all their voters. As the first comprehensive examination of voter behavior in Web3, the study suggests that when combined with governance, financial incentives lead to longer staking preferences among different voter personas and increased voter turnout. The research will establish the critical decision-making and governance strategies adopted by Curve Finance and Polkadot, which allow the community to agree on significant network changes collectively. However, even in the momentary celebration of collective decision-making, the evolving governance structures built must solve either some form of centralization or extremely low voter turnouts.

## Key Words
Blockchain, voter persona, voting power, voter turnout, proposals, governance, centralisation

## Introduction
Blockchain technology allows for decentralized decision making - what once was hidden is now displayed publicly in any block explorer; what used to be the domain of a few now can be accessed permissionlessly; what was perceived as status quo is now challenged with every executed transaction. 

These qualities are revolutionary, but largely undocumented still. Consequently, this paper serves as an attempt to bring quantitative comparative system analysis to blockchain-based governance systems. 

Firstly, in order to lay a common ground of understanding, we describe the functioning of two systems submitted for comparison, Curve DAO and Polkadot. Secondly, we explain the motivation for case study selection. Thirdly, we seek to understand the voter personas in each of the systems. Fourthly, we analyze the correlations and analytical findings in voter behavior. We observe and decipher the principles that govern these complex environments by breaking down the types of proposals, voter behavior variation towards them, and utilizing agent-based simulations to account for market dynamics influencing voters and consequently DAO governance. 

## Objective
The purpose of this research is to broaden our comprehension of decentralized governance. It also aims to improve the approach of the ecosystem to construct governance systems. By sharing the results of this study, we intend to encourage a deeper understanding of governance structures. This, in turn, will facilitate continued commitment to transparent decision-making in the blockchain world.

This paper focuses on two main themes: voter personas and patterns in voting power accumulation. The objective is to provide valuable insights into the unique governance features of Curve Finance and Polkadot. To achieve this aim, we assess various factors such as voter turnout, proposal participation, voting power, and lock-up windows.

## Background - Curve Finance and Polkadot

In this section, we will summarize the essential governance characteristics of Curve Finance and Polkadot to provide a foundation for further analysis in this paper.

### Curve Finance

Curve Finance is a protocol that allows for the seamless exchange of ERC-20 tokens with minimal hassle and low costs. This is achieved through the use of Liquidity Pools, which require a sufficient number of pooled tokens to ensure successful swaps and incentivize liquidity providers. Curve offers rewards to those who contribute, creating a win-win situation where users can easily exchange tokens while liquidity providers receive rewards.

1. **Governance Proposals**

When looking into Curve, two types of proposals can be distinguished: Gauge proposals and Non-Gauge Proposals. Gauges and gauge weights determine how much reward a liquidity pool gets. Therefore, a gauge proposal will have explicit financial consequences for some or all token holders. Non-gauge 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 impact of proposal types on voter behavior will be discussed more in this research paper.

2. **Community Voting**

A proposer must have a minimum balance of 2500 vote-escrowed CRV (veCRV) to create a Curve DAO proposal. Each proposal lasts for one week.

To vote, CRV token holders must possess veCRV. veCRV represents CRV tokens that are locked for a certain period. The longer the CRV is locked, the more veCRV is assigned to a user, with users being able to lock their CRV for at least 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 that aims to connect different blockchains, also known as parachains, to enable seamless communication, interoperability, and scalability within its network. It facilitates the creation of interconnected blockchains to allow them to work more efficiently and benefit from shared security.

1. **Governance Proposals**
Polkadot has two types of proposals: Treasury proposals and Non-Treasury proposals. In V1 of Polkadot's governance, when a stakeholder wishes to propose spending from the Treasury, they must reserve a deposit of at least 5% of the proposed spending. The treasury proposal will have explicit financial consequences for the protocol, subject to governance, with the current default set to 24 days. On the other hand, non-treasury proposals 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 behavior will be tackled in the "Proposals" section of this research paper.

2. **Community Voting**
To vote on proposals, DOT token holders must lock their tokens. Similarly to Curve, the longer the DOT is locked for, the more voting power is assigned. The voting power of a DOT holder in Polkadot is calculated by multiplying held DOT tokens using the relevant multiplier, which increases as the locking period increases. The multipliers range from 0.1 for zero days to 6 for two hundred and twenty-four days. 


| 1 DOT is locked for | Multiplier | 
| -------- | -------- | 
| 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 holds 100 tokens and locks them for 14 days, his voting power per the above formula is 100 (Dot Tokens Held) * 2 (14 Day Multiplier) = 200. Therefore, Alex will have the voting power of 200 tokens.

### Why Curve Finance and Polkadot?

Curve Finance and Polkadot are distinct in their purposes and functionalities. 

At the same time, due to the need for upgradeable contracts and changeable system parameters, both projects incorporate governance structures, delegating system maintenance responsibilities to their respective communities, as proxied by token in order to facilitate for secure and decentralized decision-making. Both of those governance systems utilize permissionless on-chain execution, which means that the decision-making is directly translated into canonical code, without the need for an external authority or intermediary to apply the changes that tokenholders vote on. 

Within these governance systems, the use of lock-up windows  is also a notable similarity, allowing any individual tokenholder to enhance their voting power by committing to an on-chain lock, during which the holder can’t interact with their tokens.

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 when locking their tokens. This research paper will, among others, seek to study the contrast in voter behavior rooted in the shared principle of token lock-up but with differing financial incentives. 

Additionally, due to the nature of both of these projects as on-chain, permissionless, and decentralized governance frameworks, a comparative study is adequately positioned to deliver quality insights into, voter personas, their behaviors, and general insight into how blockchain-enhanced organizations function. 

### Voter Turnout
This section aims to provide a comprehensive analysis of voter engagement. The calculation of voter turnout metrics is based on the number of veCRV tokens and DOT tokens used for voting over time, relative to the total veCRV and DOT tokens locked over the same period.

**Curve Finance:** On average, X% of the circulating CRV is locked as veCRV. Out of the X% locked, an average of 38% tokens have been used for voting. This highlights that although a significant proportion of CRV is locked, a relatively low percentage is used for voting. Further investigation is required to determine the exact factors contributing to the low percentage of utilized tokens.

**Polkadot:** In contrast, only A% of the circulating DOT is locked, and out of the A% locked, only 0.11% tokens have been used for voting. This highlights a significant disparity in voter engagement between the two blockchain ecosystems, with DOT showing a much lower level of voter engagement than CRV. The low percentage of utilized tokens for voting in DOT could be attributed to several factors, such as a lack of financial incentives.

The following graphs provide a visual representation of the amount of veCRV and DOT used for voting. Upon analyzing the data, it can be observed that the average veCRV used for voting on Gauge proposals is significantly higher than the average veCRV used for Non-Gauge proposals. Conversely, the second graph shows that there is no notable difference between the amount of DOT locked for voting on treasury proposals and non-treasury proposals. These findings suggest that there are different financial incentives contributing to these variations. While Curve Finance incentivizes rewards through gauges, the incentives in Polkadot treasury proposals are limited to particular utilities.

![Screenshot 2024-04-03 at 6.25.37 PM](https://hackmd.io/_uploads/rkfgfC51R.png)

The voter turnout metrics shed light on the extent to which token holders actively engage in voting in both ecosystems. This sets the stage for a deeper exploration into the nature of governance proposals and their implications on decision-making dynamics within the Curve Finance and Polkadot communities. By examining the types and frequencies of proposals submitted in governance, we can gain further insights into the priorities and interests driving the respective ecosystems' governance mechanisms.

### Governance Proposals Breakdown
Governance proposals play a crucial role in decision-making within any community. Our analysis of two ecosystems, Curve Finance and Polkadot, reveals that financial-centric proposals make up a significant portion of all proposals. Gauge proposals constitute approximately 70% of all proposals in Curve Finance, while Treasury proposals make up approximately 80% of all proposals in Polkadot. 

![Screenshot 2024-04-01 at 9.33.00 PM](https://hackmd.io/_uploads/BJBCcId10.png)
![Screenshot 2024-04-01 at 9.33.08 PM](https://hackmd.io/_uploads/SyHC98dyA.png)


### Proposal Submission Patterns
In Curve Finance, we found that most proposals are initiated by individuals associated with the Curve.fi team, particularly two wallets linked to the founder, Michael Egorov. 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. We have provided 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   |


On the other hand, we did not observe such patterns in Polkadot. The most referenda submitted by a single author amounted to only 6% of the total proposals.


### Voter Personas and Respective Patterns

Understanding the governance proposals and the voters who participate is important.
    
The following part analyzes the behavior of voter personas and their respective patterns concerning token holdings. The voter personas are categorized based on the size of their token holdings, and the hierarchy is defined as follows: the top 1% is labeled as whales, the following 5% as sharks, the following 10% as dolphins, the following 20% as fish, and the remaining as shrimps.
    
    

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

    
**Curve Finance:** In the context of Curve Finance governance, voter personas emerge vividly when we dissect them by the size of their veCRV token holdings. Over 58% of token holders choose to lock their tokens for four years. However, an intriguing trend surfaces among the different cohorts of holders. 

In the graph below, the x-axis displays the initial lock-up windows, which range from 7 days to 4 years, and the y-axis displays the percentage of the above-described user personas who have locked their tokens. Our more significant holders, the Whales, Sharks, and Dolphins, show mild hesitation to commit for more extended lock periods. Conversely, they slightly prefer shorter commitments, particularly those under six months. Although the margin is slim, it is a telling divergence. 

It hints that more oversized 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.
    
![Screenshot 2024-04-01 at 11.04.41 PM](https://hackmd.io/_uploads/SJ2vxuuy0.png)

    
**Polkadot:** In the Polkadot ecosystem, analysis yielded a similar yet valuable correlation to Curve Finance. 4% of DOT holders initially choose to lock their tokens for a maximum of 224 days (roughly seven months). Holders with more significant positions prefer shorter lock-up periods, and this pattern is glaringly apparent. 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 markedly different behavior, with approximately 30% opting for an 8-week lock-up and about 5% committing to a 32-week lock-up.


    
![image](https://hackmd.io/_uploads/HkhHB9PqT.png)

Among different holder categories, from whales to shrimps, there is an incremental increase in the preference for longer lock-ups as we move down the scale of holdings. The distinctions and preferences between prominent and smallholders are consistent within each protocol.

However, there is a significant difference between the two protocols. As shown in the pie charts below, in Curve Finance, 67.2% of voters across all groups opt for a four-year lock-up, while in Polkadot, only 4% of the users choose the most extended lock-up window of 224 days. Even among the most minor stakeholders, the shrimps, less than 5% chose the most prolonged lock-up 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 extended periods. This indicates that sustained rewards are crucial in incentivizing token holders to stay longer.



![Screenshot 2024-04-01 at 11.04.50 PM](https://hackmd.io/_uploads/ryt5e_uJ0.png)
![Screenshot 2024-04-01 at 11.05.01 PM](https://hackmd.io/_uploads/r1F5e_O10.png)

With this understanding of voter personas and their lock-up behaviors, it is essential to dive into how they accumulate voting power in different market conditions.

## Voting Power Accumulation Patterns in Different Market Conditions
    
The study of voting power accumulation patterns and the associated dynamics between voters and their locked-up tokens are of paramount importance in understanding how voters use their tokens in upward and downward market conditions. In this regard, the two primary ways in which voters can augment their voting power (VP) are by purchasing additional tokens and locking them up, or by extending their lock-up period, resulting in an increased multiplier. VP calculation is derived from the multiplication of token balance and a multiplier based on the lock-up period.

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

However, analyzing the behavior of voters in response to changes in token prices and market conditions presents a significant challenge. It is challenging to determine whether voter behavior is influenced by changes in token locked amounts and lock-up duration or whether they are affected by the daily routines of the average Externally Owned Account (EOA) wallet.

To overcome this challenge, a quantitative methodology has been developed to simplify this complex analysis. This approach is based on a decomposition of the changes in voting power into its constituent factors. By quantifying the changes in voting power ($\Delta vp$) over time, an analysis of the two constituent factors, changes in balance ($\Delta b$) and changes in conviction ($\Delta c$), can be made.

The change in voting power between two consecutive time points, $t$ and $t-1$, can be derived through arithmetic calculations as follows:

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

This equation 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 $t$.

For this study, each timestamp where a new transaction occurs on the blockchain is considered a discrete-time point. This approach captures the dynamic nature of voting power changes with high granularity. To represent the changes in voting power across different voters and time points, a matrix formulation is used. The matrix of changes in voting power ($\Delta VP$) is defined as follows:

$$\Delta VP \in \mathbb{N}^{T  \times W}$$

Here, $T+1$ represents the total number of time points, while $W$ indicates the number of voters. The changes in voting power can be represented using the following formula:

\begin{align}
\Delta VP = B \odot \Delta C + C(t-1) \odot \Delta B \tag{1}
\end{align}

The formula can be represented in matrix form as:

\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}

The matrix $\Delta VP$ represents the change in voting power for each voter at each timestamp, while $B$ represents the balance of each voter at time $t$, $\Delta C$ represents the change in conviction between $t$ and $t-1$ for each voter, and $C(t-1)$ represents the conviction of each voter at time $t-1$. The matrices $\Delta B$ and $\Delta C$ represent the changes in balance and conviction, respectively, for each voter between $t$ and $t-1$. The symbol $\odot$ represents the element-wise multiplication of matrices.

If $\Delta vp_{t, i}$ is non-zero, the voting power of voter $i$'s wallet has been altered at time point $t$. 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 hold non-zero values simultaneously if the user changes the lock-up window and balance in the same transaction.


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

In summary, this methodology for governance conviction provides a more in-depth and comprehensive approach to analyzing voting power accumulation patterns in different market conditions. Through the matrix formulation, the changes in voting power across different voters and time points can be represented and analyzed with high granularity, providing valuable insights into voter behavior dynamics.


**Accounting for Market Conditions in Curve and Polkadot**
    
In this study, we aim to assess the impact of market conditions on how voters accumulate voting power. To achieve this, we analyze upward and downward trends in the market by employing a combination of short-term and long-term moving averages, namely the 7-day moving average (MA7) and the 30-day moving average (MA30). We define an upward trend when the MA7 exceeds the MA30 and a downward trend when the MA7 falls below the MA30.

It is crucial to acknowledge that token behavior is circumstantial, and varying market conditions may elicit different responses from holders with varying stakes, thereby exhibiting diverse behavior patterns. Therefore, we adopt a nuanced approach, which considers these factors to provide a precise understanding of how balance and conviction impact the ebb and flow of voting power within the governance systems.
![Screenshot 2024-04-01 at 11.12.56 PM](https://hackmd.io/_uploads/Bk3VGO_1C.png)

![image](https://hackmd.io/_uploads/HyA8tqw9T.png)

The charts presented above illustrate how the MA7-MA30 differential correlates with the token price. Our analysis leverages these definitions to explore how market trends affect voter behavior, specifically the influence of the token price and lock-up duration on the dynamic voting power within the governance frameworks of Curve Finance and Polkadot.

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

**Curve Finance:** In the case of Curve Finance, we encountered a challenge when studying shrimp voters due to their number exceeding 12,000 and the high computational complexity of our method. As a result, we adopted a sampling strategy, randomly selecting 2000 shrimp voters in each experiment, and repeated this process 500 times. We calculated the log ratio of conviction impact to balance impact in each experiment and grouped the results by upward and downward market trends. The grouped histograms below showed distinct patterns.

![Screenshot 2024-04-01 at 11.18.38 PM](https://hackmd.io/_uploads/r1y5Qd_JA.png)
In the grouped histograms, we noticed distinct patterns:

During downward trends, the log ratio values were mainly 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, and 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, as three peaks around -0.3, 0.5, and 1 indicate that shrimp behavior is inconsistent during upward markets. However, most shrimps preferred changing their lock-up window, a tendency that was even more pronounced than during the downward trends.
    
**Polkadot:** When analyzing Polkadot's market trends, we observed a deviation from the typical pattern observed in Curve Finance. Instead of a normal distribution, there was a noticeable long tail in the data. Upon closer inspection, we discovered a fascinating insight: a particular 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.

![Screenshot 2024-04-01 at 11.20.53 PM](https://hackmd.io/_uploads/ByQGEdu10.png)


### Conclusion
The research examined voter personas, governance proposals, voter personas and voting power accumulation patterns to determine key trends and patterns in voter behavior. 

Firstly, the research highlights the importance of financial incentives in driving voter turnout, with Curve Finance exhibiting higher levels of voter turnout compared to Polkadot.

Secondly, financial-centric proposals such as Gauge proposals and Treasury Proposals make up the majority of proposals in Curve Finance and Polkadot respectively. However, in Curve Finance, it was found that majority of proposals are initiated by individuals linked to the Curve.fi team.

Thirdly, the analysis reveals the presence of distinct voter personas with varying preferences and behaviors. Whales, sharks, and dolphins exhibited preferences for shorter lock-up windows. Furthermore in Curve Finance, the majority of voters locked their tokens in the highest lock-up window. This trend stood in stark contrast with voters in Polkadot. Understanding these personas is crucial for designing effective governance mechanisms that cater to the diverse needs and motivations of token holders.

Lastly, the study highlights the impact of market conditions on voter behavior. During upward trends, token holders in both Curve Finance and Polkadot exhibit a propensity to adjust their lock-up durations to maximize their voting power. Conversely, during downward trends, there is a more uniform tendency among voters to increase their lock-up durations.

This research contributes to our understanding of decentralized governance in blockchain ecosystems and provides valuable insights for the design and optimization of governance mechanisms. Further research in this area will be crucial to ensuring the scalability and effectiveness of decision-making as the blockchain landscape evolves.

### References
[^1]: Visit https://hackmd.io for more details.
[^2]: https://tanishaisawesome.com
