DAO Governance

Written by Alireza Aghaee.

Introduction

This is a summary of “DAO Governance” by Han, Jungsuk, Jongsub Lee, and Tao Li, published on SSRN on Feb 2023. Decentralized autonomous organizations (DAOs) are non-centralized organizations that run according to a set of rules for making decisions that are encapsulated in smart contracts and implemented using blockchain technology. In (Han, Lee, and Li 2023), the authors create a theoretical model of DAO governance with token-based voting and strategic token trading to examine potential conflicts of interest between a single large participant, a Whale, and numerous small participants. The findings indicate that ownership concentration has a negative relationship with platform growth, but this relationship will be weakened by platform size, token illiquidity, and long-term incentives.

Model

Setup

There is an infinite-horizon, discrete-time model with a platform that facilitates user transactions. The platform is a DAO run by its token holders, and to use the platform, one needs tokens. These token holders can vote on platform changes using smart contracts. Participants may disagree with a platform service change proposal due to potential conflicts of interest from the proposed changes’ benefits and costs. According to a rule, a vote will decide the platform’s final decision.

The timeline of the model is as follows. At ${\textstyle t=0}$, the platform issues one unit mass of the token. The initial cost determines participation. In ${\textstyle t=1}$, token owners vote on the proposal. Votes determine implementation. From ${\textstyle t=1}$, the platform gives token owners utility flows.

The formal setup of the model is as follows:

• Participants: Two types of participants: small participants, referred to as “users,” and a larger participant, referred to as the “whale.” Both types are risk neutral, with a discount factor of ${\textstyle \delta }$. The risk-free rate is ${\textstyle r_{f}={\frac {1}{\delta }}-1}$.
• Participation: There is a continuum of potential users uniformly distributed on the interval ${\textstyle [0,1]}$. To participate, a user indexed by ${\textstyle i}$ must pay a one-time participation cost of ${\textstyle \phi _{i}>0}$ in ${\textstyle t=0}$ and purchase tokens at an exogenously given initial offering price of ${\textstyle {\bar {P}}}$ with no transaction costs. ${\textstyle {\mathcal {U}}}$ is the set of participating users, and ${\textstyle x_{i,t}}$ is the unit of tokens held by user ${\textstyle i}$ in period ${\textstyle t}$.
• The Whale: The whale receives ${\textstyle y_{0}}$ units of the tokens at this initial stage, and ${\textstyle y_{t}}$ is the unit of tokens held by the whale in period t. The Whale is myopic or “short-termist”; it must liquidate its position before a finite horizon of ${\textstyle T\geq 2}$.
• Utility: A user or whale holding ${\textstyle X_{t}}$ tokens in period ${\textstyle t\geq 1}$ derives platform utility as
  $$U\left(X_{t}\right)=A(a)NX_{t}$$
  where ${\textstyle N}$ represents the total number of participating users given by
  $$N=\int _{0}^{1}\mathbb {1} (i\in {\mathcal {U}})di$$
  that captures the network effect, and ${\textstyle A(a)}$ captures the technology (or efficiency) component. The technology component ${\textstyle A(a)}$ is determined by the action ${\textstyle a\in \{R,I\}}$ where ${\textstyle a=}$ ${\textstyle I}$ means that the proposal is implemented, and ${\textstyle a=R}$ means it is rejected.
• Vote: In ${\textstyle t=1}$, the platform implements the proposal ${\textstyle (a=I)}$ if the total mass of votes in favor of its implementation exceeds the minimum exogenous threshold of ${\textstyle {\bar {x}}}$ :
  $$\mathbb {1} \left(a_{w}=I\right)y_{1}+\int _{\mathcal {U}}x_{i,1}\mathbb {1} \left(a_{i}=I\right)di\geq {\bar {x}}$$
• Conflict of interests: implementing the proposal would destroy value for users if ${\textstyle A(R)>A(I)=(1-\theta )A(R)}$. If approved, the whale benefits privately, and this private benefit increases with its holding. The whale’s benefit from implementing the proposal is ${\textstyle By_{0}}$, where ${\textstyle B}$ is a random variable that is either ${\textstyle {\bar {B}}>0}$ or zero with probability ${\textstyle 1-\mu }$. Users learn ${\textstyle B}$’s value at ${\textstyle t=1}$.
• Price/Value: ${\textstyle P(a)}$ is the intrinsic value of the tokens to users given the status of the proposal implementation ${\textstyle a}$ and the mass of participating users ${\textstyle N}$. It is given by the present value of utility flows per unit of tokens. Without the whale, the price would converge to this intrinsic value.
  $$P(a)=\sum _{s=0}^{\infty }\delta ^{s}A(a)N={\frac {A(a)N}{1-\delta }}.$$
• Trades: Tokens can be traded with trading costs that are convex in volume to capture illiquidity consequences. Authors assume a quadratic function for trading costs as a function of the number of tokens traded, ${\textstyle \Delta X}$:
  $$C(\Delta X)={\frac {\lambda }{2}}(\Delta X)^{2}$$
  where ${\textstyle \lambda >0}$ is a parameter that captures the severity of illiquidity problem. Short sales are not allowed.

Problems

• User Problem: Given the platform’s action ${\textstyle a}$ in ${\textstyle t=1}$, a representative user’s value in period ${\textstyle t\geq 1}$ can be represented in a recursive form as:
  $$V_{t}^{a}\left(x_{t-1}\right)=\max _{\Delta \tau _{t}}A(a)N\left(x_{t-1}+\Delta x_{t}\right)-P_{t}^{a}\Delta x_{t}-{\frac {\lambda }{2}}\Delta x_{t}^{2}+\delta V_{t+1}^{a}\left(x_{t-1}+\Delta x_{t}\right),$$
  subject to the constraints:
  $${\begin{aligned}&x_{t}=x_{t-1}+\Delta x_{t}\\&x_{t}\geq 0.\end{aligned}}$$
  The first term in the equation is the utility flows given the token holdings at the end of the period, the second term is the cost of acquisition (or the proceeds from selling), the third term is trading costs, and the fourth term is the continuation value given the choice.
• User Solution: The value function of a user in period ${\textstyle t\geq 1}$ with the token holdings ${\textstyle x_{t-1}}$ at the beginning of period ${\textstyle t}$ can be written as
  $$V_{t}^{a}\left(x_{t-1}\right)=\alpha _{t}+\beta x_{t-1}$$
  where ${\textstyle \alpha _{t}}$ is the present value of future trading gains (pinned down in the paper) and ${\textstyle \beta }$ is the marginal value of tokens: ${\textstyle \beta =P(a)}$. The optimal trading strategy of tokens in period t given price ${\textstyle P_{t}^{a}}$ is ${\textstyle \Delta x_{t}={\frac {P(a)-P_{t}^{a}}{\lambda }}}$
• Token Price: The market clearing condition, besides the optimal trading of all users (that is inevitably the inverse of the Whale’s trades,) implies the equilibrium token price as:
  $$P\left(\Delta y_{t};a\right)=P(a)+{\frac {\lambda }{N}}\Delta y_{t}$$
• Whale’s Problem: The whale’s value, given ${\textstyle y_{t-1}}$, in a recursive form is as follows:
  $${\begin{aligned}V_{w,t}^{a}\left(y_{t-1}\right)=\max _{\Delta y_{t}}A(a)N\left(y_{t-1}+\Delta y_{t}\right)-P\left(\Delta y_{t};a\right)\Delta y_{t}\\-{\frac {\lambda }{2}}\Delta y_{t}^{2}+\delta V_{w,t+1}^{a}\left(y_{t-1}+\Delta y_{t}\right),\end{aligned}}$$
  subject to the constraints:
  $${\begin{aligned}&y_{t}=y_{t-1}+\Delta y_{t}\\&y_{t}\geq 0\end{aligned}}$$
  and the boundary condition:
  $$y_{T}=0$$
  The boundary condition ensures that the holdings are completely liquidated by period ${\textstyle T}$. Optimally reducing its position over the investment horizon allows the Whale to maximize its expected utility, considering the trade-offs between token payoffs and trading costs. The paper shows that in equilibrium, the Whale will optimally liquidate its position gradually through time and not all at once. This is because of the illiquidity-induced convex trading costs.

Equilibrium

At ${\textstyle t=0}$, each user maximizes their expected utility by choosing whether to participate or not and buying the tokens at the initially-offered price of ${\textstyle {\bar {P}}}$. That is, user ${\textstyle i}$ solves

$$\max \left(V_{0},\phi _{i}\right)$$

where ${\textstyle V_{0}}$ is the ex-ante value of participating in the platform’s activities:

$$V_{0}=\max _{x_{0}\geq 0}-{\bar {P}}x_{0}+\delta \mathrm {E} \left[V_{1}^{a}\left(x_{0}\right)\right]$$

The paper carefully solves the model and derives both players’ equilibrium actions and values given the state realization. Based on the derived equilibrium, the authors make four theoretical predictions:

• Prediction 1 The growth rate of platforms is negatively correlated with their ownership concentrations, i.e.,
  $${\frac {\partial V_{0}}{\partial y_{0}}}<0$$
• Prediction 2 The higher service value of platforms reduces the negative correlations between the growth rate of platforms and their ownership concentrations, i.e.,
  $${\frac {\partial ^{2}V_{0}}{\partial y_{0}\partial A(R)}}>0$$
• Prediction 3 The illiquidity of tokens reduces the negative correlations between the total value of platforms and their ownership concentrations, i.e.,
  $${\frac {\partial ^{2}V_{0}}{\partial y_{0}\partial \lambda }}>0$$
• Prediction 4 Long-term incentives of the Whale reduce the negative correlations between the growth rate of platforms and their ownership concentrations, i.e.,
  $${\frac {\partial ^{2}V_{0}}{\partial y_{0}\partial T_{L}}}>0$$

Empirical Analysis

Data

The study uses voting platform data to examine DAO investors’ voting records from July 20, 2020, through July 31, 2022. They acquired voting data for 460 DAOs with at least 650 votes that were most likely to have an existing underlying business. The data includes the voting token name, symbol, contract address, proposal information, start and deadline dates, voter address, vote date, and the number of votes.

The researchers manually searched DAO voting token contracts to establish whether investors used governance tokens or staked tokens, including vote escrowed/locked tokens. They manually searched CoinMarketCap for DAO-related coins and downloaded their daily price and volume data. The final dataset comprised 207 DAOs with non-missing price, volume, and TVL data.

The total value locked (TVL) in the sample of platforms over time shows a clear boom-and-bust cycle in the DeFi industry as a whole, peaking around the end of 2021. The average platform in the sample has a TVL of $1.2 billion, but the median TVL is only $103 million, indicating a highly skewed distribution. The average and median weekly TVL growth are both negative, and the weekly returns of associated tokens are even more negative. The authors note that the market for governance tokens is highly concentrated, with the largest three whales commanding almost two-thirds of voting power on average. The average number of platform participants is 212, and the average platform age is six months. Finally, the authors report that the distribution of the illiquidity measure is also highly skewed, with an average of 0.112 and a median of 0.017.

Empirical Findings

To test their theoretical predictions about the relationship between platform growth and proxies for voting power concentration, the authors use weekly panel regressions on the collected sample of DAOs. Voting data is converted to weekly series, and weekly averages of voting power concentration are used when multiple proposals exist in a particular week. The Herfindahl-Hirschman Index of voting power and the top three voters’ fraction of total votes are used as concentration measures. These measures were lagged by one week when used as the independent variables.

The study identifies a negative correlation between TVL growth and the HHI of voting power. Particularly, a one standard deviation increase in HHI is associated to a 1.1 percentage-point decrease in weekly TVL growth. The impact is economically substantial as the average weekly TVL growth is only -0.9%. Additionally, the top three voters’ ownership negatively affects platform growth, with the marginal effect being significantly greater than the average weekly TVL growth. These findings align with the study’s first theoretical prediction that more decentralized voting power increases platform growth.

The study tests two additional predictions. Firstly, it is hypothesized that a platform with a broader user group and higher network value would reduce the negative effect of the HHI of voting power on TVL growth. Secondly, the study expects token illiquidity to have a similar dampening effect, as whales would suffer significant price impacts when attempting to amass a large stake. Token illiquidity is measured using the (Amihud 2002) illiquidity ratio. Whales may accumulate significant voting power to pass proposals that benefit them but harm other investors. This is more costly when tokens are illiquid, prompting them to align their incentives with minority token holders.

The study adds an interaction term between the HHI of voting power and platform size (proxied by lagged TVL) to the baseline regression specification to test the latter predictions. The results show a positive and statistically significant coefficient on the interaction term, indicating that a higher valuation reduces the negative relationship between platform growth and ownership concentration. A similar result is obtained using an interaction term of HHI and token illiquidity instead.

The study tests its last prediction by examining events where platforms transitioned from the one-token-one-vote model to a staking model, which assigns vote weights and yields proportional to a “locking period." Using an event-study framework, the TVL growth of a set of DAOs that switched to a staking model during the sample period is compared to that of a control group of DAOs that did not adopt staking models. The treated platforms exhibit an 8.3 percentage-point higher growth rate during the event window than control platforms, which is economically significant considering the average weekly growth rate of the sample DAOs is slightly negative.

Conclusion

The research paper fills a significant gap in the literature on DAO governance by incorporating micro-foundations of the conflicts of interest among different token holders. The paper develops a theoretical model that explains how whales, large token holders in a DAO, may disrupt the long-term growth of the platform through “rug pulls," in which they inflate token prices before unwinding their positions. The model predicts a negative correlation between whales’ voting power concentration and DAO growth, which will be significantly alleviated for larger platforms and alternative voting mechanisms, including staking and vote escrow models. The empirical evidence strongly supports these predictions, providing insights into alternative voting mechanisms to improve the effectiveness of this new type of digital organization.

Amihud, Yakov. 2002. “Illiquidity and Stock Returns: Cross-Section and Time-Series Effects.” Journal of Financial Markets 5 (1): 31–56.

Han, Jungsuk, Jongsub Lee, and Tao Li. 2023. “Dao Governance.” https://ssrn.com/Abstract=4346581.