Exploring Decentralized Governance: A Framework Applied to Compound Finance

Abstract

This research proposes a methodology which can be used for measuring governance decentralization in a Decentralized Autonomous Organization (DAO). DAOs, commonly, have the ambition to become more decentralized as time progresses. Such ambitions led to the creation of decentralized governance models that use governance tokens to represent voting power. Relevant research suggests that the distribution of the governance tokens follows centralized accumulations in a few wallets. By studying the accumulations of voting power from a DeFi protocol, this research presents a framework for identifying and measuring decentralization via analyzing all the various governance sub-systems instead of focusing on one or a small group. Governance within a DAO is a multi-layered process. By examining the decentralization of each layer or subsystem within the overarching governance structure, we can compose a comprehensive understanding of the entire protocol. To demonstrate this method, this paper uses the Compound Finance protocol as a case study. The first sub-system that this research discusses is the delegated and self-delegated wallets which are the only entities that can participate in the voting process in the Compound platform. The second sub-system is the actual proposals and votes that have taken place in the protocol’s governance. Data is derived directly from the protocol’s web data and for two time periods.

Appendix A Proof for Gini and Nakamoto Coefficients When \(n = 2\) and \(u_1 = u_2\)

Gini coefficient using Eq. 1:

$$\begin{aligned} Gini = \frac{\sum _{i=1}^{n}\sum _{j=1}^{n}\left| u_{i}-u_{j}\right| }{2n^{2}\bar{u}} \end{aligned}$$

(4)

With $n = 2$ (the number of addresses) and $\bar{u} = v$ (the mean of votes for each address), we get:

$$\begin{aligned} Gini = \frac{\left| v - v\right| + \left| v - v\right| }{2 \times 2^{2}v} \end{aligned}$$

(5)

The term in the numerator becomes 0 (because $|v - v| = 0$), hence:

$$\begin{aligned} Gini = 0 \end{aligned}$$

(6)

This confirms our previous intuition that the Gini coefficient would be 0 in this case, indicating perfect equality.

Nakamoto Coefficient using Eq. 2:

$$\begin{aligned} N = \min \left( n : \sum _{i=1}^{n} j_i > \frac{1}{2} \sum _{i=1}^{N} j_i \right) \end{aligned}$$

(7)

Here, $j_i$ represents the sorted list of addresses by votes in decreasing order. But since we only have two addresses and each has an equal amount of votes, the list is either [v, v] or [v, v] depending on how you sort it.

If we take $n = 1$, then $\sum _{i=1}^{n} j_i = v$, and $\frac{1}{2} \sum _{i=1}^{N} j_i = v$. Since the two quantities are equal, $n = 1$ does not satisfy the condition of n being the minimum such that $\sum _{i=1}^{n} j_i > \frac{1}{2} \sum _{i=1}^{N} j_i$. Thus, we have to take $n = 2$, which satisfies the condition, because $\sum _{i=1}^{2} j_i = 2v$, and $\frac{1}{2} \sum _{i=1}^{N} j_i = v$.

So we get:

$$\begin{aligned} N = 2 \end{aligned}$$

(8)

This indicates that it would take both addresses to reach a majority of the voting power. This is consistent with our previous explanation that the Nakamoto coefficient would be 2 in this case.