VOTING MECHANISMS IN DAO

Voting Mechanisms in DAO

Written by Alireza Aghaee.

Introduction

Decentralized autonomous organizations (DAOs) are a new type of organizational structure that is built on blockchain technology. DAOs operate without a central authority and are governed by a community of members who make decisions through a voting process. This process of decision-making is crucial to the functioning of DAOs, and various voting mechanisms have been developed to ensure that the process is fair and efficient. Voting mechanisms are used to make decisions within a DAO, and there are several different types of voting mechanisms that can be used, each with its own strengths and weaknesses. In this article, we will explore some of the most popular voting mechanisms used in DAOs and discuss the pros and cons of each.

One of the most basic voting mechanisms is called “one member, one vote," also known as the plurality vote, where each member has one vote, and they can cast that vote for one candidate or proposal. This system is simple and easy to understand, but it can also be vulnerable to manipulation and can lead to outcomes that are not representative of the community’s preferences. For example, it can lead to a situation where a candidate or proposal wins with only a small percentage of the vote, which can be unfair to the other candidates or proposals. Furthermore, it is discouraging investment since holding a larger stake in the enterprise does not lead to a larger control power. That’s why this mechanism is used mostly in non-economic decisions.

Another type of voting mechanism that has been developed is known as “weighted voting." Members with more tokens in the DAO have more voting power under this system. This can be used to give members who have made significant contributions to the organization more power. Because these systems encourage investment, almost all DAOs use a variant of the weighted voting mechanism. In weighted voting systems, each member has a voting power that is proportional to a function of his token holding. The properties of this function can have interesting economic implications on the voting outcomes that will be discussed in the next section. Depending on the function we use to weigh votes, it can result in a concentration of power in the hands of a small number of members, which can be problematic. So weighted voting systems can either promote or discourage decentralization.

The first type of weighted voting mechanism is the traditional voting system, also known as one token one vote. In this system, each member has one vote, and they can cast that vote for one candidate or proposal. This system is simple and easy to understand, but it can be easily manipulated by a small number of members who hold a large number of tokens. Additionally, it does not take into account the intensity of preferences, meaning that a member’s vote for one candidate or proposal is worth the same as any other member’s vote.

A more advanced weighted voting mechanism used in the DAO ecosystem is Quadratic Voting. This system gives each member a certain number of voting tokens, and they can choose to use those tokens in any way they want. The cost of voting tokens increases quadratically with the number of tokens being used, so the more tokens a member uses to support a candidate, the more expensive it becomes to use more tokens for that candidate. This creates an incentive for members to be strategic about how they use their tokens and it also helps to prevent a small number of members from dominating the voting process. A proper mathematical analysis of the voting mechanism will be followed in the 2. In that section, we also show how these voting mechanisms promote decentralization.

There are also other innovations in the control mechanisms in DAO that are not separate voting mechanisms, but instead, come on top of it. One of these approaches is called "liquid democracy". This is a voting system that allows members to delegate their voting power to other members. For a retail token holder whose primary job is not investment, it may not be economical to read and engage on every proposal. Moreover, properly understanding many proposals requires a solid understanding of blockchains or other technical aspects and it may be beyond the average investor’s expertise. Vote delegation promotes efficiency by allowing investors who are not willing or unable to vote, to delegate them to other stakeholders that have the expertise and willingness to strive for improvement. On the other hand, liquid democracy opens doors to exploitation. A proper discussion about these other innovations in the voting systems in the DAO ecosystem will be followed in section 3.

Voting Mechanism

Almost all economic enterprises incorporate a method of weighted voting mechanisms, in which the voting power is proportional to a function of one’s stake. In traditional public firms, for example, a simple affine function is used for weighing, so that the voting power is proportional to the shares holding. In the DAO ecosystem, however, other voting schemes are becoming increasingly popular, predominately to promote decentralization. Promoting decentralization mainly stems from control rights that are no more proportional to cashflow rights.

One of the decentralization-promoting mechanisms in the DAO ecosystem is quadratic voting. In this system, each member has a certain number of voting tokens, and they can choose to use those tokens in any way they want. For example, a member could use all of their tokens to support one proposal, or they could spread their tokens out among several alternatives. Additionally, the cost of voting tokens increases quadratically with the number of tokens being used. So, the more tokens a member uses to support a proposal, the more expensive it becomes to use additional tokens for that proposal. This creates an incentive for members to be strategic about how they use their tokens, and it also helps to prevent a small number of members from dominating the voting process. Quadratic voting also allows members to express the intensity of their preferences in addition to the direction, by using more tokens to vote for the options they like more. We will see in the rest of this section that quadratic voting is just a special case of weighted voting schemes.

To formalize the notation, and shed light on the difference between cashflow rights and control rights, imagine a DAO with S tokens outstanding, collectively held by ${\textstyle n}$ token holders. Holding a token in the DAO entitles the holders to two kinds of rights: cashflow rights and control rights. For example, if you own one UNI token from Uniswap, you are entitled to some remuneration from the transaction fees that the system collects from the people swapping their tokens. Moreover, this token entitles you to cast your vote when there is a proposal on the Uniswap system. The cash flow rights of shareholder ${\textstyle i}$, denoted by ${\textstyle C_{i}}$, are directly proportional to his percentage holding ${\textstyle S_{i}}$. However, her control rights, ${\textstyle V_{i}}$, is pinned down by a voting function ${\textstyle v:{\mathcal {N}}\bigcup \{0\}\to {\mathcal {R}}}$ such that

$${\begin{aligned}C_{i}&={\frac {S_{i}}{\sum _{j=1}^{n}S_{j}}},\\V_{i}&={\frac {v(S_{i})}{\sum _{j=1}^{n}v(S_{j})}},[1]\end{aligned}}$$

Where ${\textstyle v}$ is an increasing function (larger stake, larger say) that passes through the origin (${\textstyle v(0)=0}$, no token no say).

Firstly, observe that for any linear voting function ${\textstyle v(x)=ax}$, the voting power ${\textstyle V}$ reduces down to the common one-token-one-vote system. Since for these specific voting functions, the denominator is fixed (${\textstyle =aS}$), we will have ${\textstyle \partial V_{i}/\partial S_{i}=1/S}$. The proportionality of control right can be demonstrated mathematically as

$${\frac {\partial V_{i}/\partial S_{i}}{\partial C_{i}/\partial S_{i}}}=1.$$

This voting function is also insensitive to the number of shareholders and their diversity. Formally, ${\textstyle \partial C_{i}/\partial n=0}$. A voting function that promoted decentralization has to have the following two conditions:

• It should value an additional vote from an additional mind more than the identical additional vote from a token holder who already has cast his votes. In other words, it has to exhibit a diminishing marginal increase in voting power with respect to token holdings. Formally, it should be the case that ${\textstyle V_{SS}<0}$. A direct consequence of this property would be that the marginal improvement in control rights is always smaller than the corresponding marginal improvement in cash flow rights, which is proportional to the reciprocal of total circulating tokens, ${\textstyle 1/S}$.
• It should decrease one’s voting power when the rest of the tokens are redistributed in a more decentralized fashion. Particularly, for a fixed sum of tokens, two tokenholders should collectively have more voting power than if one of them holds it all. Formally, ${\textstyle V(S_{1})+V(S_{2})>V(S_{1}+S_{2})}$. Consequently, for a fixed total supply of tokens, voting power is generally decreasing in the number of token holders, ${\textstyle {\partial V_{i}}/{\partial n}<0.}$

The following theorem shows that the concavity of the voting function ${\textstyle v}$ is sufficient for voting power ${\textstyle V}$ to satisfy the two conditions above.

Theorem 1. A concave voting function ${\textstyle v}$ is sufficient to promote decentralization. Formally, if voting function ${\textstyle v}$ is concave, then

$${\begin{aligned}V_{SS}&<0,[2]\\{\frac {\partial V}{\partial n}}&<0,{\text{ or equivalently, }}V(S_{i})|n=N<V(S_{i})|n=N+1\end{aligned}}$$

Proof. Take the tokenholder ${\textstyle i}$ and fix other investors’ tokens as ${\textstyle \{S_{j}\}_{j\neq i}}$. We have to show that ${\textstyle v''(S)<0}$ results in ${\textstyle V_{SS}<0}$. According to Equation [1],

$$V_{S}(S_{i})={\frac {v'(S_{i})(\sum _{j=1}^{n}v(S_{j}))-v(S_{i})v'(S_{i})}{(\sum _{j=1}^{n}v(S_{j}))^{2}}}={\frac {v'(S_{i})(\sum _{j\neq i}^{n}v(S_{j}))}{(\sum _{j=1}^{n}v(S_{j}))^{2}}},$$

$$\implies V_{SS}(S_{i})=(\sum _{j\neq i}^{n}v(S_{j})){\frac {v''(S_{i})(\sum _{j=1}^{n}v(S_{j}))^{2}-v'(S_{i})(2((\sum _{j=1}^{n}v(S_{j})))v'(S_{i})}{(\sum _{j=1}^{n}v(S_{j}))^{4}}}=$$

$$\implies V_{SS}(S_{i})=(\sum _{j\neq i}^{n}v(S_{j})){\frac {v''(S_{i})(\sum _{j=1}^{n}v(S_{j}))-2(v'(S_{i}))^{2}}{(\sum _{j=1}^{n}v(S_{j}))^{3}}}.$$

Equation [2] is directly proven here since the denominator in ${\textstyle V_{SS}}$ is always positive and the nominator is always negative. To prove the second part of the theorem, notice that we only have to concern the denominator in [1] since the nominator remains constant. To that end, we have to show that conditional on a fixed total number of tokens, the denominator grows as the number of holders grows. Assume the marginal token holder buys m tokens from the last token holder indexed by N, who originally had k tokens. Then we only have to prove that for integers ${\textstyle m<k}$,

$$v(k)<v(k-m)+v(m).[3]$$

Let ${\textstyle l=k-m>0}$, then the inequality reduces to ${\textstyle v(l+m)<v(l)+v(m)}$ for arbitrary integers ${\textstyle l}$ and ${\textstyle m}$ and the concave function ${\textstyle v}$ that passes through the origin. Fix ${\textstyle l}$ and Define ${\textstyle g(x)=v(l)+v(x)-v(l+x)}$. Observe that ${\textstyle g(0)=0}$, and ${\textstyle g'(x)=v'(x)-v'(x+l)}$. Since ${\textstyle v}$ is concave, ${\textstyle v'}$ is a decreasing function, and therefore ${\textstyle g'(x)\geq 0}$. So the inequality in [3] is proven. ◻

Theorem 1 states that with a concave voting function ${\textstyle v}$, even with a fixed total number of tokens, an additional token holder reduces the power of other incumbent token holders with unchanged holding. Furthermore, the marginal control right associated with buying one more token is decreasing, while its marginal cashflow right is fixed.

With this analysis, we can see that quadratic voting is just a special case of weighted voting with a voting function defined as ${\textstyle v(S)={\sqrt {(}}S)}$. Note that in simple terms the cost of votes is proportional to the tokens one holds, and hence is proportional to the cashflow rights. So the quadratic cost of the vote translates in our setting to a square root voting function. Quadratic voting has other additional features on top of what is discussed here. Lalley, S. P., & Weyl, E. G. (2016) show that if individuals take the chance of a marginal vote being pivotal as given, like a market price, quadratic voting is the unique pricing rule that is always efficient.

One of the most significant drawbacks of quadratic voting is that there are no measures in place to deal with instances of cheating, here mostly referred to as “Sybil attacks". In simple terms, the problem arises from the fact that if a token holder divides her holding into two wallets and votes the same proposal with both, she will receive more voting power in comparison to the case that she votes with only one wallet or identity. So Sybil attacks make use of fake identities to sway community-based decisions and tilt them in the attackers’ favor. In quadratic voting, the prevention of Sybil attacks is a crucial objective in order to ensure the system’s security. In order to successfully execute extensive quadratic voting, an anti-sybil identification program such as a KYC is required.

Other Innovations in Voting

The previous chapter demonstrated that the majority of differences in voting mechanisms result from a twist in the voting function used to weigh votes. This section, on the other hand, discusses innovations that cannot be expressed as voting function twists. Much of this innovation is not truly novel, innovative, or unique to the DAO ecosystem. Nevertheless, they are relevant for this article because they are widely used in the DAO ecosystem.

Liquid Democracy

DAO members may be apathetic to proposals because they lack the mental bandwidth to comprehend the issues at hand. Particularly if the abovementioned persons consider participation in a DAO to be a part-time activity, they may be unwilling to dedicate the time required to make significant decisions. Delegated voting, often known as “liquid democracy," is one possible solution to such challenges. Delegated voting is simply the act of appointing someone to vote on your behalf. In this situation, the delegate is most likely a reputable member of the DAO or somebody with shown competence on the problems at hand.

When liquid democracy or vote delegation is possible, a DAO designates specialists to serve on an electorate with the authority to make decisions on behalf of DAO members. Members delegate their votes to trusted experts of their choice, who are better equipped to make sound decisions on the DAO’s future. This technique is more centralized than others, but DAO members have the authority to transfer delegation and assign new participants to the electorate at any moment. The advantages of this type of DAO voting mechanism are that smarter and more informed judgments in the best interests of the DAO are more likely. However, as in our world’s political democracies, bribery and corruption could be used to influence decision-making.

Quorum Voting

The token-based quorum is a fundamental method for voting in a DAO (Decentralized Autonomous Organization). In order for a proposal to be approved, a specific number of members must take part in the voting process. If the required number of participants is reached, the proposal with the most votes will be accepted. However, if the threshold is not met, the proposal will not be passed.

Quorum voting introduces a minimum level of absolute majority on top of the relative majority in the voting mechanism. In absence of any Quorum, only the number of voters who voted ‘for’ and ‘against’ a proposition matters in the result even if only a minority have participated in it. The described voting procedure is simple and straightforward, making it less expensive and less demanding. However, the approach permits a single DAO member to amass too much power and decide how to administer DAO funds. Furthermore, the method makes proposal passing a dangerous endeavor because it is a simple process that does not require much attention from other members.

While token-based quorum voting attempts to promote active participation and consider the views of the majority, it also poses certain challenges. One issue is determining the appropriate quorum. A higher number of required voters may lead to a large number of proposals failing due to low participation. On the other hand, a low quorum could lead to bad decisions and a deviation from the intended direction of the DAO.

Regardless of the quorum, encouraging members to take part in the voting process is a significant and costly challenge for most DAOs. Some members may choose to remain inactive in order to prevent a proposal from passing or may not be interested in the decision-making process. Additionally, the token-based model ties voting power to financial stability, allowing members with more tokens to influence and bribe others, potentially turning the voting process into a political activity.

Rage Quitting

One example of how sponsorship has been used to boost security in the DAO voting process is the rage quitting voting method. This approach may be able to provide a solution to the relative majority of challenges. Members must sponsor a proposal before it can be voted on. If the plan is approved by a majority, it enters a grace period during which voters can reconsider and withdraw their support for the vote or the DAO. If the idea receives insufficient support after this step, it is dropped.

The key advantage of this voting process is that it prevents majority voters from acquiring an advantage over minority voters. However, the voting process is exceedingly lengthy, which may make it unsuitable for all DAOs.

conviction voting

Conviction voting is another novel DAO voting technique. It is based on the community’s aggregated preference and uses time as a utility. Members can vote on various in-progress initiatives, and the longer their vote remains unchanged, the more powerful the vote gets. The voting utility’s growth slows progressively as it approaches a predetermined maximum. Voters can modify their vote at any time, in which case the voting utility of their previous vote will drop over time.

This approach is an excellent way to demonstrate how interested voters are in a proposal and how their opinions may be swayed by internal or external forces. A majority vote is not required to advance a proposal; rather, the beliefs of the community are at the heart of decision-making. It’s also an effective approach to avoid new DAO members having too much influence on the DAO protocol.

On the disadvantage, the method takes a long time to reach a conclusion, making it unsuitable for DAOs that demand quick judgments. If more DAOs implement conviction voting, it is likely that it will be used in conjunction with another, faster process.

Multi-sig voting

Multisig voting is a DAO voting technique that aims to create a balance in an organization between central authority and decentralization. In this concept, DAO members can signal on suggestions, while centralized and predefined committee votes on the proposal. This model is one of the fastest voting processes and maybe suited in circumstances where immediate action is critical to the DAO’s existence. However, there is a risk of the centralized authority abusing its position and voting in a way that is no longer in the best interests of the majority of the DAO community.

Holographic Consensus

One goal in the DAO ecosystem is to raise the global adoption of the DAO concept, which is the theoretical point of reference denoting the ultimate decision that would be made under ideal conditions while devoting the fewest possible resources to achieve this goal. There are two difficulties that need to be addressed in this situation: the scalability of the voting process (frequency), and the degree to which the outcome represents the collective opinion of the DAO. The term "scalability-resilience paradox" was used to describe this situation. The scalability of the voting process might be negatively impacted by the measures that are used to ensure high levels of voter participation. On the other hand, if there is insufficient involvement, this could lead to unfavorable suggestions being approved.

In order to achieve maximum scalability, it is necessary for the global opinion of the DAO to be attained with the least amount of voting power being mobilized as possible. Holographic consensus, or HC for short, is a strategy that seeks to alleviate this problem by having highly representative decisions made at the local level. A prediction market is used to determine the outcomes of these decisions. While the DAO is the ultimate wager on each proposal, individual DAO members bet money on those ideas they believe will emerge victorious. The backers of the winning proposals receive monetary rewards, and the money that the DAO gives them is categorized as some form of administrative expense to ensure that the DAO operates well. HC is quite difficult and not very democratic because the cost of involvement can be high for some people, depending on their location. Despite the fact that it improves scalability and robustness, it is quite complicated.

Conclusion

Voting mechanisms in DAOs are a crucial aspect of decision-making within these organizations. Weighted voting systems, such as one token one vote, can give members with more tokens in the DAO more voting power, but can also result in a concentration of power in the hands of a small number of members. Quadratic Voting is a more advanced system that promotes decentralization and prevents a small number of members from dominating the voting process. Furthermore, innovations such as liquid democracy can be used in conjunction with voting mechanisms to promote efficiency and decentralization. It is important for DAOs to carefully consider the pros and cons of each voting mechanism and to choose the one that best fits their specific needs for their specific use case.