With the development of decentralized autonomous organizations (DAOs), their governance risks have gradually emerged. Traditional decentralized measurement methods have difficulty revealing the interest alliances hidden behind voting behavior, especially the threat of covert manipulation such as Dark DAO. VBE (Voting Bloc Entropy), as an innovative indicator, quantitatively evaluates the degree of centralization of DAOs and reveals governance risks through clustering and entropy calculations. This article will briefly explore the core framework of VBE and its practical application in DAO governance.
A few months ago, Compound DAO passed Proposal 289, which was a typical governance attack. Five addresses exploited the governance loopholes of Compound DAO to steal 5% of the control of the community treasury: approximately US$24 million in assets. Through this proposal, control will be handed over to a multi-signature wallet that is completely uncontrollable by the community.
Before this incident, the existing decentralization indicators failed to clearly identify the expected risks. The current popular analysis indicators are actually relatively backward. For example, the Nakamoto coefficient and the Gini coefficient are centered on the distribution of tokens in different addresses. This obviously ignores the hidden connections behind the addresses and the existence of Dark DAO. Dark DAO is a general term that describes a decentralized alliance that manipulates on-chain voting through opaque means (such as bribery).
So how do we penetrate the surface address information, reveal the cluster connection relationship behind the address, and dig out the hidden risks? Of the three words DAO, the most important but also the most difficult to quantify is the first word: D (Decentralization). https://www.initc3.org/ has published an indicator that attempts to pull out the "secret alliance" behind the address group, VBE (Voting Bloc Entropy), which revolves around the following three core concepts: Voting: Voting behavior and decision-making patterns. Bloc (Block/Interest Alliance): In VBE, Bloc refers to a group of voters with highly similar behaviors, regardless of whether these addresses belong to the same entity or have a public connection. Entropy: Entropy is a concept used to measure uncertainty or uniformity of distribution in a system. VBE uses it to evaluate the concentration and power distribution of voting blocks.
High entropy: Voting behavior is dispersed, multiple voting blocks have different views on proposals, and governance is more decentralized.
Low entropy: Voting behavior is concentrated, a few blocks control the results of proposals, and governance is easy to manipulate.
It is worth mentioning that VBE is also pronounced as "vibe", which symbolizes the atmosphere of the community - an abstract but crucial quality.
The core principle of VBE: The consistency of interests of voters in multiple proposals (i.e. the formation of voting groups) is a manifestation of centralization. VBE measures the degree of centralization of DAO organizations by clustering participants with similar utility functions in multiple votes and measuring entropy values.
So how does VBE penetrate the analysis and quantify the abstract community "vibe" into specific indicators? Let's jump into the rabbit hole to find out!
The VBE framework can be divided into two key parts: Clustering Metric and Entropy. The following are its key contents and implementation methods: :
1. Clustering
VBE defines ?-threshold ordinal clustering (?-TOC), and the rules are as follows:
Formula interpretation:
The goal of this formula is to determine whether the voting behaviors of two token holders are similar, so as to group them together (cluster). Specifically, it defines "similarity" through the following two conditions:
Clustering condition 1 (consistent voting tendency): A simple example is: if two people both support (positive) or both oppose (negative) in a certain election, that is, their voting signs are the same, then they are considered to have consistent behavior in this election.
Clustering condition 2 (preference differences are small enough): A simple example is: even if two people have different signs in a certain election, but the difference in their preference intensity (such as the degree of support and opposition) is small enough (less than the set threshold ϵ), their behaviors can be considered similar.
UEP (see the formula below): preference utility of address Pi for the election set E
k: election index, indicating the kth election
Although more fine-grained measures can be clustered based on cardinal utility, ordinal equivalence is an effective indicator of preference consistency.
?-TOC can be calculated based on historical voting data.
Special treatment of indifferent voters: All indifferent voters with utilities close to 0 are also classified into an additional category, labeled A’. These voters have little interest in the election results, and their voting behavior reflects low participation in governance.
2. Entropy
VBE uses min-entropy as a measure of entropy. The formula is as follows:
Formula interpretation
A: represents all addresses (sets).
tokens(A'): represents the number of tokens held by address (set) A′.
maxA′∈A: represents the maximum value of token holdings among all addresses (sets).
T: represents the total amount of tokens held by all addresses.
Entropy is used here to measure the "information content" of token distribution, but it focuses on the contribution of the largest token holder (or group). Greater concentration means lower entropy (less information).
Fineer-grained entropy (such as Shannon entropy) can be used for more complex analysis, but is difficult to estimate in practice and has high computational cost.
Combined with the above definitions of clustering and entropy, for the election set E, the player set P and its corresponding utility U(E,P), the token distribution function tokens, the clustering measure C and the entropy function F, the specific instantiation formula of VBE is:
The VBE core theorem provides a general framework for analyzing how system changes affect the degree of decentralization. The basic logic of the core theorem analysis is:
Compare two systems whose only difference is a certain "transformation" T, such as increased voter apathy, elections turning to private mode, etc.
Study the impact of this transformation on the maximum voting block in the two systems.
Calculate and compare the VBE of the two systems based on this change.
In the VBE core theorem, let T represent a function that changes the player set, election set, player utility and/or token distribution, defined as:
where the total amount of tokens in the system remains unchanged.
Let B and B′ be the voting blocks with the largest token holdings clustered by ϵ-TOC in the original system (E,UE,P,tokens) and the transformed system (E′,UE′,P′,tokens′), respectively, then the following conditions are met:
tokens(B): represents the proportion of tokens held by the largest voting block B, which is used as a weight in the entropy measurement.
When the proportion of tokens held by B′ increases, the relative entropy of B decreases, resulting in an increase in VBE.
If B′ forms a new governance advantage (i.e., majority control is obtained by B′, majority by token holdings), VBE will strictly increase; if the token ratio remains unchanged, VBE is equal.
This core theorem provides a paradigm for subsequent specific theorems. It only needs to:
Define a system transformation T and describe how it modifies the maximum voting block.
Through the core theorem, the impact of the transformation on the VBE value is evaluated, thereby quantifying the change in the degree of decentralization of the system.
(In the examples mentioned in this section, the detailed derivation and proof are in Sections 3.2~3.8 of the paper at the end of the article. Please read the details if you are interested)
1. Sybil Attack
VBE can effectively identify multiple accounts controlled by a single entity and treat them as a single voting block.
Even if whales "disguise" decentralization through account diversification strategies, VBE can still reveal the true degree of centralization of the system.
In contrast, measurement methods based only on account balances may mistakenly believe that the degree of decentralization of the system has increased because these methods ignore the true distribution of control rights of tokens.
2. Governance indifference
Centralization effect:
The large-scale emergence of indifferent voters will lead to the concentration of voting rights in a larger unified block.
This shows that indifference may lead to a more centralized system power structure in practice.
"Inactivity whale" phenomenon:
A collection of inactive voters can be regarded as an "inactivity whale" whose behavior is potentially systemically important.
Even if they do not vote, the amount of tokens held by this group may significantly affect the decentralization of the system.
3. Delegation
Intuitively, delegation seems to make the system more centralized: tokens originally held by a large number of players are transferred to a small number of representatives. However, through VBE's analysis, this situation is actually more complicated. Delegation often makes DAOs more decentralized:
In the case of high apathy: Delegation is most effective because it spreads the tokens of "apathetic whales" across multiple representative blocks, reducing the centralization risk of the system.
Note: If the representatives themselves form new "whales", the degree of decentralization of the system may decrease instead.
4. Herding
The core goal of DAO and other democratic systems is to allow token holders to vote according to their true preferences, but herding (such as coalition behavior caused by public voting) often hinders this goal. Token holders may be forced to follow influential members or agree with their peers due to reputation risks, thus forming large voting entities. This social effect deviates voting from personal true expectations and leads to increased centralization. Even if tokens are evenly distributed, traditional metrics may still misjudge the system as decentralized if herd effects prompt everyone to support the same result. VBE can reveal how reputation risks strengthen centralization and reflect the true level of decentralization:
The importance of privacy: The guarantee of voting privacy helps to reduce the centralized pressure caused by herding, thereby enhancing the decentralization of the system.
The prevalence of the herd effect: The herd effect is a common phenomenon in DAO design, which may lead to unfairness and inefficiency of the system. Therefore, the design needs to consider how to reduce the impact of social dynamics on voting behavior.
5. Voting Slates
Voting slates are often used to "hide" some unpopular proposals in a large number of popular and harmless proposals, thereby increasing the probability of these unpopular proposals passing. VBE reflects that bundling proposals together does reduce decentralization: by considering a narrower set of elections, thereby smoothing the utility function, different voting blocks are merged into larger voting blocks.
How to deal with: In order to maintain decentralization, voting slates should be used with caution, especially when dealing with elections with significantly different preferences.
6. Vote Bribing(Bribery)
There is an intuitive relationship between vote bribing and decentralization, namely that successful vote bribing threatens decentralization: in this case, the entity that obtained the votes of other players now controls a higher proportion of tokens than before. However, traditional decentralization measures (based on the distribution of tokens in accounts) fail to capture this: bribed voters, while voting as instructed by the briber, still technically hold their tokens. In contrast, VBE attributes all bribed players to the briber's voting block, because the utility functions of these bribed players are now aligned with the briber's expected results. Interestingly, as with the results of the analysis of governance apathy, vote bribing can lead to a counter-intuitive result: namely, vote bribing can lead to a more decentralized system, especially when it undermines a larger voting block (such as a lazy whale block or a large voter coalition). But we ignore this marginal case here and assume that the voted blocks that are bribed represent a majority by token holdings. Therefore, while bribery does not necessarily increase centralization unconditionally, it poses a real threat to decentralization.
Successful bribery must be systematic, i.e., it must involve a large number of tokens, and can only occur when the system is highly decentralized. Intuitively, if a DAO is highly centralized, the briber can directly coordinate with a few large players to ensure the election result; or, if the briber is a whale himself (holding a large number of tokens), only a few small players need to be bribed to accumulate enough tokens to launch a successful attack. In contrast, in a more decentralized system, the players are smaller, so the briber needs to scale their attack if he wants to win the election. That is, in this case, successful bribery requires large-scale coordination among multiple small players.
7. Quadratic Voting, QV
QV attempts to weaken the power of whales, but may inadvertently expand the influence of vote buying:
If there are enough unincentivized "small players" in the community, vote buyrs can manipulate election results at a lower cost because QV will amplify the influence of "small players".
Wyrm attack risk: If the system lacks real identity verification, whales can disperse tokens to multiple accounts, bypassing QV's influence penalty on whales, thereby increasing the total voting weight. This actually weakens decentralization.
VBE can be used to identify hidden voting blocks in QV, thereby more accurately assessing the degree of decentralization of governance.
Comparison Issues: VBE is a framework, and the results between different VBE instances or variants cannot be directly compared. Therefore, to analyze the changes in the degree of decentralization, it is necessary to evaluate under the same VBE parameters.
Limitations of VBECe,min: It focuses on the largest voting block and ignores the contribution of small voting blocks. This may lead to incomplete results in diverse scenarios. Other entropy measures (such as Shannon entropy) may provide a more complete perspective.
Strictness of clustering measures: The current ϵ-TOC clustering method only considers completely consistent voting behaviors, which may be too strict. ϵ\epsilon, looser clustering methods (such as clustering based on partial consistency) can provide more sophisticated analysis, but will also increase computational complexity.
Dark DAO itself is a decentralized organization that aims to subvert the existing decentralized credential system by intervening in the voting decision-making process of other DAOs. As we have said before, in a centralized environment, malicious behavior will be carried out in the form of cooperation between whales. As the degree of decentralization of DAO increases, the cost of bribery (big households) will increase, and bribers will need to coordinate more widely because they must target more users, thereby increasing the threat of Dark DAO.
Similar to ordinary DAOs, Dark DAOs are designed to achieve trust minimization: it ensures that bribes are "fair", that is, the bribe recipient will only receive compensation if the briber obtains access to the credentials agreed by the bribe recipient. In addition, Dark DAOs are "opaque", which means that the participation process is private.
Dark DAOs have the following three key properties:
Opaque: Dark DAO participants cannot be distinguished by other credential holders on the chain, and their participation scale and number are completely hidden.
Fair exchange: The payment of bribes is conditional. The bribe recipient can only receive compensation after the briber successfully obtains the vote support of the bribe recipient.
Limited Scope: Bribe recipients who participate in a Dark DAO will not contribute any resources to the Dark DAO beyond the promised voucher and a pre-agreed cost. (For example, bribe recipients may also be required to pay normal transaction fees.)
The goal of a Dark DAO is to undermine the voting decisions of the target DAO. Here are the main ways to achieve this:
1. Vote buying
Dark DAOs achieve their goals through bribery, such as paying token holders to vote for a specific outcome.
Payment can be conditional, such as payment after the outcome is reached or a fixed reward distributed based on the total number of votes.
Not only token-weighted voting can be affected, even "one person, one vote" systems (such as Gitcoin Passport or Worldcoin) can be abused by using keys or identity credentials to bribe votes.
Dark DAOs can greatly reduce the cost of bribery, for example through a "pivotal bribe" strategy: only paying the main reward to the key voters who change the results, and other participants only paying very low fees, thereby changing the voting results at a very small cost.
2. Coordinated price manipulation
Dark DAOs are not limited to distributing bribes, but can also indirectly reward participants through collective action.
For example:
Participants collectively establish short positions in target assets;
Voting drives the result of falling asset prices;
Distribute the proceeds after closing the positions.
This method may also extend to consensus protocol attacks or market manipulation.
3. Undermining perceived election integrity
The existence of Dark DAO itself may raise doubts about DAO elections.
Even if Dark DAOs have limited participation, they can still influence the community’s trust in elections by concealing their size or selectively disclosing their participation (e.g., holding at least 10% of tokens).
4. Exploiting quadratic voting and quadratic funding
Dark DAOs can use address splitting to circumvent QV restrictions. For example, by dispersing tokens to multiple addresses, voting weight can be increased.
Even with a decentralized identity verification system, Dark DAOs can still manipulate the results by “temporarily distributing” tokens to other users and controlling their voting behavior.
Similar means can also be used for QF to manipulate fund allocation.
5. Subverting privacy pools
Privacy pools are designed to balance privacy and compliance, but Dark DAO can undermine this mechanism through identity trading.
For example: a compliant user can rent out his compliant identity through Dark DAO, allowing non-compliant users to temporarily use his address for money laundering or evading sanctions.
On the other hand, Dark DAO can also reversely strengthen the security of privacy pools, such as requiring addresses to maintain a minimum balance, thereby limiting the weakening or collapse of privacy pools.
(The part about the Dark DAO instance framework is in 6. Basic Dark DAO and 7. Dark DAO Lite in the original paper at the end of the article. If you are interested, please go to read the details)
Github_DarkDao
https://github.com/DAO-Decentralization/dark-dao
This Dark DAO framework shows how to use Web3 technology to complete complex transactions and coordination under completely anonymous conditions.
In addition to buying tickets, the Dark DAO framework can also adapt to more complex market manipulation and privacy management needs. For example, users can use the framework to manipulate prices and achieve indirect market profits by setting collective action goals (such as shorting assets) and result-driven reward rules. In addition, the framework can also be used for privacy pool attacks to help rent compliant identities and indirectly undermine the balance between privacy and compliance.
The paper also proposed a lighter Dark DAO Lite variant, which simplifies the complete anonymity of Dark DAO to limited anonymity, simplifying the process of trustless collaboration. Dark DAO Lite can achieve limited privacy protection through a decentralized identity authentication system (such as Gitcoin Passport or Worldcoin) combined with zero-knowledge proofs, while ensuring that each user's voting rights are fairly calculated. This design will reduce the cost of implementing attacks, increase the concealment of attacks, make them more flexible, and make them more difficult to detect and prevent.
So whether it is Dark DAO or Lite version, its privacy and efficiency are enough to pose a fatal threat to decentralized systems. For example:
Impaired governance transparency: Dark DAOs can undermine public trust in the governance process, especially when their size and objectives are unclear.
System vulnerability: The technical complexity of Dark DAOs increases the attack surface of the protocol itself, such as tampering with the rules or distribution mechanisms through malicious smart contracts.
The previous article outlined the characteristics of VBE indicators and Dark DAO. The following is an application of VBE indicators in observing DAOs, a DAO oVBE Dashboard. The following is a detailed introduction to the dashboard:
https://public.tableau.com/app/profile/daovbe/viz/DAOoVBEDashboard/Voting-BlocEntropyOverview
Overview: Voting-Bloc In the overview on the homepage, we can see that this dashboard includes VBE data from 27 DAOs and sorts the charts on the right: Entropy Overview
In the Dashboard Overview, we can see these eight parameters:
AVG(VBE): refers to the average value of the VBE value in the entire statistical time period. (IC3 official reminder needs to pay attention to the cross-DAO comparison of the VBE parameter)
SUM(Avg Participation Rate): The sum of the average proportion of token holders who participated in the vote. Used to measure the overall activity and participation of the vote.
SUM(Avg Votes per Voter): The sum of the average votes of all voters is used to measure the concentration of voting rights in the vote.
SUM(Bribeable Proposals): The sum of all proposals that may be manipulated, used to measure the potential risk of corruption.
AVG(Max Cluster %): The average of the proportion of the largest voting block in all votes. This indicator reflects the degree of concentration of voting blocks. The higher the value, the more serious the concentration of voting results.
AGG(Median Voters to Bribe): The aggregation of the number of median voters who need to be "bribed" in order to influence the voting results.
CNT(Proposal): The total number of proposals in the DAO.
SUM(Unique Voters): The sum of all unique voters after deduplication of all votes in the statistical time period, used to measure the diversity of participants and the coverage of DAO governance.
Double-click a specific parameter in the list to open the details and observe the changes in the data and the comparison between different DAOs:
In the paginated details, you can observe the details of each DAO. The chart in the upper left corner is the VBE value and the maximum voting cluster ratio of each time window during the statistical period.
Click on a time point in the line chart, the upper right side will show the comparison of proposal categories in the window, the lower right side will show the overview of the voting clusters in the time window, and the lower left corner will show the details of the proposals in the time window.
The comparison of VBE between different DAOs needs to pay attention to the differences in the basic data sets, but the changes in VBE and voting clusters within the same DAO are a more intuitive way to analyze the trend of changes in the degree of decentralization of the DAO.
Combining VBE's framework and VBE's analytical inferences on DAO, there are several specific guiding principles for DAOs seeking to implement or improve meaningful decentralization:
VBE assesses the degree of decentralization of DAOs by measuring the entropy of voting groups. In fact, VBE is a flexible framework that can be combined with any desired clustering method to identify groups, as well as any definition of entropy.
The following are the open questions worthy of attention raised at the end of the paper:
Privacy and Data Collection:
How to collect enough data to facilitate VBE evaluation while ensuring voting privacy is an unresolved problem.
DAO forks and escape mechanisms:
DAOs may encounter catastrophic failures. How to study the impact of the use of DAO forks and escape mechanisms on decentralization is an important issue.
The impact of VBE on DAO decision-making:
Are high VBE values related to community growth, participation, and financial performance? And how it is related to democratic participation in non-blockchain environments is still a direction worth studying in the future.
VBE is an in-depth exploration of the concept of "decentralization" in DAO, providing a new perspective. By focusing on the interest alliances behind voting behavior and their degree of centralization, it quantitatively analyzes the essence of decentralization.
We love DAO and hope that DAO can continue to develop healthily. In this paper, Dark DAO is discussed separately and occupies an important space. Just like the hidden order, Dark DAO has a lasting and unignorable impact on the governance models of different DAOs. The existence of Dark DAO is not only inevitable, but also an important factor in shaping the future governance ecosystem. Therefore, DAO builders should learn to examine themselves from the perspective of Dark DAO, learn the ideas and technologies of Dark DAO, and explore strategies to coexist with it, so as to achieve a more robust and inclusive governance system.
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