With the development of decentralized autonomous organizations (DAO), its governance risks have gradually emerged. Traditional decentralized measurement methods are difficult to reveal the interest alliances hidden behind voting behavior, especially the threats of covert manipulations such as Dark DAO. VBE (Voting Bloc Entropy), as an innovative indicator, quantitatively evaluates the degree of centralization of DAO through the calculation of clustering and entropy, and reveals hidden governance risks. This article will briefly explore the core framework of VBE and its practical application in DAO governance.

01 Background Introduction

A few months ago, Compound DAO passed Proposal 289, which was a typical governance attack. Five addresses exploited Compound DAO The governance vulnerability stole 5% of the community's treasury control: approximately US$24 million in assets. Through this proposal, control will be given to a multi-signature wallet that is completely uncontrollable by the community.

Before this incident, existing decentralization indicators failed to clearly predict expected risks. The current popular analysis indicators are actually relatively backward, such as Both the Nakamoto coefficient and the Gini coefficient focus on the distribution of tokens in different addresses. This obviously ignores the secret links behind the addresses and the existence of Dark DAO. Dark DAO It is a general term describing a decentralized alliance that manipulates on-chain voting through opaque means (such as vote-buying).

So how do we penetrate the surface address information, reveal the cluster connection relationship behind the address, and unearth hidden risks? Among the three words DAO, the most important but also the most difficult to quantitatively analyze is the first word: D (Decentralization, decentralization), https://www.initc3.org/ published an attempt to pull out the address group behind The indicator of the "Secret Alliance", VBE (Voting Bloc Entropy, Voting Collective Entropy), 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 Are there any public connections?

Entropy): Entropy is a concept used to measure the uncertainty or uniformity of distribution in a system, and 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 proposal results, and governance is easily manipulated.

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 (that is, the formation of voting blocs) is a manifestation of centralization. VBE measures the degree of centralization of a DAO organization by clustering participants with similar utility functions in multiple votes and measuring the entropy value.

How does VBE penetrate the analysis and quantify the abstract community "vibe" into specific indicators? Let’s start by jumping down the rabbit hole to find out!

02 VBE: Voting Bloc Entropy

The framework of VBE can be split 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), the rules are as follows:

Formula interpretation:

The goal of this formula is to determine whether the voting behavior of two token holders is similar, thereby grouping them together (clustering). Specifically, it defines "similarity" through the following two conditions:

Clustering condition 1 (voting tendencies are consistent): A simple example is: if Two people support (positive) or both oppose (negative) an election, that is, their vote signs are the same.If they are the same, it is considered that their behavior in this election is consistent.

Clustering condition 2 (preference difference is small enough): A simple example is: even If two people have different signs in an 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), they can also be considered to behave similarly

UEP (see formula below): the preference utility of address Pi for the election set E

k: election index, indicating the k-th election

ϵ: threshold, used to measure whether the intensity difference is negligible

Although more fine-grained measures can be clustered based on the cardinal utility (Cardinal Utility), ordinal equivalence is already effective in indicating preference consistency.

?-TOC can be calculated based on historical voting data.

Special treatment of apathetic voters: All apathetic voters whose utility is close to 0 are also grouped 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 minimum entropy (min-entropy) as A measure of entropy. The formula is as follows:

Interpretation of the formula

A: Represents all addresses (set).

tokens(A'): Indicates the number of tokens held by address (set) A′.

maxA′∈A: meansThe maximum amount of token holdings among all addresses (set).

T: Indicates the total amount of tokens held by all addresses.

Entropy is used here to measure the "information content" of a token distribution, but it focuses on the contribution of the largest token holder (or group). Greater centralization means lower entropy (less information).

Fine-grained entropy (such as Shannon entropy) can be used for more complex analyses, but is difficult to estimate realistically and is computationally expensive.

The instantiation formula of VBE

Combined with the above definitions of clustering and entropy, for the election set E, the player set P and their corresponding utility U(E,P), Token distribution function tokens, clustering metric C and entropy function F, the specific instantiation formula of VBE is:

VBE core theorem

VBE The 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:

Comparing the two systems, the only difference between the two is some kind of "transformation" T, such as increased voter apathy, election Switch to private mode, etc.

Study the impact of this transformation on the largest voting blocks in both systems.

Calculate and compare the VBE of the two systems based on this change.

In the core theorem of VBE, let T represent a function that changes the player set, election set, player utility and/or token distribution, defined as ：

Among them, the total amount of tokens in the system remains unchanged.

Let B and B′ be the original system (E,UE,P,tokens) and the transformed system (E′,UE′,P′, respectively) tokens′), the voting block with the largest token holdings clustered by ϵ-TOC satisfies the following conditions:

tokens(B): Indicates 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 value of B decreases, resulting in an increase in VBE.

if B′ If a new governance dominant party is formed (that is, majority control is obtained by B′, majority by token holdings), VBE will strictly increase; if the token ratio remains unchanged, VBE will be equal.

This core theorem provides a paradigm for subsequent specific theorems, just:

Define a system transformation T and describe how it is modified Maximum voting block

Derivate through the core theorem to evaluate the impact of transformation on the VBE value, thereby quantifying changes in the degree of decentralization of the system.

Extended analysis and application of the core theorem

(In the examples mentioned in this section, the detailed derivation and proof are in Chapters 3.2~3.8 of the paper at the end of the article. If you are interested, please read the details)

1. Sybil attack

VBE is able to effectively identify multiple accounts controlled by a single entity and treat them as a single voting block

Even if whales "pretend" to be decentralized through account dispersion strategies, VBE can still reveal the true degree of centralization of the system.

In contrast, measures based solely on account balances may falsely assume that the system is increasingly decentralized because these methods ignore the true nature of tokens Distribution of control.

2. Governance indifference

Centralization effect:

The large-scale emergence of apathetic voters will lead to the concentration of voting power into a larger unified block.

This suggests that in practice, apathy may lead to a more centralized system power structure.

The "apathy whale" phenomenon:

A collection of indifferent voters can be thought of as an "inactivity whale" whose behavior has potential systemic importance.

Even if they do not vote, the amount of tokens held by this group may significantly affect the decentralization of the system.

3. Delegation (Delegation)

Intuitively, delegation voting seems to be Making the system more centralized: tokens originally held by a large number of players are transferred to a small number of representatives. However, through VBE analysis, the situation is actually more complex. Delegated voting often makes the DAO more decentralized:

In the case of high apathy rate: Delegated voting is most effective because it transfers the tokens of "apathy whales" Dispersed into multiple representative blocks, the risk of system centralization is reduced.

Note: If the representative itself forms a new "whale", the degree of decentralization of the system may actually decrease.

4. Herding

The core goal of DAO and other democratic systems is Let token holders vote based on their true preferences, but bandwagon effects (such as coalition behavior triggered by public voting) often hinder this goal. Token holders may be forced to follow influential members or align with their peers due to reputational risks, forming large voting entities. This social effect deviates voting from individuals' true expectations, leading to increased centralization. Even though tokens are evenly distributed, traditional metrics may still misjudge a system as decentralized if crowd effects encourage everyone to support the same outcome. VBE can reveal how reputational risk reinforces centralization and reflects the true level of decentralization:

The importance of privacy: Guaranteeing voting privacy helps mitigate herding centralization pressure brought by the effect, thus enhancing the decentralization of the system.

The universality of the herd effect: In DAO design, the herd effect is a common phenomenon that may lead to system injusticePeaceful and inefficient. Therefore, design needs to consider how to reduce the impact of social dynamics on voting behavior.

5. Voting Slates

Voting Slates are usually used to combine some different Popular proposals are "hidden" within a large pool of popular, harmless proposals, thereby increasing the likelihood that these unpopular proposals will pass. VBE reflects that bundling proposals together indeed reduces decentralization: by considering a narrower set of elections and thus smoothing the utility function, different voting blocks are merged into larger voting blocks.

How to respond: In order to maintain decentralization, voting groups should be used with caution, especially when dealing with elections with significantly different preferences.

6. Bribery

There is an intuitive connection between bribery and decentralization Nexus, i.e., successful vote buying threatens decentralization: in this case, the entity that obtained the votes of other players now controls a higher proportion of the tokens than before. However, traditional measures of decentralization (based on the distribution of tokens across accounts) fail to capture this: Voters who were bribed voted according to the briber’s instructions but still technically held their tokens. Instead, VBE places all bribed players into the vote-buyer's voting block because the utility functions of these vote-buyers are now aligned with the vote-buyer's expected outcomes. Interestingly, as with the analysis of governance apathy, vote buying may lead to a counter-intuitive result: vote buying may lead to a more decentralized system, especially if it disrupts a larger voting block (e.g. lazy whale block or some large coalition of voters). But here we ignore this marginal case and assume that the bribed voting blocks represent a majority by token holdings. Therefore, while vote buying does not necessarily unconditionally increase centralization, it poses a real threat to decentralization.

Successful vote-buying must be systemic, that is, 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 vote briber can directly coordinate with several big players to ensure the election results; or, if the vote briber himself is a whale (holding a large number of tokens), he only needs to bribe a few small players. Accumulate enough tokens to launch a successful attack. In contrast, in a more decentralized system, the players are smaller, so vote bribers need to scale up their attacks if they want to win the election. That is, successful vote-buying in this case requires large-scale operations among multiple small players.Model coordination.

7. Quadratic Voting (QV)

QV attempts to weaken whales power, but may inadvertently expand the influence of vote buying:

If there are enough unmotivated "small players" in the community, vote buying can use Lower costs to manipulate election results because QV It will amplify the influence of “small players”.

Sybil attack risk: If the system lacks real identity verification, whales can spread tokens across multiple accounts, bypassing QV’s influence penalties on whales, thereby Increase total vote weight. This actually weakens decentralization.

VBE can be used to identify implicit voting blocks in QV to more accurately assess the degree of decentralization of governance.

Limitations of VBE

Comparison issues: VBE is a framework and it is not possible to directly compare results between different VBE instances or variants. Therefore, to analyze changes in the degree of decentralization, it needs to be evaluated 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 less comprehensive results in diverse scenarios, and other entropy measures (such as Shannon entropy) may provide a more complete perspective.

Strongness of clustering metrics: Current ϵ-TOC clustering methods only consider fully consistent electoral behavior and may be too strict. ϵ\epsilon, looser clustering methods (such as clustering based on partial consistency) can provide more refined analysis, but also increase computational complexity.

03 Dark DAOs

Dark DAO itself is a decentralized organization that aims to subvert the existing decentralization process by intervening in the voting decision-making process of other DAOs. Centralized credential system. We mentioned earlier that in a centralized situation, malicious behavior will be carried out in the form of whale cooperation, and with the DAO As the degree of decentralization increases, the cost of bribing (big players) will increase, and bribers will need to coordinate more extensively because they must target more users, thus increasing the threat of Dark DAO.

Similar to ordinary DAOs, Dark DAO is designed to minimize trust: it ensures that bribes are "fair", that is, the bribe recipient will only receive the bribe if the briber has access to credentials that the bribe recipient agreed to. get rewarded. In addition, Dark DAO is "opaque", which means that the participation process is private.

Dark DAO has the following three key properties:

Opacity: Dark DAO’s participation Participants cannot be distinguished from other certificate holders on the chain, and the scale and number of their participants are completely hidden.

Fair exchange: The payment of the bribe is conditional. The bribe recipient will only receive payment if the briber successfully obtains the vote of the bribe recipient.

Limited scope: Bribery recipients participating in Dark DAO will not contribute any resources to Dark DAO except for the promised credentials and pre-agreed costs. (For example, bribe recipients may also be required to pay normal transaction fees.)

The goal of Dark DAO

The goal of Dark DAO is to disrupt the voting decisions of the target DAO. The main implementation methods are listed below:

1. Vote buying

Dark DAOs achieve their goals through bribery, such as paying token holders to vote for a specific outcome.

The payment method can be conditional, such as payment after the result is achieved or fixed remuneration distributed according to the total number of votes.

Not only token weight voting will be affected, but even "per person one vote" systems (such as Gitcoin Passport or Worldcoin) can be abused by changing the key Or identity credentials used for vote-buying.

Dark DAO can greatly reduce the cost of bribery, such as through the "pivotal bribery" strategy: only paying main rewards to key voters who change the outcome, Other participants pay minimal fees to change the outcome of the vote at very little cost.

2. Coordinated price manipulation

Dark DAO is not limited to distributing bribes, but can also indirectly reward participants through collective actions.

For example:

Participants collectively establish short positions in the target asset;

Voting promotes the result of falling asset prices;

Distribute profits after closing positions for profit.

This approach 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 the DAO election.

Even if Dark DAO’s participation is limited, it may influence the community’s response to the election by concealing the scale or selectively disclosing participation (such as holding at least 10% of the tokens) of trust.

4. Exploiting quadratic voting and quadratic funding

Dark DAO can use address splitting to circumvent QV restrictions. For example, by distributing tokens to multiple addresses, voting weight is increased.

Even with a decentralized authentication system, Dark DAO can still manipulate the results by "temporarily distributing" tokens to other users and controlling their voting behavior.

Similar means can also be used in QF to control fund allocation.

5. Subverting privacy pools

Privacy pools are designed to balance privacy and compliance, but Dark DAOs can disrupt this through identity buying and selling.

For example: a compliant user can rent out his compliant identity through Dark DAO, allowing non-compliant users to temporarily use his address to launder money or evade sanctions.

On the other hand, Dark DAO can also reversely strengthen the security of the privacy pool, such as requiring addresses to maintain a minimum balance, thereby limiting the weakening or collapse of the privacy pool.

Extension: a Dark DAO instance framework

(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 read the details)

Github_DarkDao

https://github.com/DAO-Decentralization/dark-dao

This Dark DAO framework shows how to use Web3 technology to achieve complete anonymity Complete complex transactions and coordination under certain 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 conduct price manipulation 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 in privacy pool attacks to help rent compliant identities and indirectly undermine the balance between privacy and compliance.

The paper also proposes a lighter variant of Dark DAO Lite, which simplifies Dark DAO's complete anonymity to limited anonymity and simplifies trustless collaboration. process. Dark DAO Lite can achieve limited privacy protection through a decentralized authentication system (such as Gitcoin Passport or Worldcoin) combined with zero-knowledge proofs, while ensuring that each user’s voting power is calculated fairly. This design will reduce the implementation cost of 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 orIt is the Lite version, and its privacy and efficiency are enough to pose a fatal threat to decentralized systems. For example:

Erosion of governance transparency: Dark DAOs can undermine public trust in the governance process, especially when its scale and goals are unclear.

System vulnerability: The technical complexity of Dark DAO increases the attack surface of the protocol itself, such as tampering with rules or distribution mechanisms through malicious smart contracts.

04 Use VBE to observe DAOs

The previous article summarized the indicator characteristics of VBE and the characteristics of Dark DAO. The following is an application of VBE indicator when observing DAO, 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 Entropy Overview

Overview: Voting-Bloc In the overview on the home page, we can see that this dashboard contains 27 DAO VBEs Data, and chart sorting is done on the right: Entropy Overview

< p style="text-align: left;">In Dashboard Overview, we can see these eight parameters:

AVG(VBE): Point to The VBE values ​​are averaged over the entire statistical period. (IC3 official reminder needs to pay attention to the cross-DAO comparison of VBE parameters)

SUM(Avg Participation Rate): The average proportion of token holders who participated in voting in the vote sum. Used to measure overall voting activity and participation.

SUM(Avg Votes per Voter): Sum the average votes of all voters to measure the concentration of voting power in the vote.

SUM(Bribeable Proposals): The sum of all proposals that may be manipulated, used to measure potential corruption risks.

AVG(Max Cluster %): The average of the largest proportion of voting blocks among all votes. This indicator reflects the concentration of voting blocks. The higher it is, the more serious the concentration of voting results is.

AGG (Median Voters to Bribe): The aggregation of the number of median voters who need to be "bought" in order to influence the voting results.

CNT(Proposal): The total number of proposals in the DAO.

SUM (Unique Voters): The sum of all independent voters after deduplication of all votes in the statistical period, used to measure the diversity and diversity of participants Coverage of DAO governance.

Double-click a specific parameter in the list, we can also open the details and observe the changes in the data and the comparison between different DAOs:

DAO paging details

You can observe the details of each DAO in the paginated details. The chart in the upper left corner shows the VBE value and the maximum voting cluster ratio of each time window (window) during the statistical period.

Click on the time point in the line chart, the upper right side will be displayed in the window When comparing proposal categories, an overview of the voting clusters within the time window will be displayed on the lower right side, and the proposal details within the time window will be displayed on the lower left corner.

VBE comparison between different DAOs requires attention to the differences in basic data sets, but VBE changes and voting cluster changes within the same DAO are more intuitive to analyze the DAO. Methods for changing trends in the degree of decentralization.

05 Cross-extension of VBE and DAO

Combining VBE’s framework and VBE’s analysis and inference of DAO, there is a DAO that seeks to implement or improve meaningful decentralization. Several specific guiding principles:

Extension topics

VBE by measuring the entropy of voting blocs To evaluate the degree of decentralization of DAO. In fact, VBE is a flexible framework that can be combined with any desired clustering method to identify cliques, as well as any definition of entropy.

The following are the open issues 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 issue that has yet to be solved.

DAO’s fork and escape mechanism:

DAO may encounter catastrophic failure , 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:

Whether high VBE values ​​are related to community growth and participation degree and financial performance? And how it relates to democratic participation in non-blockchain environments remains a direction worthy of future research.

06 Learning Summary

VBE is an in-depth exploration of the concept of "decentralization" in DAO, providing a new perspective by focusing on the interests behind voting behavior The alliance and its degree of centralization quantitatively analyze the essence of decentralization.

We love DAO and hope that DAO can continue to develop healthily. In this paper, DarkDAO is discussed separately and occupies an important space. Just like the hidden order, Dark DAO has formed a lasting and non-negligible impact on the governance models of different DAOs. The existence of Dark DAO is not only inevitable, but will also be an important factor in shaping the future governance ecology. Therefore, DAO builders should learn to look at themselves from the perspective of Dark DAO, learn the ideas and technologies of Dark DAO, and explore strategies to coexist with it to achieve a more robust and inclusive governance system.