Exploring the Most Important “D” in DAOs: VBE, Voting Bloc Entropy
With the development of Decentralized Autonomous Organizations (DAOs), governance risks have gradually emerged. Traditional decentralized measurement methods struggle to reveal the interest alliances hidden behind voting behaviors, particularly the threats of covert manipulations such as those from Dark DAOs. Voting Bloc Entropy (VBE), an innovative metric, quantifies and evaluates the centralization level of a DAO through clustering and entropy calculations, uncovering governance risks. This article will briefly explore the core framework of VBE and its practical applications in DAO governance.
Background Introduction
A few months ago, Compound DAO passed Proposal 289, which became a typical case of a governance attack. Five addresses exploited a governance vulnerability in Compound DAO to seize 5% of the community treasury’s control — worth approximately $24 million. Through this proposal, control would be handed over to a multi-sig wallet that was completely uncontrollable by the community.
Before this event occurred, existing decentralized metrics failed to clearly predict the risks. The currently popular analytical indicators are actually relatively outdated. For example, the Nakamoto coefficient and the Gini coefficient both focus on the distribution of tokens across different addresses. This obviously overlooks the hidden connections behind the addresses and ignores the existence of Dark DAOs. A Dark DAO is a general term used to describe decentralized alliances that manipulate on-chain voting through opaque methods, such as vote buying.
How can we penetrate beyond the surface-level address information to uncover the underlying cluster relationships and identify hidden risks? Among the three words in DAO, the most important but also the hardest to quantify is the first one: D (Decentralization). https://www.initc3.org/ has proposed a metric designed to reveal the “hidden alliances” behind address clusters, called VBE (Voting Bloc Entropy), which revolves around the following three core concepts:
- Voting: Voting behavior and decision-making patterns.
- Bloc(Bloc/Interest Alliance): In VBE, a “Bloc” refers to a group of voters who behave similarly in terms of voting patterns, regardless of whether these addresses belong to the same entity or have any known connections.
- Entropy: Entropy is a concept used to measure the uncertainty or uniformity of a system. VBE applies it to assess the concentration and power distribution within voting blocs.
- High entropy: Voting behavior is decentralized, with multiple voting blocs having different opinions on proposals, leading to more decentralized governance.
- Low entropy: Voting behavior is concentrated, with a few blocs controlling the proposal outcomes, making governance more susceptible to manipulation.
It’s worth noting that VBE is also read as “vibe,” symbolizing the community’s atmosphere — an abstract but crucial characteristic.
The core principle of VBE is that the alignment of interests among voters across multiple proposals (i.e., the formation of voting blocs) is a sign of centralization. VBE measures the degree of centralization within a DAO by clustering participants with similar utility functions across multiple votes and calculating entropy values.
So, how does VBE conduct this in-depth analysis and how does it quantify the abstract concept of the community “vibe” into concrete metrics? Let’s jump down the rabbit hole and explore!
VBE：Voting Bloc Entropy
The framework of VBE can be broken down into two key components: Clustering Metric and Entropy. Below are the key elements and implementation details:
- Clustering
VBE defines 𝜖-threshold ordinal clustering (𝜖-TOC) with the following rules:
- Formula Interpretation:
- The goal of this formula is to determine whether the voting behaviors of two token holders are similar, thereby grouping them together (clustering). Specifically, it defines “similarity” through the following two conditions:
- Clustering Condition 1 (Consistent Voting Tendency): A simple example is: if two individuals both support (positive) or both oppose (negative) a proposal in a particular election, meaning their voting signs are the same, they are considered to have consistent behavior in that election.
- Clustering Condition 2 (Sufficiently Small Preference Difference): A simple example is: even if two individuals have different signs (one supports and the other opposes) in a particular election, as long as the difference in their preference strength (such as the degree of support or opposition) is small enough (below the threshold ϵ), they can still be considered to have similar behavior.
UEP (see the formula below): The preference utility of address Pi for the election set E.
- k: Election index, representing the k-th election.
- ϵ: Threshold, used to measure whether the preference strength difference is negligible.
- Although more granular metrics can be used for clustering based on cardinal utility, ordinal equivalence is effective in indicating preference consistency.
- 𝜖-TOC can be computed based on historical voting data.
- Special treatment for apathetic voters: Voters with utility close to 0, who show little interest in election outcomes, are grouped into an additional category, labeled as A‘. These voters’ behavior reflects low participation in governance.
- Entropy
VBE uses min-entropy as the measure of entropy. The formula is as follows:
Formula Interpretation
- A: Represents the set of all addresses.
- tokens(A’): Represents the number of tokens held by address set A’.
- maxA′∈A: Represents the maximum token holding among all addresses in set A.
- T: Represents the total number of tokens held by all addresses.
- Entropy here is used to measure the “information content” of the token distribution, but it focuses on the contribution of the largest token holders (or groups). A higher concentration of tokens corresponds to lower entropy (less information content).
- More granular entropy measures, such as Shannon entropy, can be used for more complex analyses, but they are harder to estimate and come with higher computational costs.
VBE Instantiation Formula
Given the previous definitions of clustering and entropy, for an election set E, a player set P, and their corresponding utility U(E, P), token distribution function tokens, clustering metric C, and entropy function F, the specific instantiated formula for VBE can be expressed as:
VBE Core Theorem
The VBE core theorem provides a general framework for analyzing how system changes impact the degree of decentralization. The basic logic of the core theorem analysis is as follows:
- Compare two systems, where the only difference between them is a certain “transformation” T, such as an increase in voter indifference, a shift to a private election mode, etc.
- Study how this transformation impacts the largest voting bloc in both systems.
- Based on this change, calculate and compare the VBE of the two systems.
In the VBE core theorem, let T be a function that alters the player set, election set, player utility, and/or token distribution, defined as:
In this case, the total token supply within the system remains unchanged.
Let B and B′ represent the largest voting blocs by token holdings, as clustered by ϵ-TOC in the original system (E,UE,P,tokens) and the transformed system (E′,UE′,P′,tokens′), respectively. The following conditions are satisfied:
- tokens(B): Represents the proportion of tokens held by the maximum voting block B, which is used as a weight in entropy measurement.
- As the proportion of tokens held by B’ increases, the relative entropy value of B decreases, leading to an increase in VBE.
- If B’ forms a new governance advantage (i.e., a majority control is obtained by B’ through token holdings), then VBE will strictly increase; if the token proportion remains unchanged, VBE will be equal.
This core theorem provides a paradigm for subsequent specific theorems, requiring only:
- Define a system transformation T and describe how it modifies the maximum voting block.
- Use the core theorem to derive and evaluate the impact of the transformation on the VBE value, thereby quantifying the change in the degree of decentralization of the system.
Extension Analysis and Application of the Core Theorem
(In the examples mentioned in this section, detailed derivations and proofs can be found in sections 3.2 to 3.8 of the paper at the end. If interested, please refer to the details.)
- 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 themselves as decentralized through account dispersion strategies, VBE can still reveal the true degree of centralization in the system.
In contrast, measurement methods based solely on account balances may incorrectly conclude that the system’s degree of decentralization has increased, as these methods overlook the true distribution of token control.
2. Governance Apathy
- Centralization Effect:
The large-scale emergence of apathetic voters can lead to the concentration of voting power into a larger unified block.
This indicates that the phenomenon of apathy can, in practice, lead to a more centralized power structure within the system.
- “inactivity whale”:
The collection of apathetic voters can be viewed as an “inactivity whale,” whose behavior has potential systemic significance.
Even if they do not vote, the amount of tokens held by this group may significantly impact the degree of decentralization in the system.
3. Delegation
Intuitively, delegated voting might seem to make the system more centralized: tokens originally held by a large number of participants are transferred to a small number of representatives. However, through VBE analysis, this situation is actually more complex. Delegated voting can often lead to greater decentralization in DAOs:
- In cases of high apathy: Delegated voting is most effective, as it distributes the tokens of the “apathetic whales” across multiple representative blocs, thereby reducing the risk of system centralization.
- It’s important to note: if the representatives themselves form new “whales,” the decentralization of the system might actually decrease.
4. Herding
The core goal of DAOs and other democratic systems is to allow token holders to vote based on their true preferences. However, the herding effect (such as alliance behavior triggered by public voting) often obstructs this goal. Token holders may be compelled to follow influential members or align with their peers due to reputation risks, thereby forming large voting blocs. These social dynamics cause voting to deviate from individual true preferences, leading to increased centralization. Even if token distribution is uniform, traditional metrics may still misjudge the system as decentralized if group dynamics push everyone toward the same outcome. In contrast, VBE can reveal how reputation risks reinforce centralization and provide a more accurate reflection of the true degree of decentralization：
- The Importance of Privacy: Ensuring voting privacy helps mitigate the centralizing pressure caused by the herding effect, thereby enhancing the decentralization of the system.
- The Prevalence of the Herding Effect: In DAO design, the herding effect is a common phenomenon that can lead to unfairness and inefficiency within the system. Therefore, it is essential to consider how to reduce the impact of social dynamics on voting behavior during the design process.
5. Voting Slates
Voting slates are often used to “hide” unpopular proposals within a large batch of popular, harmless ones, thereby increasing the likelihood of passing those unpopular proposals. VBE reflects how bundling proposals together reduces decentralization: by considering a narrower set of election choices, the utility function is smoothed, and different voting blocs are merged into larger blocs.
How to Address This: To maintain decentralization, voting slates should be used cautiously, especially when dealing with elections that have clearly differing preferences.
6. Bribery
Bribery has an intuitive relationship with decentralization, in that successful bribery threatens decentralization: in this case, the entity that obtains votes from other players now controls a higher proportion of tokens than before. However, traditional decentralization metrics (based on token distribution in accounts) fail to capture this: although the bribed voters vote according to the instructions of the briber, they still technically hold their tokens. In contrast, VBE (Voting Bloc Entropy) groups all bribed players into the briber’s voting bloc, because the utility function of these bribed players is now aligned with the briber’s expected outcome. Interestingly, similar to the analysis of governance apathy, bribery could result in an outcome that contradicts intuition: bribery may actually lead to a more decentralized system, especially when it disrupts a larger voting bloc (such as a lazy whale bloc or a large voter coalition). But here, we ignore such marginal cases, assuming that the bribed voting bloc represents the majority based on token holdings. Therefore, although bribery does not necessarily unconditionally increase centralization, it does pose a real threat to decentralization.
- Successful bribery must be systemic, meaning it must involve a large number of tokens, and this only occurs when the system is highly decentralized. Intuitively, if a DAO is highly centralized, a briber can directly coordinate with a few large players to ensure the election outcome; or, if the briber is a whale (holding a large amount of tokens), they only need to bribe a few small players to accumulate enough tokens to launch a successful attack. In contrast, in a more decentralized system, players are smaller, so if a briber wants to win the election, they need to scale up their attack. That is, in this case, successful bribery requires large-scale coordination across many small players.
7. Quadratic Voting (QV)
- QV aims to diminish the power of whales, but it could inadvertently amplify the influence of bribery:
- If there are enough unmotivated “small players” in the community, bribes can be used at a lower cost to manipulate the election results because QV amplifies the influence of small players.
- sybil attack risk: If the system lacks true identity verification, whales can distribute their tokens across multiple accounts, bypassing the influence penalty QV imposes on them, thus increasing their overall voting power. This actually weakens decentralization.
VBE can be used to identify latent voting blocks within QV, providing a more accurate assessment of the decentralization of governance.
VBE’s Limitations
- Comparative Issues: VBE is a framework, and it cannot directly compare the results of different VBE instances or variations. To analyze changes in decentralization, evaluations must be conducted under the same VBE parameters.
- Limitations of VBECe,min: VBECe,min is biased towards the largest voting block and overlooks the contributions of smaller voting blocks. In more diversified scenarios, this may lead to results that are not comprehensive enough. Other entropy metrics (such as Shannon entropy) might provide a more complete perspective.
- Strictness of Clustering Metrics: The current ϵ-TOC clustering method only considers perfectly consistent voting behavior, which may be too strict. ϵ\epsilon, a more relaxed clustering method based on partial consistency (such as ε-based clustering) could offer a finer analysis but would also increase computational complexity.
Dark DAO
Dark DAO is a decentralized organization with the goal of subverting existing decentralized credential systems by intervening in the voting decision processes of other DAOs. As mentioned earlier, in a centralized system, malicious actions often take the form of cooperation among large whales. As the decentralization of a DAO increases, the cost of bribing (larger players) also rises, requiring bribe-givers to coordinate more widely by targeting more users. This, in turn, increases the threat posed by Dark DAOs.
Similar to ordinary DAOs, the design goal of a Dark DAO is to achieve minimal trust: it ensures that bribery is “fair,” meaning that the bribe-receiver only receives compensation when they agree to give the bribe-giver access to voting credentials. Additionally, a Dark DAO operates with “opacity,” meaning the participation process is private.
A Dark DAO has the following three key attributes:
- Opacity: Participants in a Dark DAO cannot be distinguished from other credential holders on-chain. The scale and number of participants remain completely hidden.
- Fair Exchange: Bribe payments are conditional. Only after the bribe-giver successfully secures the voting support of the bribe-receiver will the bribe-receiver be compensated.
- Limited Scope: The bribe-receivers participating in the Dark DAO will not contribute any additional resources to the Dark DAO beyond the agreed-upon credentials and pre-arranged costs. (For example, the bribe-receiver may still need to pay regular transaction fees.)
The goal of a Dark DAO is to subvert the voting decisions of a target DAO. Below are its main methods of achieving this:
- Vote Buying
Dark DAO achieves its goal through bribery, such as paying token holders to vote in favor of a specific outcome.
- The payments can be conditional, for example, paid only once the desired result is achieved, or a fixed reward can be distributed based on the total number of votes.
- Not only token-weighted votes can be affected, but even “one-person, one-vote” systems (like Gitcoin Passport or Worldcoin) could be exploited by using keys or identity credentials for bribery.
Dark DAO can drastically reduce the cost of bribery, for example, by using a pivotal bribery strategy: paying significant rewards to the key voters whose votes are decisive in changing the outcome, while giving minimal payments to other participants. This allows the Dark DAO to alter the election results with minimal costs.
2. Coordinated Price Manipulation
- Dark DAO is not limited to distributing bribes but can also indirectly reward participants through coordinated collective actions. By manipulating market or asset prices as part of a collective effort, Dark DAO can incentivize participants to act in ways that align with its goals, further influencing the voting or decision-making process.
For example:
- Participants collectively establish short positions on the target asset.
- Voting drives results that cause the asset price to drop.
- Profits are realized upon closing the short positions, and the proceeds are distributed.
This approach could also extend to consensus protocol attacks or market manipulation
3. Undermining Perceived Election Integrity
- The mere existence of Dark DAO could cast doubt on the legitimacy of DAO elections.
- Even if Dark DAO’s involvement is limited, it can still impact the community’s trust in the election by concealing its scale or selectively disclosing its level of participation (e.g., owning at least 10% of the tokens). This undermines the perceived integrity of the election process.
4. Exploiting Quadratic Voting and Quadratic Funding
- Dark DAO could exploit address fragmentation to bypass the restrictions of Quadratic Voting (QV). For example, by distributing tokens across multiple addresses, it can amplify voting power.
- Even when decentralized identity verification systems are used, Dark DAO could still manipulate results by “temporarily distributing” tokens to other users and controlling their voting behavior.
- Similar tactics can also be used in Quadratic Funding (QF) to manipulate the allocation of funds.
5. Subverting Privacy Pools
Privacy pools aim to balance privacy with compliance, but Dark DAO can subvert this mechanism through identity trading.
For example, a compliant user could rent their compliant identity to Dark DAO, allowing non-compliant users to temporarily use their address for money laundering or evading sanctions.
On the other hand, Dark DAO could also strengthen the security of privacy pools by requiring addresses to maintain a minimum balance, thereby limiting the weakening or collapse of the privacy pool.
Extension: A Dark DAO Instance Framework
(For details on the Dark DAO instance framework, refer to sections 6. Basic Dark DAO and 7. Dark DAO Lite at the end of the original paper. Interested readers can refer there for further details.
Github_DarkDao：GitHub - DAO-Decentralization/dark-dao
The Dark DAO framework demonstrates how Web3 technologies can facilitate complex transactions and coordination under complete anonymity.
- In addition to vote buying, the Dark DAO framework can accommodate more sophisticated market manipulation and privacy management needs. For example, users can leverage the framework for price manipulation by setting collective action goals (such as shorting an asset) and rewarding outcomes based on predefined criteria for indirect market profit. Furthermore, the framework can be used for privacy pool attacks, assisting in renting compliant identities to indirectly disrupt the balance between privacy and compliance.
The paper also proposes a lighter version called Dark DAO Lite, which simplifies Dark DAO’s full anonymity to a limited form of anonymity and streamlines the trustless collaboration process. Dark DAO Lite can integrate decentralized identity systems (such as Gitcoin Passport or Worldcoin) with zero-knowledge proofs to provide limited privacy protection while ensuring that each user’s voting power is fairly calculated. This design lowers the cost of implementing attacks, increases the concealment of attacks, and makes the framework more flexible, harder to detect, and more difficult to prevent.
Both the Dark DAO and its Lite version pose a significant threat to decentralized systems due to their privacy and efficiency. For example:
- Undermining Governance Transparency: Dark DAO may erode public trust in the governance process, especially when its scale and objectives are unclear.
- System Vulnerabilities: The technical complexity of Dark DAO increases the attack surface of the protocol itself, such as through malicious smart contract manipulation to alter rules or distribution mechanisms.
Using VBE to Observe DAOs
The previous section provided an overview of the VBE metrics and Dark DAO characteristics. Below is an application of the VBE metrics in observing DAOs through an oVBE Dashboard. This section provides a detailed introduction to the features of this dashboard.
https://public.tableau.com/app/profile/daovbe/viz/DAOoVBEDashboard/Voting-BlocEntropyOverview
Overview: Voting-Bloc Entropy Overview
In the overview section on the homepage, the dashboard displays VBE data for 27 DAOs, with charts on the right side showing an Entropy Overview.
In the Dashboard Overview, we can see the following eight parameters:
- AVG(VBE): The average VBE value over the entire statistical period. (IC3 official reminder: be cautious when comparing VBE parameters across different DAOs.)
- SUM(Avg Participation Rate): The sum of the average participation rates of token holders in the voting process. It measures the overall activity and engagement in voting.
- SUM(Avg Votes per Voter): The sum of the average number of votes per voter, used to measure the concentration of voting power in the voting process.
- SUM(Bribeable Proposals): The total number of proposals that could be manipulated, used to gauge the potential corruption risk.
- AVG(Max Cluster %): The average percentage of the largest voting bloc in all votes. This metric reflects the concentration of voting blocs; a higher value indicates a more centralized voting outcome.
- AGG(Median Voters to Bribe): The aggregation of the median number of voters needed to be “bribed” to influence the vote outcome.
- CNT(Proposal): The total number of proposals in the DAO.
- SUM(Unique Voters): The total sum of unique voters during the statistical period, counting each voter only once. This measures the diversity of participants and the coverage of governance within the DAO.
By double-clicking on specific parameters in the list, we can open the details and observe how these data points change and compare across different DAOs.
DAO Pagination Details
In the pagination details, you can observe the detailed situation of each DAO. The chart in the upper-left corner displays the VBE values and the maximum voting bloc percentage for each time window during the statistical period.
Clicking on a point in the line chart will display a comparison of proposal categories for that time window in the upper-right corner, an overview of voting blocs for that time window in the lower-right corner, and proposal details for that time window in the lower-left corner.
When comparing VBE across different DAOs, it’s important to consider differences in the underlying datasets. However, within the same DAO, the changes in VBE and voting blocs provide a more intuitive way to analyze the trends in the decentralization of that DAO.
VBE and DAO Cross-Extensions
Combining the framework of VBE and the analysis derived from VBE for DAOs, there are several specific guiding principles for DAOs seeking to implement or improve meaningful decentralization:
Extended Topics for Thought
VBE evaluates the decentralization of DAOs by measuring the entropy of voting blocs. In practice, VBE is a flexible framework that can combine any clustering method required to identify blocs, as well as any definition of entropy.
The following are open questions raised at the end of the paper that are worth attention:
- Privacy and Data Collection:
How to collect enough data to facilitate VBE evaluation while ensuring voting privacy remains a problem to be solved.
- DAO Forking and Escape Mechanisms:
DAOs may encounter catastrophic failures. How to study the impact of DAO forking and escape mechanisms on decentralization is an important issue.
- Impact of VBE on DAO Decision-Making:
Is a high VBE value related to community growth, participation, and financial performance? How does it relate to democratic participation in non-blockchain environments? This remains a direction for future research.
Learning Summary
VBE is a deep exploration of the concept of “decentralization” within DAOs, providing a fresh perspective by focusing on the interest alliances behind voting behaviors and their degree of centralization. It quantitatively analyzes the essence of decentralization.
We love DAOs and hope they continue to grow in a healthy and sustainable way. In this paper, Dark DAO is discussed in detail and occupies a significant portion. Like an invisible force, Dark DAO has a lasting and undeniable impact on the governance models of various DAOs. The existence of Dark DAO is not only inevitable but also a crucial factor in shaping the future governance ecosystem. Therefore, DAO builders should learn to view their projects from the perspective of Dark DAO, understand its ideas and techniques, and explore strategies for coexisting with it to create a more robust and inclusive governance system.
Feel free to explore the details of the topics mentioned in this summary by reading the corresponding sections in the paper and leave your thoughts in LXDAO!
https://arxiv.org/pdf/2311.03530
References:
[1] DAOs need a vibe check DAOs Need a Vibe Check
[2] arxiv.org[2311.03530v1] DAO Decentralization: Voting-Bloc Entropy, Bribery, and Dark DAOs
[3] IC3 on X x.com