Forwarded the Original Title: Ten years of DAO: Unlocking new dimensions of governance and in-depth analysis of key governance indicators

The history of DAOs now spans a decade, having experienced a significant boom in 2021. This organizational model has steadily integrated into society, with numerous large-scale DAOs subsequently conducting diverse governance experiments and expansions, leading to the development of various governance studies.

This article compiles reference parameters that serve as governance indicators for analyzing different governance structures. While each parameter typically quantifies a specific indicator, it’s important to note that the significance of each indicator varies depending on the DAO type.

Analysis of important indicators

The following indicators do not include indicators related to “complexity” and “coherence” for the time being, and “voting” is uniformly used as an example. The specific application scope can be extended to various data such as funds, media, etc.

Herfindahl-Hirschman index, HHI

It is a widely adopted method for measuring concentration, named after two economists. It calculates the sum of squared market shares of all entities in a market.

To put it simply, the proportion of each different unit is multiplied by the square.

For example, A has 50%, B has 30%, and C has 20%

50 * 50 = 2500

30 * 30 = 900

20 * 20 = 400

The three add up 2500 + 900 + 400 = 3800

3800 is the concentration index of ABC

Maximum 10,000 (1 person accounts for 100%)

Concentration of Power Index (CPI)

A variant derived from HHI, which is basically the same as HHI, but considering that a situation is in a specific DAO, such as OP, different governance institutions will have different weights. Therefore, the score for each representative must be adjusted based on their respective weights.

For example:

If a representative has a weight of 300 points but is involved in both the Token House and the Citizens’ House, their total weight would be:

His total weight is:

30032.33% + 30034.59% = 200.76

Since this calculation pertains to governance indicators, it does not account for all representatives, only those participating in governance. Consequently, when the community’s governance activity decreases, it can also result in an increase in the index value.

Nakamoto coefficient

Mainly focused on one question: How many participants are needed to control the entire system?

This question is very interesting, and in fact it is also very useful for capital market strategies.

If there are 5 people in the system, their voting rights are:

• A: 30%
• B: 25%
• C: 20%
• D: 15%
• E: 10%

The minimum number of people required to control the entire system is 30 + 35 = 55. The minimum number of people required is 2, so the Nakamoto coefficient is 2.

If the Nakamoto coefficient of a system is 20, it means that at least 20 people need to join forces to control the system. This system is very decentralized.

The higher the coefficient, the higher the degree of decentralization, and vice versa.

Proposal Submitter Diversity (Shannon Diversity Index)

There are multiple measurement approaches. One uses the HHI above to evaluate the concentration of proposals submitted; the higher the concentration, the lower the diversity.

Another approach uses the Shannon Diversity Index.

Assume 4 proposal submitters, who submitted the following number of proposals over a period of time:

• Proposer A submitted 5 proposals
• Proposer B submitted 3 proposals
• Proposer C submitted 2 proposals
• Proposer D submitted 1 proposal

Next, calculate the proportion of the number of proposals from each proposer to the total number of proposals.

The total number of proposals is: 5 + 3 + 2 + 1 = 115

The ratio of each proposer is:

• A：≈ 0.4545
• B：≈ 0.2727
• C：≈ 0.1818
• D：≈ 0.0909

Next calculate the natural logarithm of each ratio (using the “ln” button on a calculator):

• A：−0.7885
• B：−1.2993
• C：−1.7047
• D：−2.3979

Next, multiply each proportion by its corresponding logarithmic value:

• A：0.4545 × −0.7885 ≈ −0.3582
• B：0.2727 × −1.2993 ≈ −0.3540
• C：0.1818 × −1.7047 ≈ −0.3090
• D：0.0909 × −2.3979 ≈ −0.2171

Finally, sum all the values: the result is 1.2383. A higher value indicates greater diversity in the system. Compared to HHI, the Shannon Index is more intuitive, especially in cases of high diversity, as it better highlights differences (with HHI, a smaller value corresponds to more dispersion).

Gini index

This is an index that is very suitable for graphical representation. The steps are as follows. It is usually used to evaluate the distribution of resources. For example, when an organization has multiple projects, the Gini index can be used to understand whether the resources are evenly distributed. It can also analyze factors like wages and working conditions. If multiple values are identical, they will form a straight line on the graph.

1. List the proportion of voting power of each member：

First, you need to know the proportion of voting power each member has. For example, if there are 5 members, their voting power proportions might be:

• A: 40%
• B: 30%
• C: 15%
• D: 10%
• E: 5%

1. Sorted in ascending order by voting power：

Sort these voting power proportions from smallest to largest so we can see the inequality more easily:

• E: 5%
• D: 10%
• C: 15%
• B: 30%
• A: 40%

1. Calculate cumulative voting power proportions:

Now, we calculate the cumulative voting power proportions of each member by starting with the smallest and adding them up one by one:

• E: 5%
• E + D: 5% + 10% = 15%
• E + D + C: 5% + 10% + 15% = 30%
• E + D + C + B: 5% + 10% + 15% + 30% = 60%
• E + D + C + B + A: 5% + 10% + 15% + 30% + 40% = 100%

These cumulative values—5, 15, 30, 60, and 100—can be plotted on a graph (from the bottom left to the top right).

When voting power is evenly distributed within an organization, this line approaches a straight diagonal line. The more the curve bends downward, the more severe the inequality in the distribution of votes.

Z-Score Decentralization Metric

Z-Score Decentralized Metric is used to determine how closely an individual’s power (e.g., voting rights) in a system aligns with the average power of others in the system. It answers the question: “How far is an individual’s power from the average level compared to everyone else?”

Z-Score may be positive or negative

• If the Z-Score is very close to 0, it means that the person’s power share is about the same as the average of other people.
• If the Z-Score deviates a lot from 0, it means that the person’s power is far different from the average level. Either his power is very large or very small.

This is a statistical index that can also be used to identify data such as salary structure, etc.

Assume there are 5 members and their voting power proportions are:

• A：40%
• B：25%
• C：15%
• D：10%
• E：10%

Average voting power:

• average = 20%

Calculate each individual’s power difference:

Next, we need to see how much the power of each member differs from the average.

For example：

• A：40% − 20% = 20%
• B：25% − 20% = 5%
• C：15% − 20% = −5%
• D：10% − 20% = −10%
• E：10% − 20% = −10%

Calculate standard deviation: The standard deviation is used to express the deviation of each member’s voting power from the mean.

The standard deviation is the average of all the squared numbers and then takes the square root.

Divide each individual’s deviation by the standard deviation. For example, if D’s deviation is −10% and the standard deviation is 11.4%, the Z-Score is:

-10 / 11.4 = −0.88

But why not just look at the difference?

• Z-Score provides standardization. For example, when comparing different DAO organizations, a 10% difference in voting power might appear similar, but converting it to Z-Scores enables direct comparisons across organizations.
• Z-Score highlights relative differences. For instance, if D’s deviation remains −10%, but the standard deviation changes due to shifts in overall power distribution, D’s Z-Score will also change, reflecting these dynamics.

It can also be used to analyze salary changes. For example, if a person’s salary remains unchanged while the standard deviation of salaries across the company increases due to a general pay raise, the Z-Score can reveal how that individual’s salary has effectively changed relative to the company average.

While Z-Score may not be ideal for analyzing voting in DAOs, it is valuable for assessing changes in project resource allocation or individual contributions.

Dynamic CHanges in Voting Power

Voting Power Mobility Index

This index measures how much voting power “moves around” among members in a system. If voting power consistently remains concentrated in the hands of a few, it suggests a rigid power structure with limited participation opportunities. If voting power frequently shifts between members, it indicates an “active” system where everyone has a chance to participate, leading to a fairer and more decentralized system.

Assume this is the distribution of voting rights in Q1 and Q2:

• First quarter
  • A’s voting rights: 40%
  • B’s voting rights: 30%
  • C’s voting rights: 30%
• Second quarter
  • A’s voting rights: 35%
  • B’s voting rights: 40%
  • C’s voting rights: 25%

Step 2: Calculate the change in voting power for each member

Variation of each memberThis is the voting power in the second quarter minus the voting power in the first quarter:

• Change in A: 35% - 40% = -5% (decrease by 5%)
• Change in B: 40% - 30% = +10% (increase by 10%)
• Change in C: 25% - 30% = -5% (decrease by 5%)

Step 3: Add the changes of all members together

In this step, we put everyone’s absolute value of change (regardless of increase or decrease, only take the size) and add them together to get the ”Voting Power Mobility Index” of the entire system.

• Absolute value of change in A: 5%
• Absolute value of change in B: 10%
• Absolute value of change in C: 5%

Total change = 5% + 10% + 5% = 20%

This 20% is the “Voting Power Mobility Index”. It said 20% of the voting power in the system changed between the two quarters.

This concept is similar toZ-Score is very similar, and you can also add standard deviation to see the rate of change.

Changes in cumulative voting power

We look at the “top members” with the most voting power to see if their share of voting power is increasing. If the shares of these top members are getting larger and larger, it means that the power in the system is becoming more and more concentrated; if there is not much change, it means that the power of the system is still dispersed and everyone’s voting rights are relatively even.

Assume we have voting power data for Q1 and Q2:

• First quarter
  • A’s voting power: 40%
  • B’s voting power: 25%
  • C’s voting power: 20%
  • D’s voting power: 10%
  • E’s voting power: 5%
• Second quarter
  • A’s voting power: 45%
  • B’s voting power: 20%
  • C’s voting power: 15%
  • D’s voting power: 15%
  • E’s voting power: 5%

We rank each quarter’s member voting power from largest to smallest:

• First quarter：A > B > C > D > E
• Second quarter：A > B > D > C > E

Step 2: Calculate the voting power share of the “top 20%” members

To observe “concentration of power,” we typically look at the cumulative voting power of those “top members” in different quarters to see if they are increasing.

Among the 5 members, the top 20% of the members are the 1 member with the highest voting power (A).

• First quarter: A’s voting power = 40% (cumulative voting power of top 20% = 40%)
• Second quarter: A’s voting power = 45% (cumulative voting power of top 20% = 45%)

As can be seen, the voting power share of the top 20% increased from Q1 to Q2.

Step 3: Calculate the voting share of the “top 40%” members

We can also look at the cumulative share of the top 40% (out of 5 members, that’s the top 2).

• first quarter: Cumulative voting rights of A + B = 40% + 25% = 65%
• second quarter: Cumulative voting rights of A + B = 45% + 20% = 65%

Here you can see that there is no change in the cumulative voting power share of the top 40%.

This calculation allows you to see whether a change such as representation is simply a shift in voting rights, or whether there is a large concentration of votes.

Funding Transparency

This metric is typically not strictly quantified. It often involves comparing published financial reports against total liquid funds or assessing the level of detail disclosed. While subjective and of limited significance, aspects such as the method of disclosure, the level of detail, and whether audits are conducted can still be used for a simple evaluation.

Decision-Making Time

The usual approach to analyzing decision-making time focuses on the preparation phase before proposals are submitted.

For example, calculate the average duration of the “feedback collection” phase for each proposal.

Since voting time is often fixed, measuring it usually lacks significance unless there is a scenario where all votes are consistently cast very quickly (which is rare).

Common time parameters:

• Opinion collection time
• Multi-signature processing time
• Proposal review time

Governance-Related Incentive Mechanisms

The fairness of incentive mechanisms is often assessed using the Gini Index. However, this requires resolving the issue of quantifying “governance contribution,” which is typically done by converting fixed contributions into proportional incentives.

Quantifying governance contributions is challenging for long-term consistency. Below are some possible approaches:

• Composite Contribution Score = (task completion ratio × weight 1) + (participation time × weight 2) + (decision-making participation × weight 3) +…
• (Weight of Task 1 x Quantity of Task 1) + (Weight of Task 2 x Quantity of Task 2)…

Externally relevant data includes:

• Total incentives per quarter
• Average incentives earned by individuals
• Z-Score or Gini analysis to determine whether incentives are equitably distributed or overly concentrated among a few key participants.

Other Indicators That Require No Explanation

• Voting participation rate
• Proposal approval rate
• Demographic profiling: This is similar to sociological statistics, such as age, gender, language, etc.
• Number of governance attacks/captures/anti-capture incidents

Conclusion

Exploring the hidden truth behind the data deltas requires continuous accumulation and investigation. While learning from governance experiences across various DAOs, LXDAO is also attempting to clarify governance clues through quantitative methods, laying the foundation for DAO performance analysis. This effort aims to further explore additional data and possibilities. Hopefully, this article will provide useful insights for those interested in governance analysis.

Disclaimer:

1. This article is reproduced from [LXDAO]. Forwarded the original title “Ten years of DAO: Unlocking new dimensions of governance and in-depth analysis of key governance indicators”. The copyright belongs to the original author [LXDAO]. If you have any objections to the reprint, please contact the Gate Learn team (gatelearn@gate.io), and the team will handle it as soon as possible according to relevant procedures.
2. Disclaimer: The views and opinions expressed in this article represent only the author’s personal views and do not constitute any investment advice.
3. The Gate Learn team translated the article into other languages. Copying, distributing, or plagiarizing the translated articles is prohibited unless mentioned.