Introduction

Continuing with our work exploring quantitative analysis methods for DAOs, in particular, the Banzhaf Power Index (BPI), I calculated the BPI for MakerDAO voters in an absolute participation scenario.1

What is the Banzhaf Power Index?

The Banzhaf Power Index (BPI) is a “power index defined by the probability of changing an outcome of a vote where voting rights are not necessarily equally divided among the voters or shareholders.”

Here is a short video explaining the BPI.

Here is an additional video explaining how to determine if a voter is a dictator, dummy, or has veto power.

Methods

Data Collection

I collected the following data on Maker DAO via Boardroom’s Governance API:

1. voters: dataset containing each voter (i.e., token holder) and their voting power2; and

2. delegations: dataset containing each delegation made by a token holder to another token holder.

Data was collected between May 15th and May 20th, 2024.

Voter Tables

All Voters

Voters with voting power greater than or equal to 1.00

Self-delegates

Proxy-delegates

Delegations Table

Data Analysis

For this analysis, I only included voters with a voting power greater than or equal to 1.00, after rounding the address’s voting power within two decimals of precision.

After including only the aforementioned voters, I had a total of 846 voters.

I calculated the BPI for each voter in absolute participation scenario, with and without delegates included, with the powerindex Python library.

I visualized the voting power and BPI distributions with the plotly Python library.

I assumed that in every scenario:

1. the quota3 is set at majority (fifty-one percent (51%) of the total voting power), and

2. full voter turnout (i.e., absolute participation).

From examining MakerDAO’s polling requirements, relative majority is generally the quota used in polls, so I assumed that using majority as the quota here should be appropriate.4

All Voters

For all 846 voters, I set the quota to 563,565.

Proxy-delegates

I acquired all delegations on MakerDAO via Boardroom’s Governance API, removed all self-delegations, and then removed all addresses in our voters dataset that were delegatees (i.e., delegated to) in the MakerDAO delegations dataset.

I set the quota to 59,051 for proxy-delegates.

Self-delegates

I followed the same procedure in finding proxy-delegates, but instead of searching for delegatees, I searched for self-delegations (i.e., voters who delegated their voting power to themselves).

I set the quota to 504,514 for self-delegates.

Results

Voting Power Distribution

All Voters

Proxy-delegates

Self-delegates

Banzhaf Power Index

All Voters

Table for BPI Distribution

Visualization for BPI Distribution

Proxy-delegates

Table for BPI Distribution

Visualization for BPI Distribution

Self-delegates

Table for BPI Distribution

Visualization for BPI Distribution

Findings

Banzhaf Power Index

All voters

0x74971F1bE0aFd1Bb820668aBFE411D164f17B53C had the highest BPI at 4.58329080.

0x6b412D6fB24D6F0A17641afdE687D5171839dB75 and 0x31AE14d23713f705a75807eE6878e87B37C3Ad51 had the joint lowest BPI with 0.00000000.

Thus, 0x6b412D6fB24D6F0A17641afdE687D5171839dB75 and 0x31AE14d23713f705a75807eE6878e87B37C3Ad51 are considered dummies in this scenario.5

818 addresses (~96.69%) had a BPI between 0 and 1.

Only twenty-eight (28) addresses had a BPI greater than 1.00.

Proxy-delegates

This time around, 0x74971F1bE0aFd1Bb820668aBFE411D164f17B53C had the highest BPI with 87.80493199.

There were no dummies in this scenario.

Ten (10) addresses had a BPI between 0 and 1.

Fourteen addresses had a BPI of one (1) or greater than one.

Self-delegates

0x8778b64F999aA8ed59045d8D67998a77Ab51E258 and 0x26732399F47e00739D2b4b0451aCC3F93F7e3a14 had the joint highest BPI with 4.10131702.

Only thirty-two (32) addresses had a BPI of 1.00 or greater. Approximately ninety-six percent (~96.11%) of voters had a BPI less than 1.00.6

790 addresses had a BPI between 0 and 1.

Once again, 0x6b412D6fB24D6F0A17641afdE687D5171839dB75 and 0x31AE14d23713f705a75807eE6878e87B37C3Ad51 had the joint lowest BPI with 0.00000000.

Thus, 0x6b412D6fB24D6F0A17641afdE687D5171839dB75 and 0x31AE14d23713f705a75807eE6878e87B37C3Ad51 are considered dummies in this scenario.7

Future Directions

Future directions I may explore in updates to this pub are listed below.

1. Applying the BPI for Maker DAO’s past proposals and polls to determine the BPI distribution over time.

2. Applying the BPI for relative participation scenarios where the average number of voters8 participate for all available voters.

3. Reviewing Maker DAO’s governance documentation and MIPs for further clarity on quotas for polls, executive votes (i.e., proposals), and other decision-making processes.

4. Check for discrepancies between Boardroom’s and Maker DAO’s Governance APIs.

5. Applying other voting power indices to DAOs.

Request for Comments

I am seeking feedback on this pub for any improvements to make, errors to correct, or other areas to explore.

Please leave your feedback here, on the Ledgerback discussion forum, or on Twitter.

Contact Information

1. Twitter