This analysis is a supplement to an accompanying dashboard analyzing Uniswap on-chain and off-chain (Snapshot) voting participation and distribution data. A diverse set of metrics were calculated to examine the degree of decentralization exhibited in historical Uniswap's governance proposals across the different phases, including:

Phase 1: Temperature Check — Discourse/Snapshot (Off-chain)

Phase 2: Consensus Check — Discourse/Snapshot (Off-chain)

Phase 3: Governance Proposal — Governance Portal (On-chain)

The accompanying dashboard, including summary data tables and visualizations, can be accessed at https://signalcorps.shinyapps.io/Uniswap_On_Off_Chain_Governance/.

Voting Participants: count of unique voting addresses.

Voting Power: sum of votes cast.

Nakamoto Coefficient: based on metric originally defined in Srinivasan and Lee (2017). For this application, it is calculated as the minimum number of entities (i.e. unique voter addresses) required to control 51% or greater voting share. (Reference)

Herfindahl-Hirschman Index (HHI): measure of market concentration, most notably used by the United States Department of Justice (DOJ) & Federal Trade Commission (FTC). It is calculated by squaring the market share of each firm competing in the market and then summing the resulting numbers. For example, for a market consisting of four firms with shares of 30, 30, 20, and 20 percent, the HHI is 2,600 (30^2 + 30^2 + 20^2 + 20^2 = 2,600). The HHI can range from 1 (least concentrated) to 10,000 (most concentrated). The DOJ and other governmental agencies historically consider markets under 1,500 to be low concentration, markets between 1,500 to 2,500 to be moderately concentrated, and markets in excess of 2,500 to be highly concentrated. (Reference).)

Gini Coefficient: a measure of equality within a community, commonly used to quantify income inequality. A low/high value represents a more equal/unequal community. It is calculated as the ratio of the area between the perfect equality (dotted) line and the Lorenz Curve divided by total area under the perfect equality (dotted) line. (Reference)

Shannon Diversity Index: a popular measure used in ecology to quantify the diversity of species, often by species' respective population count, within a community. For this application, it is used to quantify the diversity of voting weight of participants. A higher value represents a more diverse and equitable community. The Shannon diversity index is calculated by taking the sum of each voter’s proportional voting power (Pi) multiplied by the natural log of Pi and then multiplying by -1. (Reference)

Data as of August 6, 2022.

Readers are encouraged to view the accompanying dashboard when reviewing the key findings presented below. The dashboard is available at https://signalcorps.shinyapps.io/Uniswap_On_Off_Chain_Governance/

1. On-chain voting participation was sparse in the initial proposals (0.1 – 2.10), with a range of voting participants from a low of 41 in Proposal 2.09 to 340 participants in Proposal 0.2. There was a reinvigoration in on-chain voting participation beginning in Proposal 2.11 with 1,965 participants that has generally sustained through to Proposal 2.23.

2. There was a marked increase in voting participation on Snapshot (i.e. Temperature Check and Consensus Check) beginning in Proposal 2.13. Prior to Proposal 2.13, the number of voting participants typically ranged from 300-500 whereas it has been consistently between 1,000 – 1,500 from Proposals 2.13 – 2.23.

3. In a vast majority of proposals, the off-chain voting on Snapshot had higher voting participation compared to the on-chain governance vote. For example, in Proposals 2.11 – 2.23, on-chain voting participation was on average 85% of Snapshot voting. This is likely due to Snapshot not requiring gas fees, unlike on-chain votes.

4. While the participant count was higher in off-chain, voting power exercised was significantly higher in on-chain voting. For Proposals 2.11 – 2.23, the average on-chain voting power exercised was 58,268,661 while Snapshot was on average 8,901,470. This implies 6.5X on-chain to Snapshot ratio.

The remainder of this analysis will focus on the findings for the recent Proposals 2.11 – 2.23, as there was a noticeable increase in the voting participation observed.

Nakamoto Coefficient

1. The Nakamoto coefficient has been 1-2 for the Temperature and Consensus phases on Snapshot since Proposal 2.11.

2. The Nakamoto coefficient has been 5 for the majority of on-chain votes since Proposal 2.11.

3. The lower-participation yet higher voting-power on-chain statistics compared with the Nakamoto coefficients suggests that a considerable proportion of Whales abstain from the off-chain phases on Snapshot but then participate in the formal on-chain governance vote.

1. The Gini coefficient observed in governance voting has been between 0.980 and 0.999 for both on-chain and off-chain. Such high Gini coefficient scores often indicate significant levels of concentration. However, a limitation of this analysis is it has not adjusted for the role that delegation may play in contributing to observed levels of concentration. Even under certain variations of robust decentralized governance, there could be high observed Gini coefficients. For example, a proposal could have a Gini coefficient of 0.99 if it had 1,000 participants comprised of 10 main delegates (representing thousands or millions who have delegated their vote) and 990 individuals with smaller amounts individually voting on this particular proposal.

2. The underlying level of concentration among UNI holders must be acknowledged. Yet, there are also significant limitations from relying too heavily on the use of a Gini coefficient as the main signal of the level of inequality amongst a community, as further described in a July 2021 article by Vitalik Buterin. Overall, the Gini coefficient alone is insufficient as a sole measure of decentralization---it should continue to be used but complemented with other measures.

As stated in the Metrics Definitions section, the United States Department of Justice and other governmental agencies historically consider markets with a HHI under 1,500 to be low concentration, markets between 1,500 to 2,500 to be moderately concentrated, and markets in excess of 2,500 to be highly concentrated.

1. The Snapshot votes in the Temperature and Consensus phases have HHI scores often at or in excess of 2,500. The lone exception since Proposal 2.11 was [Temperature] Proposal 2.22 with a moderate-to-high HHI of 2,399.

2. The HHI scores for on-chain are significantly lower with the typical score being between 850 to 1,000. The highest HHI since Proposal 2.11 was 1,511 in Proposal 2.14.

3. If adopting the DOJ’s historical score interpretation, this analysis implies relatively high concentration during the Snapshot phases and low concentration in the formal on-chain governance phase.

4. These findings compliment the Nakamoto coefficient, as the Snapshot phases had a Nakamoto coefficient of 1-2 paired with HHI in excess of 2,500, while the on-chain governance votes had a Nakamoto coefficient typically at 5 with HHI between 850-1,000.

5. The HHI suggests there is potential balance of power between the largest UNI holders without one holding dominant control. Further, the HHI illustrates that the balance of power is greater than simply the Nakamoto coefficient of 5. If under perfect equality of 5 market participants, then this would imply a HHI of 2,000. Yet, the measured on-chain HHI we observe within UNI governance is approximately 1,000.

1. The Shannon Diversity Index scores mirror the HHI scores. There is an inverse relationship present, so lower Shannon scores are correlated with higher HHI scores---indicative of higher levels of concentration.

2. A scatter plot presented below in Figure 1 demonstrates that the HHI and Shannon indices are redundant. While future iterations of this analysis will continue to measure the Shannon score, our general recommendation is to use the HHI in place of Shannon. There is minimal marginal signal gained from the additional measure. The HHI also has the benefit of enhanced interpretability due to the defined range of 1 – 10,000 and the DOJ’s precedent of concentration thresholds.

Only proposals with an on-chain vote were included in the scope of this analysis.  Therefore ‘canceled’ on-chain proposals were also excluded.

On-chain data sourced from the ethereum.events_emitted table on Flipside Crypto’s Velocity Platform. (Link to Flipside)

Off-chain Snapshot data sourced from the Snapshot GraphQL API (Link to GitHub).

Additional information and code can be found at GitHub.

This analysis is supported by grant funding from the Uni Grants Program.