Heal Noun O’Clock: Audit of Alternate Forking Mechanics

This blog summarizes the results of the research project of Proposal 528 for the Nouns DAO conducted by Cryptecon. Click here to read the full technical report.

Since the introduction of a forking mechanism to the Nouns DAO in August 2023, there have been three forks, leading to a drastic reduction in the treasury, which now stands at just 40% of its peak value of $50 million. Although part of these funds remained with nouners, a large fraction went to arbers.

Arbers see Nouns as an investment. They buy Nouns at auctions and then profit from ragequitting following a fork. They redeemed their Nouns for a proportional share of the DAO’s treasury.

Several initiatives have been started to address the growing number of arbitrageurs holding Nouns, including burning or changing the forking threshold. The idea behind these initiatives is to disincentivize arbers to participate in the daily auctions. However, the arbitrage problem currently still needs to be solved and remains a concern for the community.

This blog presents our findings from the research project of proposal 528, which analyzes the existing forking mechanics and initiatives as well as alternative, arbitrage-free exit schemes and shows their respective benefits and drawbacks. You can access the full technical report, including the mathematical model and detailed results, here.

Review of Exit Scheme Effectiveness

We investigated four different exit mechanisms to understand their impact on auction dynamics, bidder behavior, and the overall economic resilience of the system. The first one is the current scheme, that serves as a comparison for the other three (see Section 3).

Pro Rata Share (Current Exit Scheme)

Under the existing system, Nouns can be redeemed at a pro-rata share of the treasury, commonly referred to as the ‘book value’ of the Noun. This book value is calculated by dividing the total value of the treasury by the number of Nouns in circulation. This mechanism ensures that every Noun holder receives the same book value, regardless of when and what they paid for their Nouns.

• Benefits: Everyone receives an equal share of the treasury, akin to having one vote per Noun.
• Drawbacks: This mechanism facilitates arbitrage opportunities, enabling arbitrageurs to make (almost) riskless profits if the willingness to pay of nouners in the daily auctions declines. It performs less well in our mathematical model than the three alternatives.

Pro Rata Share with Tax

This mechanism adds a tax to the share the ragequitting participants get. When a fork occurs, the treasury is divided between the new and the old DAO based on the number of nouns leaving the old DAO. After this split, members in the new DAO can ragequit, receiving a treasury share proportional to their number of nouns. However, a portion of this pro-rata share is either retained in the treasury or burned, effectively introducing a tax. There are three potential destinations for the taxed share:

• Funds are burned: This scenario leaves the likelihood of subsequent forks unchanged.
• If the taxed shares from the ragequit remain with the new DAO, it (i) could incentivize other arbers to ragequit, potentially leading to a chain reaction of departures and (ii) leaves the taxed share in the possession of a majority attacker, should this be the case.
• Funds remain with the old DAO: In this scenario, the old DAO gains in treasury per noun from the fork, making a subsequent fork more probable as there are now higher incentives for arbers to participate.

Taxing the redemption value could also impact nouners with genuine, non-financial reasons to fork, leading them to view the tax as unfair. This could reduce their participation in daily auctions, inadvertently increasing the likelihood of arber wins.

• Benefits: Taxing the redemption value deters arbitrageurs from buying nouns, reducing the frequency of forks driven by financial motives.
• Drawbacks: Genuine Nouners with non-financial reasons to fork might view the tax as unfair.

Contribution-Based Share

Each participant who ragequits will receive a share of the treasury that is determined by the proportional size of the price paid at auction relative to the prices paid for other nouns that were auctioned and did not fork yet. This mechanic ensures that payouts are based on the contribution each bidder made to the treasury, aligning the payout more closely with individual contributions.

Its main implications are the following:

• Unlike the pro-rata mechanism, the share received after a fork under this mechanism does not depend on the number of nouns but rather on the price paid (in ETH) for each noun. This direct correlation ties the payout to each owner’s contribution to the treasury.
• This exit mechanic leads to more “extreme” outcomes where arbers are either willing to far outbid any nouner or simply do not participate at all. This is because under this exit mechanic, arbers cannot lose from participating in the auction except by having to wait for the next fork to get their payout, so there are opportunity costs for them to participate. Hence, whenever they can get a payout that is higher than their price and outweighs the cost of waiting for a fork, they will simply outbid everyone to make sure they win. But: if the payout is not high enough, then there is no arbitrage opportunity anymore.

The effectiveness of this mechanism depends mainly on the relationship between the total current treasury and the total prices paid for other nouns. If the treasury is larger than the total prices paid in the past, forks can still happen.

• Benefits: Fully deters arbitrage participation if the total treasury value is no more than the total prices paid in auctions.
• Drawbacks: This exit mechanism results in arbers either far outbidding Nouners for a guaranteed payout or not participating at all.

Contribution-Based Share with Treasury Cap

This scheme is similar to the previous one but with an added cap. Each individual’s share is limited to the level of their paid auction price relative to the overall size of the treasury. The payout is capped if the treasury exceeds the sum of all prices paid at auction.

• Benefits: This mechanism prevents any payout that could incentivize arbers to participate in the auction. It minimizes the risk of DAO-wide forking incentives during sudden drops in the valuations of nouners. Additionally, there is no upper limit for an ex-ante profitable bid by an arber in any circumstance; the arbitrage opportunity currently present is eliminated.
• Drawbacks: Complex to implement.

Further results

We also analyzed other ways of limiting the arbitrage opportunities by (i) simply allowing any holder of a Noun to ragequit whenever they want (an ‘atomic exit’), (ii) leaving the forking mechanic unchanged but delaying the payout after redeeming a Noun, and (iii) a consistent spending path by the DAO that shrinks the treasury (akin to the suggested burn).

Atomic Exits

Atomic exits allow nouners and arbers to ragequit at any moment, independently of a forking threshold being reached (see Section 3.1). This mechanism fundamentally alters the dynamics of the treasury and the participants’ behavior.

Our analysis indicates that the treasury can never exceed a specific value under atomic exits. This value depends on the mechanism. If the treasury surpasses this value, arbers would immediately buy nouns and ragequit for a profit, driving the treasury value back down. Since arbers do not have to wait for a fork to occur, the range of conditions under which exits happen is even broader than with forking thresholds.

• Contribution-Based Share without Treasury Cap: Under atomic exits, the treasury is under constant scrutiny. Exits occur whenever the total auction prices paid for the nouns is lower than the treasury (both denoted in ETH).
• Contribution-Based Share with Treasury Cap: Even with atomic exits, this scheme is designed to prevent profitable arbitrage under any parameter combination. The cap ensures that payouts are limited to the initial auction prices, removing the incentive for arbers to exploit the system.

Time Delays

One of the primary consequences of time delays in accessing funds after a fork is the reduction of immediate financial incentives for arbers (see Section 3.2). This delay introduces uncertainty and diminishes the net present value of future payouts, making immediate financial gains less attractive. As arbers must now wait longer to receive their funds, the potential profits from arbitrage become less appealing, decreasing such exploitative activities.

Another drawback of this approach is the significant exposure of participants to the fluctuations in the value of ETH during the vesting period. This heightened financial uncertainty may discourage Nouners from ragequitting in response to majority attacks. The exposure to ETH price volatility can significantly impact the overall value received by Nouners, potentially deterring participation from those who are risk-averse or need more immediate liquidity.

Treasury Spending

By choosing an appropriate spending path, incentives for arbers can be sufficiently reduced to prevent forking (see Section 3.3). Intuitively, by spending quickly enough, the potential payoffs for arbers are diminished by the time they have accumulated enough wins to force a fork. This reduction in payoffs lowers their optimal bids, slowing the rate at which they accumulate wins sufficiently to not make it worth for arbers to participate in the auctions at all. Consequently, even though arbers could theoretically obtain a positive payoff from a fork, they can never reach this point.

The burn aimed to implement a consistent spending path. The precise calculation of the optimal spending path, which depends on factors such as the treasury size, the number of nouns, and the specific mechanism used, is a promising area for further analysis and development. Our analysis shows its potential to combat arbitrage opportunities.

Conclusion

To address the arbitrage issue in Nouns DAO, three potential solutions emerge from the analysis:

1. A contribution-based exit scheme with treasury cap: This ties payouts to the auction price, capped relative to the treasury size, and aligns payouts to treasury contributions. While it can be very effective in mitigating arbitrage (and can even prevent it entirely) and ensures fair payouts, it is complex to implement, adds properties to nouns in the secondary market, and still correlates noun prices with ETH value.
2. A tax in the current pro-rata scheme: Introducing a tax on payouts during a fork clearly reduces financial incentives for arbitrage. This straightforward method is simple to implement, but it may seem unfair to genuine participants and could reduce auction participation. Using it to deter arbitrage may also require a very high tax rate. In addition, the community would need to decide where the taxed funds go (e.g., remain in the Nouns DAO, burnt, etc), each of which has its own pros and cons.
3. Commitment to a spending path: This solution requires the DAOs commitment to proposal spending over a substantial period of time. Consistent spending keeps the treasury size in check, lowers future payouts, and reduces the appeal to arbers. Our analysis shows that this approach can be particularly effective in limiting arbitrage opportunities under the current pro-rata exit scheme, including preventing arbers from participating at all, providing an alternative to an arbitrage-free exit scheme such as the contribution-based exit scheme. Its effectiveness, however, depends delicately on the exact spending path chosen which the community must credibly commit to maintain for the future.

Choosing the right strategy can ensure Nouns DAO’s treasury supports community projects rather than being exploited by arbers. A tax or committed spending path appears much easier to implement, but using them to effectively minimize arbitrage opportunities requires detailed analysis to tailor the level of the tax or spending to the optimal level. More generally, our work shows that designing a DAO that protects members from majority attacks and limits arbitrage opportunities is a complex problem, raising questions about the optimal DAO design or minimally viable DAO. For the complete analysis, read the full technical report from Proposal 528.