Or how a futarchy can allocate treasury.
Retro PGF is one of the most successfully implemented mechanisms for rationally allocating treasury to grow ecosystem value.
However, it comes with challenges, as deciding which project should receive funding typically relies on a vote, thus depending on individual jurors’ preferences rather than on eliciting actual information about which projects contributed most to ecosystem growth.
To overcome this, we need measurable objectives (metrics) that can be assessed for each project after the fact. Examples include the number of smart contract calls, fees generated (for an L2), or order flow (for a DEX).
Optimism has already taken steps in this direction with Retro Funding Round 4, where Citizen House badge holders vote on the weighting of metrics, which are then used to evaluate projects objectively.
In this post, we define a mechanism that extends retro-funding using measurable objectives and prediction markets, enabling project proactive funding.
Motivation for Prediction Markets
Let’s consider a retro-funding round that relies solely on metrics, similar to Optimism Retro-funding Round 4.
Such a mechanism can only efficiently fund projects with sufficient runway to reach a retro-funding round.
Additionally, relying on a deterministic retro-funding rule only incentivizes projects to increase metrics but doesn’t guarantee whether the funds are allocated most effectively.
Instead, we propose a funding mechanism for future efforts and introduce prediction markets that forecast how each project will impact future metrics.
These forecasts will allow:
- Unlocking project funding beforehand enables funding a more significant number of projects, including those that lack the necessary runway.
- Avoiding funding projects where the funding provided does not directly produce a change in metrics, e.g., projects funded via other means, projects farming for rewards for work already completed.
- Continuously eliciting information through forecasts, thereby learning about the efficacy of the allocation mechanism. For example, suppose forecasters assign the same value to conditional estimates (funding vs not funding). In that case, this strongly hints at funding not being a predictor of project success in terms of this metric, and the DAO would update the set of metrics to evaluate projects on.
Model
A DAO organizes a round of funding with an overall budget b and a set P of projects that apply for funding.
We require a curation mechanism with crypto-economic guarantees to ensure that the set P doesn’t contain spam.
Each project p comes with a single investment ask i_p > 0 that it expects to receive if selected. The mechanism can easily be extended to multiple, variable-sized asks per project, but we keep it single here for simplicity.
The DAO defines a set of measurable objectives M, or “metrics,” such as:
- “Active verified users in 6 months” for an app.
- “Attributed order flow in 1 year” for a DEX front-end.
- “Gas fees generated in 2 years” for contracts running on an L2.
We denote m(p) as the metric value for a given project, aggregated from today until the specified date.
Each metric has an associated positive weight w_m. The value the DAO assigns to each project is defined by the weighted sum of metrics \sum_{m \in M} w_m m(p). Each w_m accounts both for:
- The significance of the metric as a proxy for projects’ success, expressing the DAO’s preferences over which metric is more or less important.
- Normalizing the metric depending on its type (e.g., normalize a TVL per month metric by 2x the highest protocol’s TVL per month, etc.).
We assume a crypto-economic oracle (such as UMA or reality.eth) gathers metrics on-chain and makes them available to smart contracts.
The mechanism will output a set of actual investments \hat{i}_p with \hat{i}_p \in \{0, i_p\}.
Objective
The DAO wants to allocate funding in a way that:
- Maximizes its overall ROI on Metrics defined by \frac{\sum_{p \in P} \sum_{m \in M} w_m m(p)}{\sum_{p \in P} \hat{i}_p} or \frac{\sum_{p \in P} s(p)}{\sum_{p \in P} \hat{i}_p} with s(p) the weighted sum of metrics.
- Respects the budget \sum_{p \in P} \hat{i}_p \leq b.
Since funding is allocated proactively, we expect this mechanism to elicit accurate forecasts via prediction markets for the weighted sum of metrics of each candidate project.
Conditional Funding Market (CFM) Mechanism
The mechanism is essentially a Decision Market:
Decision markets both predict and decide the future. They allow experts to predict the effects of each of a set of possible actions, and after reviewing these predictions a decision maker selects an action to perform.
The mechanism operates as follows:
- It runs prediction markets to forecast the expected value of conditional outcome tokens, which reflect the metrics-based results of funding or not funding a project.
- It then applies a decision rule based on these forecasts.
Prediction Markets for Project Metrics
For each project, we create a prediction market with a single outcome: the weighted sum of metrics s(p) = \sum_{m \in M} w_m m(p).
A caveat of this design is not having per-metric forecasts, which would enable more granular feedback: if a metric appears to be hard to predict by market participants, the DAO will have difficulty learning from it and adjusting. Another approach enabled by the Logarithmic Scoring Rule (LMSR) (Hanson, 2002) would be to create prediction markets with multiple base events (one per metric). But for simplicity’s sake, we will not develop it in this post.
For each project, create a contract that takes (e.g.) sDAI deposits and, for 1 sDAI deposited, returns a pair of outcome tokens (\textsf{Short}, \textsf{Long}). Additionally, we assume there is substantial certainty that the weighted sum will be in the value range [v^{\text{min}}, v^{\text{max}}].
Note the usage of sDAI, which is interest-bearing. This is key to mitigating traders’ opportunity costs. Any yield-bearing stablecoin could replace it.
Short and Long tokens have a typical scalar token design. At resolution time, if:
- s(p) \leq v^{\text{min}}, only \textsf{Short} tokens redeem for 1 sDAI.
- s(p) \geq v^{\text{max}}, only \textsf{Long} tokens redeem for 1 sDAI.
- If v^{\text{min}} < s(p) < v^{\text{max}}:
- ~~\textsf{Long}~~ tokens redeem for \frac{s(p) - v^{\text{min}}}{v^{\text{max}} - v^{\text{min}}} sDAI.
- ~~\textsf{Short}~~ tokens redeem for \frac{v^{\text{max}} - s(p)}{v^{\text{max}} - v^{\text{min}}} sDAI.
A market scoring rule can guarantee truthful reports and incentive compatibility. The Logarithmic Market Scoring Rule (LMSR) is the most widely studied and is a strong choice.
Current prices represent the market’s prediction of s(p)
Conditional Tokens
We also need to make the forecast dependent on whether funding occurs for a given project. For this, we rely on conditional tokens (as introduced by Gnosis):
- A pair (\textsf{Short}^{\text{yes}}, \textsf{Long}^{\text{yes}}) which redeems for 1 sDAI if funding happens.
- A pair (\textsf{Short}^{\text{no}}, \textsf{Long}^{\text{no}}) which redeems for 1 sDAI if no funding is provided.
Two corresponding Yes and No prediction markets are created (per project).
Decision Rule
At any point, both markets’ prices will represent the aggregate forecast about the weighted sum of metrics in their respective Yes or No worlds.
The decision rule can be applied once markets have converged on a forecast. This highly depends on new information being released (especially by projects themselves) that can influence bets.
Assuming projects release all relevant information at the start of the funding round, we expect markets to converge quickly. Also, the longer markets run, the more bettors must try accounting for future information (see Hanson, 2013).
Hence, the decision rule is applied around one week after creating the markets. To prevent manipulation, the precise time the decision rule is applied can be randomized over several days.
The most straightforward decision rule is the max decision rule: if \text{price}(\textsf{Yes}) > \text{price}(\textsf{No}), fund the project; otherwise, don’t fund it.
It has been shown that this rule isn’t incentive-compatible with truthful reporting and creates manipulation opportunities for traders (Othman, Sandholm, 2010). Namely, this could result in Yes odds being greater than No odds, thus funding the project, when truthful reporting would have recommended the contrary.
However, we expect to experimentally observe the effects of manipulation and adjust accordingly. Multiple possible mitigations have already been researched:
- Picking the last trader from a reputable set, as indicated by (Othman, Sandholm, 2010).
- Using mixed strategy rule to pick the decision (Chen et al, 2011). This would leave room for making sub-optimal decisions but might be an acceptable trade-off in aggregate.
In any case, a practical mitigation is to run enough small rounds to limit the potential downside of any such sub-optimal decision.
Curation Mechanism
We require a mechanism to elicit curated projects to prevent spam and instantiate the CFM mechanism only for relevant projects. Specifically, we would like a mechanism that favors projects with a higher chance of achieving funding.
For this, we use a repeated auction, where projects bid for their inclusion in a slot, as this has some interesting properties for bootstrapping prediction markets. Other approaches include stake-based curation or curation from a reputable jury.
A slot’s duration, e.g. a week, can be modulated by the DAO. Whenever a slot starts, a new auction is launched. Projects compete by posting bids together with some metadata.
This auction can be a first-price auction, a second-price auction with commit-reveal, or a Dutch auction.
The auction winner earns the right to submit her project to the CFM mechanism (see below) for the given slot. The auction revenue is used to bootstrap prediction market liquidity.
The auction winner must then define the initial price of the Yes market (see below) by defining the ratio by which 1 sDAI is split in \textsf{Long}^{\text{Yes}} and \textsf{Short}^{\text{Yes}}. The project owner is incentivized to input the most accurate ratio, which will limit her impermanent loss as a liquidity provider. Prediction markets will benefit from the project owners revealing private information through these starting prices.
A limitation of this mechanism is that only projects with enough financial backing might compete in the auction and get funded. A solution is to enable all projects to produce project tokens, enabling funding by selling tokens and then rewarding investors with a cut of the retroactive funding if it happens (see Retroactive Public Goods Funding. Note: The Optimism team has long been… | by Optimism | Optimism PBC Blog | Medium).
Liquidity Subsidies
Sufficient liquidity must be available to ensure the proper functioning of prediction markets, especially until the decision rule is applied. However, LPs face impermanent loss whenever the Short/Long price moves away from the initial price when the AMM pool was launched.
A key element of this mechanism is the expectation that the DAO will subsidize this liquidity by rewarding liquidity providers (akin to liquidity mining). These rewards must be sufficient so that, when added to AMM fees, they compensate for impermanent loss.
This subsidy is justified as a payment for the information the DAO gains from operating the prediction markets.
Additionally, a key means for the DAO to limit the total cost of this subsidy is to define an initial market price (e.g., based on past project data) and incentivize liquidity provision at that price. The curation mechanism described above already achieves this.
Funding Algorithm
For each project selected by the CFM mechanism, the funding algorithm then:
- Computes the ROI.
- Distributes the budget b in a manner that maximizes aggregate ROI.
As long as all project funding requirements are relatively small compared to the budget, we expect a simple greedy algorithm to work: distribute funding to selected projects with the highest ROI first.
Additionally, since projects are funded proactively, we assume that the DAO wants to retain some control over project funding to prevent misuse of funds. This can be implemented through the gradual delivery of funding, along with a backstop mechanism that can halt financing at any time if a project is observed to be non-compliant with predefined guidelines. However, this backstop mechanism must cancel the winning prediction market as its forecasts become irrelevant. Hence, it must be used sparingly, otherwise threatening forecasters’ long-term participation in the mechanism.