Optimism Collective: DAO & Retroactive Funding

• Optimism Collective is a decentralized autonomous organization within the Ethereum ecosystem that retroactively allocates funding to projects delivering public goods.
• It employs advanced computational social choice principles, including the moving phantoms mechanism, to achieve strategyproof and welfare-maximizing outcomes.
• Its innovative RetroPGF process has distributed over $100M in OP tokens and reserved an additional $1.3B for future projects.

The Optimism Collective is a decentralized autonomous organization (DAO) at the center of the Ethereum and Optimism blockchain ecosystems, charged with retroactively allocating governance tokens and funds to projects that have delivered measurable public goods. Its flagship initiative, the Retroactive Project Funding (RetroPGF) mechanism, represents a large-scale implementation of social choice principles in decentralized governance, with wide-ranging computational, economic, and algorithmic implications.

1. Organizational Structure and Purpose

The Optimism Collective operates as a DAO specifically tasked with supporting and growing the digital public goods infrastructure of the Ethereum and Optimism ecosystems. Rather than awarding grants prospectively, the Optimism Collective distributes rewards ex-post, assessing projects on their demonstrated contributions and impacts. The primary instrument for doing so is RetroPGF, a funding mechanism which, as of August 2025, has completed four major rounds and allocated over $100M in OP tokens, with an additional$1.3B reserved for future funding.

RetroPGF is managed by badgeholders—vetted members of the ecosystem who are granted the right to evaluate applications and allocate budget across competing projects. These allocations are determined by decentralized, transparent voting processes, with each badgeholder casting cumulative token-based ballots for candidate projects.

2. The Retroactive Project Funding Process

The core operational flow of RetroPGF can be formalized as a budget allocation problem:

• Each badgeholder $i$ submits a ballot $X_{(i)} = (x_{i,1}, \dotsc, x_{i,m})$, constrained by $\sum_p x_{i,p} = c$ where $c$ is the per-voter token allowance, and $m$ is the number of projects.
• The aggregate allocation is $a = (a_1, \dotsc, a_m)$, subject to $\sum_p a_p \leq B$ for budget $B$.

Funding rules have evolved over the rounds, utilizing token-weighted cumulative voting, Quadratic Voting, Mean, Median, and other aggregation rules. Allocations are distributed in OP tokens, the native digital asset of the ecosystem.

3. Challenges in Current Funding Mechanisms

A detailed social choice analysis (Briman et al., 22 Aug 2025) reveals several shortcomings of the mechanisms employed thus far:

• Manipulation Susceptibility: Many aggregation rules, such as the Mean or Quorum Median, are vulnerable to strategic misreporting, low bribery resistance, and control manipulation.
• Efficiency–Fairness Tradeoffs: Rules may fail axiomatic requirements, e.g., Pareto efficiency, monotonicity, or proportionality, leading to allocations that poorly reflect collective impact or preference.
• Quorum/Median Inconsistencies: Certain rules are sensitive to participation thresholds and skewed ballot distributions, causing misalignment between actual project impact and funding outcomes.

Given the massive scale of committed funds, robust governance and improved incentive alignment are necessary for trustworthy public goods allocation.

4. Computational Social Choice Approaches: Moving Phantoms Mechanism

To address vulnerabilities and inefficiencies, computational social choice principles are incorporated by adopting the utilitarian moving phantoms mechanism (originally Freeman et al., 2019). This approach introduces synthetic phantom voters whose ballot positions are dynamically adjusted to "tune" the aggregate outcome toward social welfare maximization.

The moving phantoms mechanism is formally defined as:

• For project $p$, the final allocation is

$$A^{(F)}(a_p) = \operatorname{med}(f_0(t^*), f_1(t^*), \dots, f_n(t^*), x_{1,p}, \dots, x_{n,p}),$$

where $t^*$ is chosen such that

$$f_0(t^*) + \sum_{i=1}^n f_i(t^*) + \sum_{i=1}^n \sum_p x_{i,p} = 1.$$

Variants include:

• Independent Markets Algorithm: $f_k(t) = \min\{t(n-k), 1\}$ distributes phantom influence linearly.
• Majoritarian Phantoms Algorithm:

$$f_k(t) = \begin{cases} 0 & \text{if } 0 \leq t \leq \frac{k}{n+1} \ t(n+1)-k & \text{if } \frac{k}{n+1} < t \leq \frac{k+1}{n+1} \ 1 & \text{if } \frac{k+1}{n+1} \leq t \leq 1 \end{cases}$$

The mechanism simultaneously:

• Satisfies budget feasibility ($\sum_p a_p \leq B$).
• Maximizes utilitarian social welfare via $\ell_1$ minimization:

$W = \frac{1}{n} \sum_{i=1}^n \|a - X_{(i)}\|_1$

• Ensures strategyproofness (truthful voting is dominant).

5. Analysis and Simulation Methods

Computational social choice analysis employs formal axiomatic comparison, simulation with Dirichlet and Mallows models for vote distributions, and multiagent systems techniques to stress-test mechanism robustness against vote perturbations and strategic manipulation.

• Ballot model: Voters submit $X_{(i)}$, with tokens assigned per project and normalized.
• Rule comparisons center on manipulation costs, ability to withstand outlier strategy, participation, and proportional fairness metrics.

Findings indicate moving phantoms mechanisms outperform prior rules in terms of social welfare, bribery resistance, and representativeness.

6. Broader Impact on Decentralized Governance

The Optimism Collective’s RetroPGF mechanism, studied as a case of large-scale decentralized public goods allocation, exemplifies the intersection of blockchain governance and computational social choice. Its iterative governance design—evolving from simple token-weighted voting to sophisticated median-based mechanisms with moving phantoms—contributes to a foundational framework for decentralized, transparent, strategy-resistant funding.

These developments bear directly on the future of DAOs and decentralized governance, setting important precedents for multiagent mechanism design, public goods economics, and strategyproofness requirements in large-scale resource allocation.

7. Mathematical Formalizations (Summary Table)

Concept	Formalization	Application
Feasible Allocation	$a_p \geq 0$, $\sum_p a_p \leq B$	Funding constraints
Voter Ballots	$X_{(i)} = (x_{i,1}, ..., x_{i,m})$, $\sum_p x_{i,p} = c$	Badgeholder voting
Moving Phantoms Outcome	$A^{(F)}(a_p) = \text{med}(f_0(t^*), ..., x_{n,p})$	Median-based allocation
Social Welfare ($\ell_1$)	$W = \frac{1}{n}\sum_i \| a - X_{(i)} \|_1$	Outcome optimization

Conclusion

The Optimism Collective represents a rigorously analyzed, large-scale experiment in decentralized governance and public goods funding, leveraging advances in computational social choice and mechanism design. Its ongoing adaptation of allocation mechanisms—incorporating moving phantoms for strategyproof, welfare-maximizing outcomes—establishes technical standards and theoretical benchmarks for other DAOs and public goods initiatives within blockchain ecosystems and beyond.