Voter participation is key to establishing a successful, trusted retrofunding system. Simplicity for voters plays a crucial role in securing participation. This is part 2 of GoXS’ evaluation of Retro Funding Voting Design Tradeoffs, where we show how we measure if voters can easily understand how to achieve their best results.

The GovXS framework is designed to evaluate any retrofunding voting system. As an open-source tool, it allows for analysis of previous voting rounds and helps communities achieve their prioritized design goals by identifying optimal voting rules. The framework applies both axiomatic analysis and agent-based simulations to ensure comprehensive evaluation.

More information:

• Making Optimism Retro Funding Strategyproof (Incentive Compatibility in Optimism Retro Funding)

• GovXS Presents: Evaluating Voting Designs for Optimism Retro Funding (Workshop with Optimism Badgeholders)

Introduction

Over the course of four rounds of Optimism Retro Funding, 375 eligible voters participated in the distribution of more than 60 million OP tokens. Optimism implemented voting experiments round by round, enabling voters to carry out a range of tasks, including allocating tokens to projects, weighing the importance of Impact KPIs, determining the total funding for each round, and much more.

Here, simplicity for voters is important for several reasons. When the wording, structure, and design are clear and intuitive, voters can easily navigate the system, find the information they need, and participate with minimal effort. This not only reduces the burden on voters but also increases their willingness to engage, and, ultimately, improves the quality of decisions made.

In contrast, even seemingly minor design choices, such as the positioning of elements on the ballot, can create confusion, leading to mistakes and a higher number of irregular ballots.

Poorly designed voting systems can undermine the legitimacy of the results, eroding trust in the retrofunding process. When voters struggle to understand the system or perceive it as overly complicated, both voter participation and the quality of project applications decline. This ultimately harms the overall effectiveness of the retrofunding system, as highly engaged, reputable expert badgeholders and high-quality projects may lose confidence in the system.

Measuring Simplicity for Voters

Optimism defines simplicity for voters as “Voters can easily understand how the voting design works and how to best behave to achieve their goals”.

Optimizing Voter Experience (UX)

To design an easy-to-use voting system we must consider multiple elements: the information presented on the ballot, such as project details, application data on a project's positive impact, and more. Additionally, the design may need to provide information about a voter’s decision-making power relative to others. It must also clarify how to vote—whether through token distribution, ranking, or other mechanisms—and clearly present the question being voted on. All of these factors influence the system's ease of use for voters.

Testing the full voting process with real users is certainly the best way to measure ease of use. This approach is commonly called UX testing. However, this can be a time-consuming process, as it involves creating a detailed mock-up of the entire voting flow, and any design changes require a new round of testing.

Measuring if Voters can Easily Understand How to Best Achieve their Goals

As an alternative approach, we propose three normative axioms to assess whether a voting system enables voters to intuitively grasp how to achieve their desired outcomes. In essence, these axioms help determine if the voting rules are easily understood, and produce outcomes as expected.

Drawing on Social Choice Theory, which defines desirable social choice functions from an axiomatic standpoint, we apply theoretical analysis to validate whether these axioms hold for a given voting design. This method offers definitive results, ensuring that the desired properties are maintained under any circumstances, in any voting scenario (e.g., regardless of the number of voters, projects, or round size), without relying on assumptions about voter behavior.The GovXS Evaluation Framework provides three axioms to verify “Simplicity for Voters”.

The GovXS Evaluation Framework provides three axioms to verify “Simplicity for Voters”.

a) Monotonicity

Monotonicity guarantees that additional support for a project leads to an increase in funding. Voters typically expect this property to hold in most voting systems. However, counterintuitively, some voting designs result in non-monotonic outcomes. A prime example is Instant Runoff Voting where only candidates with the most top votes advance to the next round. In such cases, voting for a project doesn't guarantee an increase in funding.

b) Reinforcement

The Reinforcement property is crucial in decentralized systems, where the collective voting power of community subgroups should aggregate into a consistent and reinforced outcome. Voters in a retrofunding process would naturally expect voting rules to adhere to this principle. However, in systems that impose a minimum quorum for a project to receive funding, unexpected outcomes can arise: in particular, a project might miss the quorum in all subgroups. However, when subgroup votes are aggregated by simply summing up individual votes, the project surpasses the quorum, and the final outcome changes. This illustrates how reinforcement can be disrupted in certain voting designs.

c) Pareto Efficiency

To illustrate this axiom, here’s an example: An economy contains two people and two goods, apples and bananas. Person 1 likes apples and dislikes bananas (the more bananas she has, the worse off she is), and person 2 likes bananas and dislikes apples. There are 100 apples and 100 bananas available. The only Pareto efficient allocation is that person 1 has all the apples and person 2 has all the bananas.

For any other allocation, one of the persons has some units of the good she does not like and would be better off if the other person had those units. With this axiom, we can analyze if a voting rule meets the preferences of all voters optimally, without unfairly disadvantaging any voter.

Voting Rules in the Evaluation

GovXS evaluated four different voting designs that have been applied in past funding rounds.

• Round 1 (R1 Quadratic Voting): Optimism implemented Quadratic Voting, allowing voters to allocate tokens with increasing costs to cast multiple votes.

• Round 2 (R2 Mean): The funding allocation was determined by averaging the votes across all participants, applying the Mean Rule.

• Round 3 (R3 Quorum Median): A minimum vote and token threshold were introduced, and the Normalized Median rule was applied to reduce the influence of outlier votes. Only projects that met a minimum number of votes were considered.

• Round 4 (R4 Capped Median): Optimism introduced the Impact Metric Score, where voters prioritized KPIs rather than direct funding allocations. Projects submitted KPI data to validate their achievements, and funding was distributed based on voter preferences using the Normalized Median, with caps on allocations and redistribution of overflow funds. In our analysis, we include a simplified version that skips calculating the Score based on Impact Metric Share.

The formal specification of all voting rules in the evaluation can be found here.

Evaluation Results

Overall, the voting rule that supports Simplicity for Voters best, is R2 Mean Rule. In our evaluation, we found that all other voting rules have weaknesses, as the following detailed results show.

Monotonicity: All voting rules applied in OP Retro Funding Round 1–4 satisfy Monotonicity

All voting rules that OP Retro Funding tested in Rounds 1-4 satisfy Monotonicity. Voters can expect that increasing the support of a project never leads to decreased funding allocation. To make this tangible, here’s an example using the R2 Mean Rule:

Consider a voter who increases their allocation to project $p$ from $x_i,p$ to some $x’_i,p > x_i,p$ . The mean allocation to project $p$ is given by:

Increasing $x_i,p$ increases the numerator, leading to an increase in $a_p$, while the denominator also increases, but not enough to reduce $a_p$. Thus, increasing $x_i,p$ cannot decrease the final allocation $a_p$. Therefore, the Mean Rule satisfies monotonicity.

The proofs for R1 Quadratic Voting, R3 Quorum Median, and R4 Capped Median can be found in our paper “A Social Choice Analysis of Retroactive Funding”.

Reinforcement: Round 3 and Round 4 voting designs do not satisfy Reinforcement

For the Reinforcement metric, we found that two of the four voting rules used in Optimism Retro Funding satisfy the Reinforcement axiom. Most notably, the Median rules in Rounds 3 and 4 do not. Here’s why:

Reinforcement means that if two separate voting profiles produce the same outcome individually, combining them should give the same result. Looking at the Normalized Median rule, we see it meets this axiom.
Consider two voting profiles $V_1$ and $V_2$, each with $n_1$ and $n_2$ voters respectively. The median allocation to a project under $V_1$ is $a_p^1$ , and under $V_2$ is $a_p^2$. The combined profile $V_3 = V_1 \cup V_2$ has $n_1+n_2$ voters.
Given that $a_p^1 ≥ a_q^1$ and $a_p^2 ≥ a_q^2$, the median allocation in the combined profile $V_3$ will still satisfy $a_p^3 ≥ a_p^3$ because the median will maintain positions from both $V_1$ and $V_2$. Hence,  the Normalized Median rule complies with reinforcement.

However, things change when additional rules, like a quorum or funding caps, are introduced. For example, with the R3 Quorum Median rule, let’s say $V_1$ and $V_2$ both vote [0.9, 0.1] for two projects with a quorum of 0.2.
The individual winners in $V_1$ and $V_2$ would be [1, 0], but when combined, the outcome could shift to [0.9, 0.1], breaking the Reinforcement property. The same happens with R4 Capped Median, where funding caps are applied.

All proofs are available in our paper “A Social Choice Analysis of Retroactive Funding”.

In summary, adding a quorum or funding caps makes it harder for voters to predict how their vote will affect the result, complicating their ability to achieve their goals.

Pareto Efficiency: Only R2 Mean satisfies Pareto Efficiency

A voting rule is Pareto-efficient if no alternative outcome can make at least one voter strictly better off without making another voter worse off. Verifying Optimism’s Round 1–4 voting rules we find that several of them don’t meet this property. Only the R2 Mean Rule satisfies Pareto efficiency:

All other voting rules in the evaluation do not satisfy Pareto Efficiency.

Ensuring Simplicity for Voters in Retro Funding

The examples above demonstrate how even small adjustments in voting design can produce results that are difficult for voters to predict, ultimately hindering the goal of achieving ‘Simplicity for Voters.’ That said, the axioms we established for evaluating simplicity should not be viewed as rigid requirements.

In our recent article, we show that all voting rules we’ve evaluated for Optimism Retro Funding are not strategyproof, which poses a risk to further developing it.  There can be trade-offs between design goals like 'strategyproofness' and 'simplicity,' which may occasionally come into conflict. The GovXS Voting Design Evaluation Framework allows any community to prioritize design goals in a structured and transparent fashion. By aligning these priorities, we can assess and determine whether a voting rule meets the desired criteria, enabling communities to identify the best solution tailored to their specific needs.

Conclusion

Our evaluation of Retro Funding Voting Design Tradeoffs takes a novel approach to optimizing Simplicity for Voters. We can apply Social Choice axioms to problems that are typically only addressed through field tests and UX testing. This approach, part of the GovXS Evaluation Framework, allows us to rigorously assess the simplicity and effectiveness of voting rules without the need for extensive real-world testing.

Our analysis shows that while all voting rules used in Optimism Retro Funding Rounds 1-4 meet the Monotonicity criterion, only the R2 Mean rule fully satisfies both Reinforcement and Pareto Efficiency. More complex rules, such as the quorum and capped median in Rounds 3 and 4, introduce difficulties in voter simplicity. This makes it harder for participants to intuitively understand how to best behave to achieve their goals.

By leveraging Social Choice Theory, the GovXS approach enables communities to evaluate and prioritize voting design goals in a structured process. This ensures a more inclusive and trusted retrofunding process, helping voters achieve their best outcomes while maintaining the system's overall legitimacy.

About the GovXS Voting Design Evaluation Framework

The GovXS Voting Design Evaluation Framework is a tool to secure robustness, fairness, and trust in Retrofunding Voting Systems. It covers design objectives like Resistance to Malicious Behavior, Incentive Compatibility, Simplicity for Voters, and more.

The open-source framework allows to prioritize design goals, and analyze a voting design with formal rigor, applying axiomatic analysis and agent-based simulations.

Resources

• Making Optimism Retro Funding Strategyproof (Evaluation results on Incentive Compatibility in Optimism Retro Funding)

• A Social Choice Analysis of Retroactive Funding (PDF, formal description the of GovXS Voting Design Evaluation Framework)

• GovXS Simulator (Open-source Github repository)

• GovXS Presents: Evaluating Voting Designs for Optimism Retro Funding (Workshop with Optimism Badgeholders)

About GovXS

GovXS is a research initiative under the Token Engineering Academy. Team members include Nimrod Talmon, PhD, Angela Kreitenweis, Eyal Briman, and Muhammad Idrees. GovXS is a member of the Token Engineering Academy Applied Research Network. Sign up to receive further updates related to GovXS.