Diversified governance: Who has the final say in a decentralized community? (Part 2)

By: Tobin South, Leon Erichsen, Shrey Jain, Petar Maymounkov, Scott Moore, E. Glen Weyl

Compiled by: Tiao

Translator’s Preface:The last three sections of "Diversified Management" contain a lot of mathematical descriptions of this mechanism. I also had a headache during the translation process, but because of its formalization and mathematical nature, it is easy to develop into applications and iterations.CommunityThose interested in governance technology will benefit.

This article is the second half of the article on Plural Management.Diversified governance: Who has the final say in a decentralized community? (Part 1)》

Section 3 Model Details

The multi-governance protocol delineates two key categories of activity: a prioritization subsystem and an approval subsystem. These subsystems exist together as part of a broader organizational structure where individuals can earn governance points for various actions. These points can be allocated at the start of the organization and naturally distributed to new members as they participate (making the founders' control effectively diminish over time). Points can be stored in any simple ledger and modified as they interact with the protocol.

There are many additional considerations around the sharing, control, and visibility of these governance points. For example, should the organization run governance points dynamically to publicly disclose each member’s score? (thereby essentially creating an implicit authoritative ranking?) Should individuals be able to directly transfer governance points to another member? (Doing so can simplify the process of joining new members and allow senior members to leave gracefully, but it can also weaken meritocracy and lead to backdoor dealings or conspiracies?) We will return to these open questions in the conclusion.

3.1 Priority Setting

Overview:All issues are listed on a board, and members use a quadratic funding mechanism to spend management points to set the priority of the issue (for example, if each member spends Pi points, the total priority is (√Pi)). Large point holders can be added to the matching pool. When a contribution is made to an issue, the priority points and matching points are frozen, and if the contribution is voted in, these points will be distributed to the contributor.

The first subsystem to consider is the step of setting priorities through an issue board. On the board, each major task or strategic challenge should be assigned an issue, similar to how most open source projects operate on GitHub.

Each member can spend a portion of their governance points to set priorities. This is a dynamic process, and members can add or withdraw points for each issue at any time. For each member who has allocated Pi to run points to set priorities for an issue, we calculate the total priority of the issue by taking the sum of the square roots of their respective priorities (translator's note: the points spent), and then squaring the sum. Therefore, the quadratic priority of issue j is QPj = (∑√Pji ). This works exactly the same as quadratic funding, and we also borrow the concept of a matching fund. The matching fund is generated by points used for voting, or is further increased by large governance point holders (such as early founding members), who can choose to allocate funds to the matching pool to incentivize new contributors to join.

In practice, the matching fund may not always have enough points to fully subsidize the quadratic priority. To address this issue, the total contribution payout (CP) will be adjusted based on the proportion of the matching fund [2].

When a contribution is made to an issue, the issue's rewards are frozen [3]. The contribution then goes through a voting process as follows. If the vote fails, the issue goes back to the board for other contributions to be proposed.

3.2 Approval

Overview:Contribution voting allows any member to vote v times for or against a contribution at a cost of v. This is a standard single-issue quadratic voting mechanism. The organization's administrators can set aside points from the issue rewards to incentivize members to predict the success probability of contributions, and reward correct predictions. This helps incentivize small point holders to understand the broader organizational needs and do due diligence on contributions. Predictors will receive a reward of 2v, and administrators can reduce the cost of voting relative to predictions by setting the parameter K.

Once a contribution is made, it goes to a vote. Any member holding governance points is eligible to vote. According to the rules of quadratic voting, the cost of casting a vote is v points. Everyone can vote for or against, with a negative vote counted as a negative of v when calculating the outcome. As with any quadratic vote, there should be an appropriate time window in which to vote, after which the decision is made based on the sum of votes cast. In the simple case, all funds invested in an issue during its priority setting period go to the contributor. All points used by members during voting go directly into a general matching fund set up for priority setting[4].

This voting behavior is simple but has a cost. It means that members can use the points they earn to exercise authority and thus influence the direction of the organization or project.CommunityEarly members who hold only a small number of points may find that the cost of influencing a vote is high relative to the points they hold. This further means that members with a small number of governance points may not be motivated to perform due diligence (which is often a lot of work) to assess whether a contribution is a good fit for the project.

To incentivize low-authority members to vote and provide a quality signal for contributions, the organization's administrators can reward voters with an additional prediction step. The administrator will choose a parameter K that reduces the cost of voting relative to prediction. If there is no prediction of a correct vote, then the cost of voting will be Kv. If v is staked at the same time as voting, then the cost will be Kv+v. The rewards for these correct predictions will come from the contribution rewards and can be seen as a processing fee to incentivize the analysis of contributions.

Predictors can choose to make no predictions at no cost, or to stake exactly v points in the hope of receiving a reward of 2v if their prediction is successful[5][6]. For large values of K (e.g., 1 or greater), voting is only profitable when the number of points is very low due to the quadratic cost of voting (although one can still minimize losses by staking v points when the predictor believes the probability of passage is greater than ). When K = 0, voting is costless, and voters should (assuming they are risk-neutral) stake as many points as possible if they believe their vote will pass. The case of K = 0 should be avoided, and indeed, Theorem 3 shows that K should be set high enough to avoid excessively reducing the expected return on contributions. In general, administrators can gradually learn and choose appropriate values of K to incentivize different combinations of behavior.

An important aspect of this mechanism is that this prediction reward is only beneficial for small votes. Due to the quadratic cost of voting, large votes with high influence will never be profitable at reasonable non-zero values of K. This is an important property that ensures that authoritative figures holding large amounts of governance points are not rewarded simply for knowing the community's preferences, but rather rewards those who seek influence through appropriate means.

Section 4 Analysis of Protocol Properties

Here we analyze the voting behavior of the protocol, aiming to demonstrate its properties and derive the parameter choices needed to achieve various goals or guarantees. We adopt the above structure and definitions, and introduce the assumption that each individual maximizes his or her utility as a linear combination of his or her preferences and the amount of money he or she would have to spend to gain more governance points (and thus the power to influence future outcomes). This analysis is similar to the quasi-linear utility setting often applied in mechanism design, and is applicable under certain conditions (e.g., those discussed by Buterin et al. (2019)). Although Gorokh et al. (2021) note that this extension may be roughly applicable to the long-standing private goods economy, its applicability is less clear in the public goods economy that we primarily study. Nonetheless, it is a standard starting point for analyzing behavior in these settings. We do not explicitly model the behavior of “administrators” who support the preferences of others by providing matching funds, but their behavior can be understood as motivated by the common interest of the community, whether for altruistic, ideological, or unmodeled monetary reasons (e.g., administrators may hold a stake in the organization’s output) [7].

We will support the above construction through a series of theorems and proofs, and show the effects of choosing specific values. First, let's focus on the voting prediction step.

Theorem 1 (An individual will always bet either 0 points or v points): For a given contribution vote, a rational individual with the goal of maximizing points, after voting v times at a cost of v, will bet 0 points if the probability of success is less than half, and v additional points if it is greater than half.

Proof: In the case where the individual has cast v votes, the return of the voting prediction round will be 2w points. Since the voting result is binary, the value returned is either 2w or 0, so for the probability of success 2wp, the individual's expected return is 2wp. Then, minus the cost of voting and betting, the total expected profit is 2wp- Kv-w = 2(p-)w – Kv.

Under v, as long as the probability of the expected preference exceeds , the expected profit will increase linearly with the increase of v. Given that Kv has been paid as a fixed cost, the individual should maximize v in any case where p＞.

This gives the intuitive result that a purely profit-maximizing forecaster should bet on the maximum possible value v when the expected probability of success is greater than 50%, and not bet at all otherwise.

Regardless of the strategy (as shown in Figure 2), voting never yields a positive return when K=1. In fact, when voters care deeply about the outcome, the return from staking is negligible compared to the quadratic cost. Typically, if voters believe a vote will pass, they choose to stake to minimize the cost. For smaller values of K, small voters can make a profit.

In fact, for individuals who purely pursue profit maximization, there is an optimal choice of v.

Theorem 2 (Optimal $v$ value): For a given value of K, an individual who only pursues profit maximization should cast v = (p-) / K votes, but this only applies when p＞, otherwise no votes should be cast. Using this result, we can ensure that the contribution reward is not over-consumed by subsidies for predictions.

Theorem 3 (Don’t over-consume contribution rewards): A conservative value of K can be chosen to ensure that the proportion of contribution rewards spent on reward prediction does not exceed .

Proof: Assume that there are N individuals who hold points and purely pursue point maximization, and there is a selected value of K; if each individual can accurately predict and only bet when they believe they will succeed, then each individual who believes that their bet will succeed and eventually succeeds will vote and bet with v=1/2K, which will bring them a return of 1/K and a profit of 2 (1/2K)-K(1/2K)-(1/2K)=1/4K. Therefore, the total loss of contribution returns in priority setting will be N/K.

Since we do not want to consume more than the contribution reward CPj, K should be set so that CPj>N/K. This maximum reward only occurs if all members holding points vote in the same direction.

In this case, it is possible to exceed the total predicted reward: a large point holder who already knows the vote will pass (assuming all members vote in favor) will vote and predict at a high point cost to further reduce the contribution reward. This holder is likely to want to reduce the reward to contributors and the cost to the voter himself, thus causing this situation. However, due to the quadratic cost, this vote will cost a very large number of voting points, so it is unlikely to occur.

From this analysis we can see that for reasonable values of K greater than 0, small votes are rewarded with small amounts, while large votes are almost always costly. This is an important effect of the design, which creates a quadratic penalty that rewards more participation and further rewards small voters for decision-making participation, while minimizing the incentive for members who currently hold a large number of points to simply seek to accumulate points.

Figure 2: Top left: Optimal value of b for maximizing profit for different values of p when K=v=1. If p＞, b should be set to v, otherwise to 0. When K = 1, profit is strictly negative. Top right: For smaller values of K, larger bets can lead to positive returns when the prediction is correct. The choice of K value can be used to incentivize or reduce pure profit-seeking behavior. Bottom: Maximum profit for members who voted for v and made the corresponding prediction.

4.1 Mixed Utility Analysis

While the analysis of maximizing point rewards is helpful in understanding incentives and behavior, it is clear that individuals do not vote simply to earn points. In fact, the primary motivation for earning points is to realize one’s preferences or beliefs in future votes.

Instead, we can define utility as (U), which consists of the management point gain in any given vote, as well as the individual's expectation of the preferred outcome ( ) and a binary indicator for achieving that outcome ( A ).

The formula is as follows:

U=A+2wp-Kv-w

It can be seen that when maximizing bets according to mixed utility, we still find the optimal point of betting at 0 or $v$ (this can naturally be deduced from (d/dw)A=0, in other words, betting has no effect on the voting results).

Now consider the criticality of the individual, :=dA/dv, that is, the ability of the individual to change the result of vote A. For the convenience of notation, we introduce W=1ifp＞else 0 to simplify the process of deriving w, which will be v or 0.

Theorem 4 (Optimal value of v under mixed utility): For a given K, when the outcome is unlikely to occur (p <), the individual should vote /2K; when the expected outcome is likely to occur, increase (p-)/K to obtain additional rewards.

Proof: We maximize the mixed utility of v.

This is similar to the result from Theorem 2, but the value of v increases when > 0. In essence, if members have no preference on the outcome ( = 0), they should vote in the same way as before to maximize their point return. If they do have a preference, they should choose a v value to vote for based on their desire and the impact of their vote on the outcome.

4.2 A detailed example

Since these numbers and analysis may seem abstract, let's use a small contrived example to help clarify.

Suppose there is a community with a founder who has 2,000 points and eight members who have contributed 1,000 points each. The total pool is 10,000 points. The founder creates a matching fund of 1,000 points to support new members. On the issue board, the project now has ten pending issues. The eight members other than the founder assign one of the issues to priority 5 (costing 25 points each). The total point pool for this issue is Capj(t)=58=200, and the quadratic priority of this issue is QFJ(t)=（58）=1600. Since there are not enough points in the matching pool to match, all contribution rewards will be reduced accordingly. If we assume that all issues are prioritized evenly, the reduction ratio will be k=0.1. As a result, the contribution expenditure is CPj(t)=200+100=300. All of these calculations are done automatically, and members only need to pay attention to the total contribution reward for each issue.

By contributing to this topic, a new member joins the community. The high reward incentivizes her to choose this topic over others, but she joins the community just out of interest. Management points are only useful in the current community.

When the contribution goes to the voting stage, no member wants to vote because they have already spent a lot of points and checking contributions is very energy-consuming. To incentivize members, the administrator (here, the founder) can set K = 0.1 to reward accurate predictions. Now every member checks the contribution, 5 members vote against it, and the other half vote in favor. Since K = 0.1, the cost for each member to predict and bet is 0.15+5=7.5 (because each member is very confident in their judgment). The founder then casts an unnecessarily large vote of 12, which costs 0.112=14.4. The vote is finally passed, and each member who made a correct prediction receives a reward of 25=10 from the reward pool (this only consumes 40 points from the contribution reward, which is basically a processing fee for participating in the vote and doing due diligence).

The contribution passes the check, and the 40 points are given to the member who made the correct prediction, while 300-40=260 points are given to the contributor, who can now use his points in future votes. All points used for voting, 26.4+7.58=86.4, are returned to the matching fund to incentivize future contributions.

Section 5 Open Questions

While diversity management is flexible in theory, it encounters practical challenges in different organizational scenarios. Its ability to adapt to modern open source environments and traditional hierarchical structures raises questions about its effectiveness and implementation strategies in the real world. This section will go into these nuances, inviting deeper exploration and collaborative research to address the complexities encountered when applying diversity management in different contexts.

(1) When developing quadratic voting mechanisms for diverse management, it is critical to recognize and strategically address the potential for collusion among homogeneous sociocultural groups within the organization (e.g., along dimensions such as geography, department, role, and origin). Building on foundational research (Miller et al.), this approach advocates for a sophisticated mechanism to actively eliminate the excessive influence of specific groups. Such a system would not only improve fairness, but also promote a truly diverse and representative decision-making process, ensuring that no single faction within the organizational structure gains undue control, thereby being more closely aligned with the realities of complex organizational structures.

(2) Can we extend this approach to create a multi-level decision-making framework within an organization? This would involve developing separate but connected systems for different organizational levels (such as departments or teams), each with its own customized voting mechanism. Such a model could facilitate more localized and contextualized decision-making while maintaining alignment with broader organizational goals. This approach deserves further exploration due to its potential to blend individual group dynamics with the overall organizational structure.

(3) Although rational actors may be motivated by extrinsic incentives, excessive use of extrinsic incentives may produce the so-called "motivation crowding" phenomenon, where intrinsically motivated contributors are reluctant to participate in the project (Frey and Jegen, 2000). Although management points themselves are not monetary, decisions to allocate rewards based on them must be made in the context of the existing organizational culture.

(4) As often found in salary-related research, transparency about status hierarchies within an organization can have a significant impact on contributor behavior (Cullen, 2023). While this can increase employee output, it can also reduce internal collaboration and potentially harm the organization’s long-term goals. Given its ease of implementation, multi-management provides a sandbox to compare and contrast how public or private records of points affect performance within a team.

(5) Currently, in order to prevent informal trading of management points and thus avoid the marketization and pricing of management authority, individuals cannot transfer points directly to other members. This helps prevent the financialization of management authority and makes certain actions more difficult or impossible. For example, if a founder wants to quickly bring in new members to increase their authority, they cannot send points directly, but must go through a complex PR reward process that is voted on by the entire community (which also prevents nepotism to a certain extent). In addition, if a member wants to leave, they cannot quickly transfer points to others unless they put all their points into a matching fund. Before integrating direct trading of points into multi-management, future research needs to evaluate the benefits of allowing direct trading of points.exchangeThe impact brought about.

(6) Deciding when and how to promote employees is a critical issue in organizations. However, in large hierarchies, employees are often promoted based on their performance in their current positions rather than their ability to set high-level priorities, which leads to poor management (Benson et al., 2018). It would be helpful to assess the impact of diverse management on promotion outcomes, such as evaluating the performance of top contributors in administrator roles.

(7) Current designs of polyglot management focus on a single organization, community, or project. Many large organizations are composed of multiple sub-organizations, such as departments, units, or project teams. Future research could explore the use of polyglot management to create multiple partially nested versions that allow individuals to exercise management authority within a sub-organization while also advancing in the larger workplace.

(8)Xiaobai NavigationNegative voting can provide useful signals, but it can also cause polarization in a group (Weber, 2021). This has been empirically observed in quadratic funding rounds run by platforms such as Gitcoin (Buterin, 2020). Running examples of multi-party governance with and without negative voting can further assess its psychological impact on cooperative behavior.

(9) When the outcome of a prediction market can be influenced by participants, the risk of collusion to manipulate the outcome increases (Ottaviani and Srensen, 2007). Therefore, analyzing the voting behavior of participants in a multi-party governance system with or without the opportunity to predict the outcome will help us understand whether there should be restrictions on the reward setting for prediction.

Section 6 Conclusion

Polyarchy is a protocol that bridges the gap between rigid hierarchies and the advantages of flat decentralized organizations, allowing for dynamic allocation of management authority based on individuals’ long-term contributions to outcomes and management decisions. By adjusting the discount parameters of the voting-prediction mechanism, administrators are able to reward new members of the community or members with low points holdings to incentivize them to do due diligence on new contributions to ensure they meet the expected standards or expectations of members with higher authority. This governance approach leverages a quadratic funding mechanism to solicit preferences from a wide range of participants, creating a closed points system that has no monetary value outside of the organization and can only be used within the project. While the design of this governance protocol has some open questions about achieving choice and positive outcomes for organizational productivity, it can be built through standard software design practices and naturally integrated into the workflow of open source projects. Overall, this polyarchy model can provide a dynamic and scalable way to allocate authority and reward participation in projects of any scope, mission, or scale.

The article comes from the Internet:Diversified governance: Who has the final say in a decentralized community? (Part 2)

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