# Discussion on a Method of Improving Matching Coordinated Subsidies

**Background introduction**

Since 2018, Vitalik has been advocating quadratic financing (QF) as a method to generate the optimal supply of public goods in a decentralized, self-organized ecosystem (Buterin, Hitzig, and Weyl, 2018). One of the most challenging issues facing QF is collusion. For example, a participant or a group of coordinated participants may control multiple addresses or collude “gaming systems” and extract unreasonable subsidies in QF.

Since 2019, Gitcoin Grants has run multiple rounds of QF. Gitcoin Grants using an innovative method: **Dual-border coordination subsidies ( ****pairwise-bounded Coordination allowance or ****) **(Buterin, 2019). However, Zoudavid believes that the explanation of the discoordination coefficient in Buterin (2019) is not very intuitive and not very convincing. In addition, the tweakable parameter in Buterin (2019) is mainly used to constrain the extractable value of any pair of investors, but it has not done enough to adjust the collusion between them. In the article ” *A Proposal to Improve Pairwise Coordination Subsidies* ” ( *A Proposal to Improve Pairwise Coordination Subsidies* ), Zoudavid proposes a new method to improve pairwise coordination subsidies with rich economic significance.

**A New Norm of Inconsistency Coefficient**

Using the notation of Buterin (2019), Zoudavid proposed a new specification for the inconsistency coefficient:

in

Is the inconsistency coefficient of vectors i and j,

as well as

Represents the investment of investors i and j in project p,

Is the sum of all items. The inconsistency coefficient measures the independence of a pair of investors in making investment decisions. There are two perspectives to understand the economic meaning of equation (1).

One perspective is to consider two vectors

as well as

, Where p represents the total number of items.

make

Represents the modulus of the vector:

make

Represents the inner product of two vectors,

make

Represents the angle between two vectors, then there is,

If the two vectors are orthogonal (e.g.,

),So

and

From (1)-(4), it is easy to see that

For (5), first consider two more extreme cases.

**Case #1:** For each p,

, Which means that there is no shared investment, which is in line with

and

(For example, orthogonal vectors). In this example,

, Which means that i and j have the greatest inconsistency.

**Case #2:** If one exists

Such that for each p, there is

, Which means that i and j made the same investment decision. Although they may have different investment amounts, they have the same percentage of asset allocation decisions. This fits

Situation (e.g., vectors in the same direction). under these circumstances,

, That is, there is maximum coordination with.

The other examples fall between cases #1 and #2:

0 sum

between,

less than 1. therefore,

**Between 0 and 1.**

**The bigger, the greater the incongruity** .

Another perspective is to understand from the perspective of probability theory

Meaning. Before the event, every investor’s investment decision is a random variable. Therefore, the vector

They are the realistic investment decisions of i and j after the fact. In equation (1),

Only the correlation coefficient between their investment decisions was sampled and estimated. **The greater the coordination coefficient, the smaller the incongruity coefficient.**

**Subsidies after adjustment of incoordination coefficient**

For project p, after the coordinated adjustment of i and j, the subsidy is

when

In other words, when i and j are perfectly correlated, this subsidy is 0.

From equation (6), Zoudavid defines the discoordination adjusted subsidy (DAS) extracted from all projects by i and j as

It’s worth pointing out that we need to use (1) to estimate

, You can use the sample data of the previous rounds of quadratic financing, not just this round. In this way, the estimation of the inconsistency coefficient can be made more robust, and the restriction on the current sample size can be reduced.

**Adjustments to the matching boundary**

Suppose an upper limit is introduced for the total subsidy drawn from all projects by any pair of investors. Let B be the generally applicable upper limit. B is similar to the adjustable parameter in Buterin (2019).

give

Add the upper limit B: Similar to Buterin (2019b), Zoudavid uses the following formula:

Obviously,

. Also similar to Buterin (2019), if there is a specific level of total subsidy, B needs to be solved under the condition that the following constraints are met (N is the total number of investors):

It is not difficult to find the solution of equation (9) by numerical method.

**Compared with existing methods**

Consider a situation: i and j have made the same investment decision (for example, there is a

Such that for each p, there is

). With Zoudavid’s method, they will not receive any subsidies. But with the current method, they can get a lot of subsidies, but they are reduced by adjustable parameters.

Take the scene described in Buterin (2019) as an example. Suppose that k coordinated agents all contribute a large amount of money w to a project. Since they are perfectly coordinated, the funds they can withdraw using Zoudavid’s method are 0. However, the funds they can withdraw using existing methods are

, Where M is an adjustable parameter.

Vitalik suggested such a situation: Suppose there are two donors A and B and three projects A, B and C, in which donors and project pairs with the same letter are colluding with each other. Now suppose that A donated X 0 X, and B donated 0 X X.

In this example,

. If you use the data from the past few rounds of quadratic financing,

There may be different estimates, and they may be more accurate.

The subsidy after the adjustment of the incoordination coefficient is

, Which is exactly half the level of the current method. After taking the upper bound into account, the total subsidy is. With the current method, the total subsidy is

.

**It can be clearly seen from the above example that in the current method, there is no adjustment for inconsistencies, only adjustments to the boundary.**

**Multiple perspectives on the method**

**(1) Advantages**

Vbuterin believes that the proposal is a very interesting insight. The interesting thing is that the dot product is used to directly estimate the irrelevant relationship between multiple coordinators.

**(2) Existing shortcomings**

On the one hand, Vbuterin believes that in essence, any agent A can always increase the coefficient of disharmony between him and B by simply creating a project and making a large donation to himself and agent B. If every A creates a project

, Then its dot product will not be affected in any way. Because there will be no other people

Donate, but this will increase their

Value to infinity, so that the fraction is 0 and for all j

Say

.

Vbuterin proposed a bound-based correlation coefficient, whose property is that two participants donating to the same project will increase their correlation score, but two participants donating to different projects will not Will reduce their relevant scores. He believes that if Zoudavid wants to have a system in which two participants donating to different projects will reduce their related scores, then it needs to somehow defeat the send-to-self attack.

However, Zoudavid pointed out that a send-to-self attack will not cause a big problem. And gave three reasons.

First, a self-transmitting attack is expensive because the attacker needs to lock up a lot of funds in his “fake” project. At the same time, its return will be limited. Suppose the attacker creates a project in which only he invests and no other investors invest. Indeed, by increasing investment in this project, he can increase his estimate of the correlation between him and other investors. However, the subsidy he can withdraw from his “fake” project is still zero. For other projects, the increase in subsidies due to the attack should be very limited, and this increase cannot be exclusive to the attacker.

Second, when calculating the inconsistency coefficient, you can simply exclude any project with only one investor. For example, it can be considered that these projects have failed in financing and are not eligible for QF subsidies. In fiat currency crowdfunding, there is usually a threshold mechanism: any project that fails to obtain sufficient support or funding commitments within a certain period of time will be considered a failure, and any funding commitments will be returned after that. Zoudavid believes that QF can incorporate a similar mechanism.

Finally, the data of previous rounds of QF can be used to estimate the inconsistency coefficient, so that its estimation is less affected by a single data point.

On the other hand, Peter Watts perceives that Coordination penalties seem to rely on an assumption: honest users will spread their funds across multiple projects that perfectly reflect their preferences (that is, each of them will receive proportionally Value project funding). In fact, he suspects that many users will only invest a small portion because of convenience or strong preferences. Therefore, there will be many highly relevant funders for real public products without sufficient subsidies.

**( ****3 ****) Further discussion**

Vbuterin proposed a method that is to move the focus one step further, not focusing on the project itself, but focusing on a pair of donors who donated to the same project, and proposed to use 3 rules to judge:

1. If both agents i and j donate to project p, then they are more relevant;

2. If both agents i and j donate to projects p and q, and there is a certain agent k that also donates p and q, then i and j are more related;

3. If both agents i and j donate to projects p and q, and there is a certain agent k that only donates one of p or q, then the correlation between i and j becomes weak.

Rule (3) will be aggregated among all agents, so donating to your own project is much less irrelevant than donating to projects that are also donated by 100 other people.

Vbuterin proposed the use of more complex matrix multiplication to describe this problem. If M is a (non-square) matrix that maps the square value of individual contributions to the project, then

The original correlation between individuals will be given, and then some other things can be done to calculate high-level measurements, but this method needs further consideration.

In response to Vbuterin’s “higher-order measures of correlation” proposal, Zoudavid did some preliminary research. Basically, in addition to the correlation between different investors, the correlation between different projects should also be considered. Just as coordinated investors tend to make similar investment decisions, related projects also tend to attract similar investor groups. When using investment data to estimate the correlation between investors, one should be aware of the interdependence between projects. For this, Zoudavid proposed that Singular Value Decomposition (SVD) is a suitable tool to study this problem. However, the solution may be too complicated to communicate with the investor community. In addition, the solution may be prone to overfitting.

Peter Watts believes that when trying to reduce fraud, the most important thing is not to lose the core tenants of the CLR. Before the determination of the local maximum based on the coordination penalty, there may be more mechanisms that can be explored, either to supplement the coordination penalty or to replace them. The measure of success should not only be the degree of fraud reduction, but also the degree to which funds are allocated to real public goods. In response to this problem, he put forward several ideas:

**Negative preference ( ****Negative the Preferences ****)**

For each user, projects can actually be divided into three categories:

A) Projects I am willing to fund (high value perception)

B) I don’t have a funded project, but I don’t mind if they get subsidies (small value perception)

C) I don’t want subsidized items (no/negative value)

Currently, there is no way to distinguish between B and C. Maybe the UI can allow users to downvote certain items, and this information will affect subsidies. Its negative vote will only affect the distribution of subsidies among unfunded projects. Therefore, vetoing all other items is equivalent to vetoing zero. And this stems from the reality that users will not provide funds for every project that can benefit them. The nature of public products is that many of them like to give small, indirect benefits, making it easier to identify items that are obviously fraudulent or that are unlikely to benefit in any way.

**Give some unique contributors higher weight**

Most attacks take advantage of the ability to perform excess impact by contributing large amounts of resources. This is because in an anti-piracy system, it is easier to accumulate funds than donors. Therefore, a simple way to reduce the effectiveness of “fake” projects is to provide higher subsidies for projects with more contributors. This limits the impact of strong preferences, but it is worth weighing.

At one extreme, there is the CLR, which allows strong preferences but is easy to be colluded. At the other extreme, subsidies can be divided according to the number of unique contributors a project receives. Peter Watts’ idea is to use a coefficient to select the best point on the spectrum.

**in conclusion**

In order to solve the problem of collusion in the method of optimal public product supply in decentralized autonomous organizations, on the basis of Buterin (2019) proposed matching and coordinated subsidies, Zoudavid proposed a new method for this rich The economically significant matching and coordination subsidies have been adjusted and improved. He proposed a new standard for incoordination coefficients and adjusted the matching boundaries to make the estimation results more robust. Compared with the current existing method, in addition to adjusting the incoordination, it also adjusts the boundary, making the subsidy more stringent. This method uses the dot product to directly estimate the irrelevant relationship between multiple coordinators, which is a highlight, but it also has the potential to deal with the supply sent to itself, and the real stakeholders cannot get enough subsidies. The problem. For this method, there are many directions that are worth exploring and further digging, including “high-order correlation measures” and mechanisms for penalty coordination.

**references**

[1] Buterin, Vitalik, Zoë Hitzig, and E. Glen Weyl, 2018, “Liberal Radicalism: A Flexible Design for Philanthropic Matching Funds”. URL:https://papers.ssrn.com/sol3/papers.cfm?abstract_id=32436561

[2] Buterin, Vitalik, 2019b, “Pairwise Coordination Subsidies: A New Quadratic Funding Design”. URL: Pairwise coordination subsidies: a new quadratic funding design

Original Author: Zoudavid

Discussers: Vitalik, Vbuterin, Peter Watts

Contributor: Demo, DAOctor @DAOrayaki

原文: A Proposal to Improve Pairwise Coordination Subsidies

Posted by:CoinYuppie，Reprinted with attribution to:https://coinyuppie.com/discussion-on-a-method-of-improving-matching-coordinated-subsidies/

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