Introduction:
1. Adjusting Quadratic Mechanism (Adapting Quadratic Mechanism) evolved from the Quadratic Funding jointly launched by Vitalik and Harvard professors in 2018. Secondary financing is a new financing mechanism to solve the financing difficulties of public projects. For a community with p public products and N community members (investors), the pth public product receives The investment is equal to the square of the sum of the square roots of the investment amount of each investor, and its return is composed of the following formula:
QF has several characteristics:
1) Increasing returns. The more people who participate in the investment, the more benefits you get (because more people equally participate in using the project)
2) Diminishing marginal returns. As the number of people increases, the increment of unit income becomes smaller.
3) For public goods, non-exclusive and non-competitive.
Summarize:
Summarize:Therefore, for the financing of public products, the optimal investment scale for the society and the optimal investment income can be generated through the secondary financing method, but this is only an ideal society where everyone is in a rational state, but the real situation However, it may develop into a multi-person conspiracy, or even a situation where one person plays multiple roles as sweeping wool.
2. Due to the above-mentioned potential problems of secondary financing, Vitalik proposed the Adjusting Quadratic Mechanism in accordance with the characteristics of Soul Binding Token (SBT), which is dedicated to solving the problems caused by excessive collusion or one person playing multiple roles. The problem of uneven distribution of benefits.
1) This is not a one-size-fits-all approach, but it will weaken cooperation while still giving certain rewards.
2) By checking the correlation of the SBT held by the soul, it is possible to distinguish highly correlated, affiliated, and even colluded souls
Mechanism Introduction: Adjusting Quadratic Funding/Voting
1. Simple Match: Lets start with the simplest logic first, assuming that project p has three investors, Abdu, Shou, and Belle, who have made contributions of A, S, and B to project p respectively. Under the verification of SBT, the three investors respectively There is no hook-up relationship. but:
In the case that A, S, and B have nothing to do with each other and are independent of each other. Using the Quadratic Funding method, you can simply calculate the financing income or voting power corresponding to Abdu, Shou, and Belle respectively. And it can be seen that the matching fund obtained by project p is proportional to the number of A, S, and B.
2. Single Membership：Thinking further, if there are two members of Abdu, Shou, and Belle who have a cooperative relationship, such as Abdu and Shou, then Vitalik provides two optimization methods:
1) Cluster Match: Combining A and S under the same root formula can reduce the revenue sharing ratio of Abdu and Shou, and increase the revenue sharing ratio of Belle, but at the same time, it does not completely punish the cooperation between Abdu and Shou:
From the above, we can see that the equation dilutes the weights of Abdu and Shou to a certain extent, giving Belle the same weight as the sum of the other two. If Abdu and Shou play two roles, the above equation will treat Abdu and Shou as an individual to reach the optimal solution.
2) Offset Match: By judging the degree of correlation between Abdu and Shou, A and S are reduced (Offset) by a certain amount of weight by dividing by a coefficient. In the case of cooperation between Abdu and Shou:
Similarly, when Abdu and Shou are in exactly the same situation, we can obtain the same optimal solution as (4):
3. Multiple Memberships：In the consideration of Single Membership, we oversimplified the cooperative relationship or symbiotic relationship that may exist in society, so here we assume a more complicated situation. There is a certain social relationship between Abdu and Shou, Abdu and Belle are also related, and Shou is related to a group other than project p.
1) Cluster Match: Similar to Single Membership, we put two related individuals under the same root formula, but we need to set the sum of the weights of each individual to 1, and get the following formula:
2) Offset Match: For the Offset Match method, we need to calculate the contribution coefficient of each individual, which is determined by analyzing the correlation of SBT held by each individual. Taking the above situation as an example, we assume that Bella is 50% related to Abdu, and Abdu is also 50% related to Bella; then assume that Abdu and Shoud are 25% related in the holding of SBT, and the weight of each individual is 1. We get the following system of equations:
Summarize:
Summarize:
By combining the special attributes of SBT with Quadratic Funding, it can theoretically and effectively solve the problem of being vulnerable to Sybil attacks or collusion attacks left over by QF, which will affect the voting governance of DAO and public projects in the future. Events such as financing should be as safe and reasonable as possible while improving effectiveness and efficiency.
