Background Quadratic Funding is an innovative proposal for providing matching funds to public goods. The main feature of Quadratic Funding (QF) is that a proposal which earns support from several small donors should receive more funds than a single donation by a rich donor, Under QF, a hundred donors, each of whom has just 0.01 ETH to contribute, should wield more influence than a single contribution of 1 ETH. However, this basic feature could be exploited by users who want to strategically manipulate their contribution amounts and targets to maximize the matching funds. These behaviors are different from organic community action, since they are consciously directed with the matching funds as the primary goal. We do not want to reward manipulation -- funds should only go to real users making donations to grants they truly value. We consider two basic types of strategic behaviors: Sybil Attack: In this scenario, many fake accounts are created to give the illusion of broad public support for some grant $F$. The funds available to a user are split into small amounts between these fake accounts, who then make many small donations $F$. As a result, $F$ receives a large matching donation amount, even though its actual support is limited.
4/28/2021A Simple Example Suppose we have users who have given money to various projecs. The contributions are indicated in the labeled bipartite graph below. Under the original LR algorithm, assuming an unlimited matching funds pool, we have Project A: receives $\left( \sqrt{1.0} + \sqrt{1.0} + \sqrt{0.25} \right)^2 \approx 6.25$ units Project B: receives $\left( \sqrt{0.75} \right)^2 \approx 0.75$ units In this very simple scenario, it isn't hard to see that if there are no other restrictions, the best Project A could do would be if all three users each gave their full budget of 1.0 units, in which case A would receive $\left( \sqrt{1.0} + \sqrt{1.0} + \sqrt{1.0} \right)^2 = 9$ units.
3/26/2021or
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