Why Quadratic Funding Is Not Optimal

Summary

IntroductionQuadratic funding has received a lot of attention recently as a mechanism for funding public goods—especially in the cryptocurrency space. QF is appealing because it is theoretically optimal under certain assumptions.The problem is that these assumptions don’t ever hold in reality.The theory behind QF is sound and elegant, and the authors of the original paper are clear about the assumptions. They don’t claim they are likely to hold in reality, and warn about the consequences when they don’t hold. Unfortunately, practitioners have sometimes been too enthusiastic, implementing QF in settings where theory actually predicts poor results.Below is a list of the assumptions that must hold for quadratic funding to have its desirable theoretical properties. When these assumptions fail, the theory predicts outcomes that are far from optimal.List of Assumptions:Below is a brief explanation of these assumptions and what happens when they don’t hold.Wealth EqualityOur interest here is in maximization of dollar-equivalent value rather than achieving an equitable distribution of value (we assume that an equitable distribution of basic resources has been achieved in some other manner, such as an equal initial distribution of resources)—Buterin, Hitzig & WeylObviously, we don’t live in a world with an equitable distribution of basic resources.Under wealth equality, larger contributions imply greater marginal utility. But in reality, larger contributions often just imply greater wealth.Consider these two example:Ten wealthy art patrons each contribute €1,000,000 to the local public art museum.Total Contributions: $10 \times €1{,}000{,}000 = €10{,}000{,}000$QF allocates: $(10 \times \sqrt{1{,}000{,}000})^2 = €100{,}000{,}000$Subsidy: €90,000,000One hundred lower‑income individuals each contribute €100 to replace lead pipes in their neighborhoodTotal Contributions: $100 \times €100 = €10{,}000$QF allocates: $(100 \times \sqrt{100})^2 = €1{,}000{,}000$Subsidy: €990,000.Intu...