Hi,
I wrote an in-depth blog post about quadratic finance and how it has been implemented.
https://mattwthomas.com/blog/fund-open-source/
It describes the mechanism and clears up some confusions about what it does and doesn’t do.
It also points out that implementations of QF/LR/CQF/CLR have actually implemented something entirely different from any of those mechanisms.
I hope people find it interesting.
What is so special about quadratic/square root, couldn’t it be (any) other functional form that satisfies Jensen’s inequality? From your post, it seems the only place functional form matters is to satisfy Jensen’s inequality.
Satisfying Jensen’s inequality means that it collects less revenue than you provide to the projects – i.e. that it is not self-funding. So, satisfying Jensen’s inequality is bad.
The special thing about the quadratic form is that it achieves the efficient allocation. I don’t show that it does this, but it is proven in the paper. There are other equations that satisfy this property. It’s just that the QF equation is especially simple.