Quadratic Funding

Quadratic funding is a system used for situations where you have a large pool of money and want to allocate that to various public goods projects in the most "optimal" way (optimized wrt some "it's an economics paper, fine, assume homo economicus" assumptions, and calculus)

It's a matching funds tool, so individuals donate to different projects, and matching funds are drawn from some big pile of money, allocated according to the equation. The big pile of money can come from wherever is suitable for whatever organization is using it, so, donations from wealthy individuals, or government expenditure, or something else.

It relies upon being able to distinguish between individuals. This means the implementations on blockchains have not been scaled past a few $M a year due to difficulty scaling sockpuppet resistance.

This is a decent overview of it: https://vitalik.eth.limo/general/2019/12/07/quadratic.html, but it does not explain exactly why the equation is the way it is. It has been hard to find good explanations, because in the original paper it very much reads as the result of some calculus.

If you'd like to read the original paper it's here https://www.radicalxchange.org/media/papers/liberal-radicalism.pdf. The derivation is written somewhat unintuitively. There are multiple variants, with different constraints and assumptions.

Implementation differences

All existing Quadratic Funding implementations differ some amount from the variants in the original paper. It is the opinion of the main author of this page (archipelago) that these differences are small enough that existing implementations are still useful, but may require some caution to use effectively.

The first variant in the paper assumes all individuals ignore impact on total spending aside from their own contributions.