It has a couple interesting properties that make it appealing for the funding of "public goods" (such as software) via grant matching mechanisms. The main ones:
- Projects with distinct supporter bases will receive more funding if they join forces as a single project with more supporters
- Projects with few supporters that give a lot of money/endorsement will receive very little boost from this
- You can also implement the possibility of "negative votes/funding" that allow people to "short" the projects that they consider a net negative
Over the past year a grant matching mechanism using quadratic funding has been trialed in a platform called Gitcoin, which supports crowdfunding Ethereum development projects: https://gitcoin.co/blog/everything-you-need-to-know-about-gi...
A post by Vitalik Buterin describing quadratic funding is here: https://vitalik.ca/general/2019/12/07/quadratic.html
Vitalik also wrote about the last 3 rounds of this funding on Gitcoin, they’ve been making tweaks and the results are extremely promising:
https://vitalik.ca/general/2020/04/30/round5.html https://vitalik.ca/general/2020/01/28/round4.html https://vitalik.ca/general/2019/10/24/gitcoin.html
The idea of quadratic funding came from quadratic voting, which was discussed in the 2018 book Radical Markets: https://vitalik.ca/general/2018/04/20/radical_markets.html
In september 2018 Vitalik together with one of the book authors and another person put out a preprint describing their ideas for quadratic funding, which is very interestingly written: https://arxiv.org/pdf/1809.06421.pdf
The broader field under which this fits is called "mechanism design", which means inverse game theory: instead of specifying the rules and seeing what the outcome is, you decide which outcome you want and try to design a game that leads to it...a very enticing idea.