Here's an explanation of Quadratic Funding from their website[1], which I guess they now refer to as "Plural Funding":

  Plural Funding (also known as Quadratic Funding or QF) is a more democratic and scalable form of matching funding for public goods, i.e. any projects valuable to large groups of people and accessible to the general public.
  
  “Matching funding” is a model of funding public goods where a fund from governments or philanthropic institutions matches individual contributions to a project. Plural Funding optimizes matching funds by prioritizing projects based on the number of people who contributed. This way, funds meant to benefit the public go towards projects that really benefit a broad public, instead of things that only have a few wealthy backers. In Plural Funding, [total funding] for a proposal is [the square root of each contribution to it → summed up, then squared.] Plural Funding strongly encourages people to make contributions, no matter how small, and ensures a democratic allocation of funds meant to benefit the public.

EDIT: formatting

Quadratic Funding is a mechanism where individuals voluntarily contribute funds for some public good (e.g. an open source software project), and then these are matched such that the total funding amount is equal to the square of the sum of the square roots of the individual contributions. Under certain assumptions, this formula results in an optimal outcome, where each individual contributes an amount that maximizes their individual utility (given what others are contributing), and total utility for society is also maximized.

https://vitalik.eth.limo/general/2019/12/07/quadratic.html

As soon as the quadratic decrease is more than my marginal tax rate, I’m better off buying an NFT from the cause I want to support than making a donation.

Note that I don't really disagree with your second. Just pointing out that your two options for how government got money is not complete.

https://jonathanwarden.com/quadratic-funding-is-not-optimal/...

In the original paper, the authors acknowledge this is a problem: "...once we account for the deficit, the QF mechanism does not yield efficiency.

Agree, coordination is a larger threat to QF. But this issue has been discussed extensively. In this article I wanted to point out all the other assumptions behind QF and what happens when they don't hold.

But yes, that part does seem solvable with a correction like that even if my preferred fix would be removing the billionaires ;)

But in the part of the article you quoted above, the author (me) specifically acknowledges the utility of enjoying saved lives. But this is a critique of the quadratic funding mechanism, which is a public goods funding mechanism meant to maximize the utility each individual independently derives from enjoying public good.

The whole point of the article is to critique this assumption -- to point out that people's motives are sometimes altruistic (they derive utility just from knowing other people benefit), but the optimality of QF assumes this vicarious utility does not exist. As the article states "When individuals make contributions for purely altruistic reasons, they don’t directly experience the utility themselves. And yet the optimality of QF assumes that all utility is direct utility, benefiting the contributor only."

(Which is why no one should ever even be allowed to have that much money)

Also this article is explicitly challenging these assumptions.

For example Gitcoin uses passport.xyz to determine if your account is considered legitimate.

It is, and in fact the authors point this out in the original paper:

"…if the size of this group is greater than 1/α and the group can perfectly coordinate, there is no limit (other than the budget) to how much it can steal."

> I have to say that the biggest flaw I see isn't theoretical, it's practical.

Exactly. The theory is fine -- given all these assumptions hold. In practice, these assumption don't hold.

For example, one of the assumptions is absence of sybil attacks, fraud, or collusion. Obviously, these assumptions may not hold.

You can defend against sybil attacks in various ways. But how do you stop people from colluding (e.g. I $10 to 1000 friends, tell them they can keep $5 if they contribute $5 to my project)? There are collusion-resistant forms of quadratic funding, such as COCM, but these do not have the desirable theoretical properties (such as optimality) that vanilla QF has.