Why quadratic funding is not optimal
48 comments
·June 9, 2025nlitened
jwarden
QF makes assumptions like this, but it's not because the authors assume these assumptions reflect reality. They are just simplifying assumptions that allow formal proof of properties like optimality.
Also this article is explicitly challenging these assumptions.
math_dandy
I’m reading a winking, ironic acknowledgement from the authors that the mathematical definition of individual utility may not map perfectly onto the psychology of a patron of the arts.
TheRealPomax
They don't have to. When you only have $100, every cent matters. Once you have 10k, dollars still matter, but cents not so much. They stop having value. And that just keeps going: once you have several hundred million, a million bucks has no value. It's not just "a small amount of money", it simply has no value anymore. You're not "spending it" so much as "whatever"ing it.
(Which is why no one should ever even be allowed to have that much money)
nkmnz
I've never heard of the specific mechanism the article talks about, but it is so full of flaws that I do not consider it a good source of thought about the topic. Just the most obvious example where the author didn't put much effort into understanding their own text:
> Three art patrons each contribute [money] to the local public art museum. [...] They each expect to experience [money] worth of individual utility from enjoying the [...] art.
> [...] utility of saved lives is experienced only once by each of the cancer patients – the three contributors don’t experience that utility (other than feeling good about those lives being saved, but that’s not the kind of utility we’re trying to maximize).
This approach of intellectual unsoundness - i.e., accepting the social and individual utility of enjoying the arts, but denying any such utility for enjoying the saved lives – is present throughout the article. And I haven't started with the author comparing random cases of contributions that differ in multiple dimensions where using a ceteris paribus approach would immediately show that his arguments are shallow...
jwarden
> accepting the social and individual utility of enjoying the arts, but denying any such utility for enjoying the saved lives
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."
refulgentis
I'm confused, aren't those flaws the article is pointing out, not claims the article is making?
zoogeny
I read it as claims the article was making. I too was confused, but perhaps that is just the communication?
I think the article was going for a comparison between extrinsic motivation (which they seem to claim the original quadratic funding requires) and intrinsic motivation. It seems they just chose a poor example. The article attempts to quantize the expected reward for the extrinsic motivation ("They each expect to experience €6,000,000 worth of individual utility") while it fails to quantize the expected reward for the intrinsic motivation ("But in the selfish scenario, total utility is 3 times higher, because the utility is experienced independently by each contributor, whereas utility of saved lives is experienced only once by each of the cancer patients).
I believe, it has to do with their narrow conception of "experience". I don't know how any rational person could expect to "experience" €6,000,000 worth of art as my first criticism. Now, it would be fair to say that the implication that the wealthy benefactors expect that experience could be seen as a criticism of quadratic funding. But to roll with that ludicrous expectation for the sake of argument and then to fail to give a similar expectation of reward from the experience of saving 60 lives is not a fair argument.
If I can "imagine" the benefactor expecting €6,000,000 worth of experience for knowing the art is on display at the local museum, I could "imagine" the benefactor expecting some non-zero-euro amount of experience for knowing 60 people survived cancer.
If we quantify the "experience" in euros for the first scenario, it seems unfair not to quantify the "experience" for the second scenario. In this case it is about being consistent in argument, which the article fails to do.
em-bee
the article claims that a contributor to art benefits from enjoying the art and a contributor to cancer research doesn't (except for feeling good), and therefore quadratic funding would favor art contributions and disfavor cancer research contributions. GP claims (and i agree) that contributors to cancer research do benefit beyond feeling good. eg because they, or someone they care about might have or get cancer later and benefit from the research.
the challenge is that measuring benefit is hard.
gbacon
Regarding both perfect knowledge and equilibrium discovery, consider Hayek’s work on what he called the knowledge problem, beginning with “The Use of Knowledge in Society.” No person or entity possesses perfect knowledge of the current state, and no one has perfect knowledge of the follow-on simple or higher-order effects. Instead, apply the insight from public choice theory that state actors make self-interested choices. Cui bono?
I am far from denying that in our system equilibrium analysis has a useful function to perform. But when it comes to the point where it misleads some of our leading thinkers into believing that the situation which it describes has direct relevance to the solution of practical problems, it is time that we remember that it does not deal with the social process at all and that it is no more than a useful preliminary to the study of the main problem.
jwarden
great quote
cogman10
Reading through it and how it's applied (mostly with crypto). I have to say that the biggest flaw I see isn't theoretical, it's practical.
QF assumes that you can know for sure who is an individual. Yet how would you know that with crypto funding?
Let's say I'm malicious and I want to pillage a QF. What stops me from setting up a bogus social project/company, registering it, and then taking my $1000 and splitting it into 1000 wallets with $1 a piece which all contribute to my scam project?
If I know a QF fund is getting setup, it'd be pretty easy to create 1000s of wallets, vary the money in them, and have them all fund my scam. I can even automate some trading between these wallets to make the source of the funds look somewhat organic.
Pillaging these funds seems like it's almost a trivial endeavor assuming you can get your own scam company associate with them. And the more money you have, the easier it'd be to pillage.
numtel
Generally, QF protocols are paired with a form of Sybil resistance.
For example Gitcoin uses passport.xyz to determine if your account is considered legitimate.
gs17
> Intuitively, this seems wrong: the art museum receives a far larger subsidy, yet many more people benefit from replacing the lead pipes, and the utility-per-individual is arguably much higher as well.
Well, yes, but those many more people getting more utility didn't contribute. If the same contribution was spread out over 10x the people each contributing $10, they'd get 10x the funding.
Their complaint here is really that ideal QF would also require assuming people actually get involved with it. I agree it has issues, but this isn't what I'd lead with. Coordination seems like a much larger threat to the concept.
jwarden
In the example in the article, many more people did contribute to the lead pipes (100 people vs. 10 for the art museum). And they still get only a fraction of the funding that the art museum gets.
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.
sokoloff
But they got 99 shares of government contribution for each share they put up for a 100x multiplier while the art patrons got 9 shares of government contribution for a 10x multiplier.
Setting aside the emotional content and looking only at the math, it’s not at all obvious to me that the project with 100 donors was somehow shorted.
jwarden
Yes good point. We'd have to actually flesh out the assumptions about marginal utility of wealth for low-income vs. the high-income group (as well as assumptions about individual utility functions), to demonstrate that this outcome was not optimal. I didn't do that in this article because it gets too mathy.
However, the optimality of QF does assume wealth equality. When you drop that assumption and assume diminishing marginal utility of wealth, you can show that QF is not optimal.
But I think you are right that the example in this article doesn't necessarily show that clearly. The example leans heavily on intuition (or emotional appeal). I think I will try to improve that section.
sdenton4
A core problem of capitalism is that it only solves the problems of people with money... This is more of the same.
Consider that any of those 100 people might have a kid who would be the next Einstein, if only they hadn't been lead-poisoned. But these hundred people also have rent to pay and food to buy, and can only set aside $100 to deal with the lead-pipes problem. The existing distribution of wealth is not a good measure of the importance of the problems that these different individuals are experiencing. And the existing distribution of wealth is thus not a great way to prioritize solving problems for maximum societal benefit.
spencerflem
Many people would consider fixing pipes a more important project despite the fact that the wealthy contributors could front a lot more cash for their pick.
gs17
But do we know the "ideal" funding values for the pipes and museum (and if we can, then why not use that)? It's only really "unfair" if we know that the pipes "deserve" a disproportionately larger multiplier. If the pipes deserve to be funded regardless of contributions (and they probably do), then the issue is using a system that could possibly fail to provide for them in the first place.
It's not a good way to allocate funds, but I don't think it's a slam dunk to say it multiplied a larger group's money more than it did a smaller group's.
jwarden
Well it's also unfair if we assume large difference in the marginal utility of wealth -- for example to go to extremes, we might assume that a $10 contribution from a low-income individuals represents the same sacrifice as a $1,000,000 contribution from a high-income individual. If that were the case, a $100 contribution from a low-income individual represents 10x the utility of a $1,000,000 contribution from a high-income individual. So in that case the lead would pipes have both more contributors, and higher utility per contributor, than the art. So total utility would be maximized by giving more money to the lead pipes.
crmd
I am very suspicious of Quadratic Funding after reading its top google result[1] which presents it as an egalitarian democratic mechanism, and this article which shows it to have the opposite effect in practice. It reminds me of the Citizens United campaign finance debate here in the US 15 years ago: aspirational sales pitch, appalling consequences.
bee_rider
I wonder about this kind of article. It is a big list of problems, so it seems like we’ll end up having a bunch of unrelated conversations here, which seems unfortunate.
But, to start chipping away… For the wealth inequality section, I gather the goal is to let people provide a signal based on how much they are willing to spend. Shouldn’t that be corrected for their wealth, because that shows how much they value the thing? If the art patrons are all 1B-aires, and the anti-lead-pipe folks are 100k-aires (just to make the math easier), we could do:
Art:
10*(sqrt(1M/1B)^2) = 1/100
Pipes:
100*(sqrt(100/100k)^2) = 1/10
Now we’ve got some measure of everybody’s preference, and can allocate the budget appropriately. Whatever the overall budgets is, 10x more for pipes than art seems… well, at least a lot closer to reasonable than ~100x more on art than pipes
spencerflem
You might also want to factor the relative marginal utility of a dollar.
But yes, that part does seem solvable with a correction like that even if my preferred fix would be removing the billionaires ;)
efitz
It sounds like a kooky idea and neglects the fact that “the government” isn’t some magical source of money; it got that money from its citizens somehow (taxes or inflation).
It’s a much simpler idea to just have citizens vote for what they want their tax money spent on, by voting for candidates who will represent their interests.
jwarden
Yep. QF basically assumes that subsidies are "free money", as discussed in the article:
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.
taeric
Government can also get money through bonds, though? And government spending of these funds can be argued to go much more directly to economic growth for the region than most any other spending.
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.
sokoloff
Bonds are an exchange of cash now for more cash later in the other direction. Eventually, that “cash later” is taxed or inflated away (printed), so it’s a difference in timing more than category.
taeric
Fair. Still largely a different form getting cash now, though? Particularly if you account for the fact that governments can go belly up.
cleak
This looks interesting, but I have no idea what I’m looking at with the original paper. Could someone provide a simple summary that doesn’t rely on knowledge of Quadratic Voting?
bts
Quadratic Voting and Quadratic Funding have some ideas in common, but they refer to separate concepts. To learn more about these topics, I would probably check out the website for RadicalxChange. IIUC RxC is the main public body attempting to realize the theoretical benefits of QF and related ideas.
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
jppittma
So I make 1,000,000 separate donations in the amount of $0.01?
timerol
Both QF and QV rely on verifying identity, so that would be counted as one donation of $10,000. The entire point is letting numbers of people balance in some way against amounts of money, so allowing one person to count multiple times breaks the system
jwarden
Total funding in this case would be: (sqrt(.01) * 1000000)^2 = 10 trillion dollars.
jwarden
Here's a very brief summary of what Quadratic Funding is (which is distinct from Quadratic Voting):
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.
jovial_cavalier
a more plain-english explanation from Vitalik's blog:
j2kun
> for funding public goods—especially in the cryptocurrency space.
Sounds like a contradiction to me. Nothing about cryptocurrency should be considered a public good, even if wealthy donors are struggling to efficiently donate money to its development.
jovial_cavalier
I had always interpreted quadratic funding as being a tax rather than a subsidy. You donate $100 and the cause receives $100, then your next marginal $100 is discounted quadratically, and the government receives the difference. I think that just straight up resolves the first two issues.
sokoloff
I think that very quickly just changes the forms of donation to be “something that doesn’t count as a donation” (buying tickets to an event or even just straight up NFTs).
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.
When people use examples like “wealthy patrons contribute large sums of money to art museum to experience individual utility from enjoying additional art”, it makes me think they understand money as little as they do art.