Why quadratic funding is not optimal | Hacker News Reader

Why quadratic funding is not optimal

jonathanwarden.com

119 pointsjwarden96 comments

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.

https://www.kysq.org/docs/Hayek_45.pdf

great quote

May I quote the same Hayek (last page):

>instead we must show how a solution is produced by the interactions of people each of whom possesses only partial knowledge.

(In the same spirit, I'm trying to move beyond dissfests towards more collaborative convos on HN)

@warden I was encouraged to see "perfect knowledge" replaced by "sufficient knowledge" in at least once instance in your post.

We should encourage Glen & Michael to work on seeing if weakening their assumptions as above would produce proofs of more useful natures, as a prelim to solving the knowledge problem :)

(Alas collabs take work, & HN is primarily an entertainment & venting channel, due to its ephemeral design)

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...

> 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."

Thank you for replying to my critique! The whole point of me reading your text was not to critique your assumptions, but to understand your arguments. It would be great if you'd do the same: make understanding the whole point of your thought, not criticizing.

I'm willing to accept this statement of your's about QF as correct: "QF assumes that all utility is direct utility, benefiting the contributor only." This still does not exclude the utility of saving lives for the savior. If the act of saving a live is worth 10m units of currency to me, the utility that I derive must be at least 10m units of currency. This is the "direct utility benefiting the contributor"! You cannot claim that QF cares only about direct utility of the contributor, but then go on and set that direct utility to 0, claiming QF didn't care about it.

If you value saving lives at a rate of $100,000 worth of utility and a cost of $100,000, then quadratic funding makes you [0] pay $150,000 of money for $100,000 worth of utility.

Make sure to carefully read articles before dismissing them twice. Thank you.

[0] you = your contribution + a magical subsidy (presumably paid by you indirectly)

The problem with the article is that they did not make the point you are conveying here.

They say: 1. QF cares only about direct utility 2. $saving a life brings $100,000 of INdirect utility for society and/or the person who's life is saved 3. we (again: who?!) don't care about the direct utility in this case

I have no idea how you can wrap your head around the idea that this is a good representation of any valid critique.

Btw, I think QF is stupid, but that's not the point here.

What an uncharitable reply. Not op, but you seem to miss the basic point of the article, I.e. you fail at your own criterion of making understanding your goal.

As someone not in this space I found the argument succinct and easy to follow. QF is optimal if you only have direct utility. To illustrate that this assumption is problematic, confront it with a hypothetical where direct utility is zero. Then you can clearly and immediately see that in this hypothetical it's not optimal.

Maybe the argument is hard to parse if you're not used to reading theoretical literature?

But OP did not follow his own terms: he refuses to take the direct utility of giving your money to charity into account and instead calculates some arbitrary utility of the saved lives, which is indirect utility.

Do you have any evidence that these supposed assumptions exist?

No one donates $100K to the opera because they enjoy attending opera $1M worth. It's absurd to accuse any opera organization of assuming that.

Someone buys a ticket to the opera for $100 because they enjoy attending opera >$100 worth. They donate $100K because they want other people to enjoy opera, or for personal advertising purposes, not charitable social purposes.

> Do you have any evidence that these supposed assumptions exist?

By existing, so you mean “hold in reality?”

The point of the article is that the assumption that underly QF do not hold in reality.

I believe they were asking for evidence that (significant numbers of) people hold those assumptions.

I don't think the author was claiming that significant number of people hold those assumptions. I thought the assumption was that the most people implementing QF believe that QF is optimal for their use case. However, the author's observed use cases tend to not match the preconditions for QF's optimality.

Exactly.

I'm confused, aren't those flaws the article is pointing out, not claims the article is making?

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.

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.

The article sets up (1) a straw man (2) with impossible to measure numbers. The author acknowledges the second fundamental flaw in the whole enterprise, but not the first.

What straw man? The assumptions underlying the theory of QF are spelled out cleanly in the original QF paper. The article is just enumerating these assumptions and showing they don't hold in reality.

The numbers in the example are indeed impossible to measure. But QF is claiming *optimality* -- that it maximizes social welfare -- when certain assumptions hold. To show that QF does not maximize social welfare when these assumptions don't hold, it suffices to show a single hypothetical counterexample.

I don't hold any cards in the game - if QF is bollocks, so be it, I couldn't care less.

The reasons why I've commented are:

1) the article does a really bad job at using words that matter to me, like "utility". If any theory – QF or OPs own line of thought – tells me that funding cancer research doesn't have utility for the person funding it, that theory is BS. I don't need a badly made up hypothetical counterexample for this.

2) The author contradicts themselves: "QF assumes that all utility is direct utility, benefiting the contributor only." – but then they go on and calculate the utility of spending money on saving lives not based on the utility of the contributors, because "that’s not the kind of utility we’re trying to maximize" (btw, who is "we"!?), but based on some arbitrary made-up value and number of saved lives.

Actually, everything you complain about is highly irrelevant. It can't be overstated how irrelevant your objection is.

> (other than feeling good about those lives being saved, but that’s not the kind of utility we’re trying to maximize).

Your interpretation of this statement is that the contributors have a fixed marginal utility for every single dollar, so that they will consider the situation where they spend $1,000,000 per live saved to be superior to the situation where they spend $100,000. In other words, you're saying that welfare is a veblen good for the donor.

The author makes the argument that the mere act of spending more money to save lives is not the type of utility we should strive for to maximize social welfare.

Your utility in question is not about feeling good about saving people regardless of cost, it's about feeling good about saving people, precisely because it costs money and you personally spent money to do it.

By the way, why is that "your utility"? Why am I putting words in your mouth? Because you're disagreeing with the author and therefore necessarily put yourself at odds with the authors objection to the first interpretation. Hence you must necessarily agree with it, otherwise you're just trolling and that would be uncharitable of me to accuse you of. So, yes, you must have mistakenly chosen the silly interpretation.

I made you spend a quadratic amount of time on your reply than I did, so maybe you have mistakenly chosen the silly path of QF yourself.

I think I disagree with nkmnz' specifics. But I'm not sure! It's possible I might agree with nkmnz across the board.

This might be a case where someone familiar with the subject could follow what you're saying just fine, but most of us HN commenters don't know enough about the subject to get it. That can happen here (e.g. on physics topics). In any case I can't really follow your arguments closely.

I don't think you're distinguishing consistently or clearly between the OP and the theory being examined in the OP.

Maybe. It would help if the author were consistently distinguishing between his own assumptions and those he's examining, e.g.:

> that’s not the kind of utility we’re trying to maximize

Who is "we"? I read it as "the author applying the assumptions of QF", yet the whole point he makes there in the name of QF would contradict the previous statement of his that "QF assumes that all utility is direct utility".

If you haven't heard of the topic of the article before, why do you impugn the article then? From your comment it seems like you can't distinguish what the QF proposal is assuming (and the author is criticizing as unrealistic) from claims of the author.

The author makes no statement about the utility of enjoying the arts vs the utility of saving lives. They're making up hypothetical examples with specific properties that demonstrate problems with QF.

Sorry to say, but your observation is wrong. They do make explicit statements about the utility of enjoying the arts:

> They each expect to experience €6,000,000 worth of individual utility from enjoying the additional €9,000,000 of art.

> Net social welfare:

> Total Utility = 3 × €6,000,000 = €18,000,000

...just to go ahead and to deny any relevancy of the utility of saved lives:

> 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).

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.

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.

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.

> They are just simplifying assumptions that allow formal proof of properties like optimality.

And when they're done, the proofs are recognized as being fully out of touch with with the reality we actually live in based on the fact that their assumptions are also out of touch, and nobody actually tries to use them to make decisions about how to do things in our very real and non-simplified society?

Yes, as you (sarcastically) imply people do indeed try to use QF to make actual decisions, not recognizing the proofs are based on assumptions that don't match reality.

There's nothing wrong with making proofs based on simplifying assumptions. A lot of incremental progress is made that way. The problem is not the QF theory, it is that people are using QF in the real world because they think it has all these great theoretical properties in the real world -- not recognizing that the underlying assumptions are unrealistic.

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)

> 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.

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.

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.

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.

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.

Great. Now, suppose the 10 wealthy people are in favor of the pipes project and the 100 average people are in favor of an art museum.

Is the art museum or the pipes project more important?

You're missing the point, which is that the group with a lot more money to start have their voices heard more.

It matters some that their multiplier is different , but in absolute numbers its still more to the program that benefits fewer people. The "utility function" is not accurate because the wealthy's utility starts out with a massive advantage.

So yes, I think it would still be unfair if you switched it given the poor majority genuinely would rather have art than lead free pipes.

The problem is that their voices are counted less due to not starting with money.

But regardless, that would be a silly thing to switch because that's not a situation that ever comes up, while the original framing is a genuine problem in our society right now.

Yes, money has utility. That should be unsurprising to everyone.

This proposal's pairing of hypothetical projects levels the playing field by a factor of 10 versus the starting point. That seems like a pretty good improvement over the purely monetary starting point.

If your objection is that government can't work this way, because some projects need to be done for the benefit of people who literally cannot even contribute so much as a penny, while other projects are optional, then I'll agree with you. It means that this funding mechanism is fundamentally flawed in regards to required projects.

But if you want to augment government spending with private contributions for certain public-private partnership projects, this might be a good way to allocate government matching funds for these optional projects.

You can't treat a lead pipe replacement project as an optional project (the responsible government or utility just has to do it), but if you wanted to trade off funds towards a skate park versus towards an art museum, this process seems better than a straight matching funds percentage process.

Or, if you want to have no partnership projects and use existing government mechanisms exclusively, that also avoids this problem.

The point is that its not socially optimal. The socially optimal solution would optimize global utility, as in it would not be influenced by the starting wealth of each person. If you allow starting wealth to influence things, their needs will be optimized for more at the expense of people who do not.

Yes, that goes against the idea that "money has utility" but the point the article was making was that its not socially optimal anymore not that is regressive compared to whatever other strategy, like straight matching funds. There's no math claim that straight matching funds is optimal either.

I think maybe we're speaking past eachother? Because yea totally I'd rather there be a multiplier based on the # of people than not given either that or a straight match. And your other options sound good too: "always fix non-optional things" and "do things democraticly (so 1 person 1 vote, not 1 dollar)"

But the article is making a very specific point about a claim of QF being mathematically socially optimal that isn't being met.

I think all of these schemes end up failing in environments other than academic papers.

If I was a wealthy person and the calculation was based on share of wealth donated, I’m pretty sure I’d find a way to become a massive employer of temporary labor locally at $100/hr but only for 8 hours, make clear my preference for the art museum or other causes, and that I like to learn about what causes matter to them.

Accordingly, those local workers for whom I like their cause and story of why it matters to them, I’ll match their donations (based on receipts showing their donations) and also setup a series of follow-up paid interviews in the future to learn about their on-going donations to a cause they obviously care so deeply about. They keep about half the money to compensate for their time and to grow their wealth, I get to socialize with some people who support the same causes I do, I no longer have an outsized donation in my name [we wouldn’t want me to have an outsized influence], and together, we can really do great things!

I don't disagree!

Collusion was one of the other problems mentioned in the article as a way that QF does not function in reality. I'm not advocating for it at all

> levels the playing field by a factor of 10 versus the starting point.

Let's say there were only 10 poor people that contributed to the pipes. The total funding would be $10,000 -- a subsidy of $9,000. So 10x multiplier both for the pipes and the art.

Then let's also say that the marginal utility of $100 for a poor person is equivalent to the marginal utility of $1,000,000 for a rich person.

So we have the same number of contributors for each project, but a much higher marginal utility-per-dollar for lead pipes. But the socially optimal funding would be at the point where the marginal utility-per-dollar are equal for both projects (per the Equimarginal Principle).

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.

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.

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.

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.

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.

I realize that no government today operates by spending money into existence with one hand and taxing it out of existence with the other, but I always assumed that QF was designed for use with that kind of system (likely a DAO responding to voters on some general purpose chain like Ethereum).

Why else would you dream up such a scheme except for the purpose of replacing the one we're using (e.g. the one where the scarcity of money is determined by bankers' willingness to issue loans)? Perhaps the author is right that QF is not optimal, but what we're doing now does not care whether a funded venture helps or harms the people, so I'd say the bar to clear is pretty low.

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.

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.

Fair. Still largely a different form getting cash now, though? Particularly if you account for the fact that governments can go belly up.

In the long run, all government debt is going to be future taxes. There are many programs that the government spends on that are efficient and produce more growth than the taxes collected would have, and there are many that don't and produce less growth than leaving the money in the hands of the taxed. Sometimes this is due to government inefficiency, and sometimes because we decided it's what we want, like medicare for elderly who will never return the investment into their health.

I'm pretty heavy against "efficient" as a goal to look for in government spending. In particular, the first spend on anything will never be as efficient as later spending. That just isn't how it works. So, if you are trying to seed something with government spend, expect some inefficiencies.

Sure, government spending is not purely an investment in future tax. Goverment is not purely a financial investment vehicle.

This is so obvious as to barely merit acknowledgement.

That's only true if you assume that governments last forever. They sometimes die with debt and their financiers take losses.

> 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.

I think your comment is operating under the assumption that the "folk theory of democracy" works: https://en.wikipedia.org/wiki/Folk_theory_of_democracy

It's a term from "Democracy for Realists", written by some democratic theorists. They disassembled the argument for it in the first half of chapter 1, and then spent the rest of the book refuting pretty much all the other competing academic theories that other democratic theorists actually believe in (scholars of democracy absolutely do not believe in the folk theory).

EDIT: Which is just to say that we need to improve the incentive structures (which QF takes a stab at doing, though there are other approaches). We need these experiments because we need to learn what actually works -- the old theories never actually did, and the prior assumptions that made this disconnect negligible are starting to fail.

I never heard of "quadratic funding" before today, but I did know about "quadtratic voting". Is "quadtratic funding" just a spin on "quadtratic voting" that makes a complete hash of everything?

The authors of the QF paper describe it as "an extension of the logic of quadratic voting." They involve similar formulas and both are theoretically optimal (or efficient), and have a single equilibrium. These properties are proven using somewhat similar math.

But they apply to quite different settings and are not really the same thing. With Quadratic Voting, people pay for votes (with cost determined by a certain formula). With Quadratic Funding, people contribute to projects (with matching funds determined by a certain formula).

QV also makes many assumptions that rarely hold in reality, just like QF does. I may write an article about this someday.

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.

1. https://www.wtfisqf.com/

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

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 ;)

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?

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.

[1] https://www.radicalxchange.org/wiki/plural-funding/

EDIT: formatting

So I make 1,000,000 separate donations in the amount of $0.01?

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

I used to think the employer drives to contribute to the company's preferred charity were bad before QF; they’re bound to get a lot worse with it, giving power to employers with lots of employees and a willingness to encourage them to donate as little as a penny.

So I have to give it out and have people donate it on my behalf?

Total funding in this case would be: (sqrt(.01) * 1000000)^2 = 10 trillion dollars.

(10 billion, surely?)

Oh right: (sqrt(.01) * 1000000)^2 = 1.0e10

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.

a more plain-english explanation from Vitalik's blog:

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

Better to learn about Quadratic Voting, and ignore the magical thinking of Quadratic Voting.

I am not deep enough to critique the article, but I have comment:

"If the wealth equality assumption does not hold, QF is anything but optimal. Consider these two examples:

    Ten wealthy art patrons each contribute €1,000,000 to the local public art museum.
        Total Contributions: 10×€1,000,000=€10,000,000
        QF allocates:  (10×sqrt(1,000,000))2=€100,000,000
    Subsidy: €90,000,000

One hundred lower‑income individuals each contribute €100 to replace lead pipes in their neighborhood

    Total Contributions: 100×€100=€10,000
    QF allocates: (100×sqrt(100 ))2=€1,000,000
        Subsidy: €990,000.

Intuitively, this seems very wrong:[..]"

Intuitively, I thought: Well, the "hundred lower‑income individuals" got there money 99x, while the "Ten wealthy art patrons" only got 9x. (1/11 for having 1/10 participants). Isn't that working as intended?

Especially if you have a progressive income/wealth tax.

Author here. @sokoloff also pointed this out in their comment. You are right, the example confuses by making the group sizes different.

I will update the article so it reads like this:

    Ten wealthy art patrons each contribute €1,000,000 to the local public art museum.
        Total Contributions: 10×€1,000,000=€10,000,000
        QF allocates:  (10×sqrt(1,000,000))²=€100,000,000
    Subsidy: €90,000,000

    Ten lower‑income individuals each contribute €100 to replace lead pipes in their neighborhood
        Total Contributions: 10×€100=€1,000
        QF allocates: (10×sqrt(100))²=€10,000
    Subsidy: €9,000.

Here, both groups get their contributions multiplied 10x. But the high-income group gets 10,000x the subsidy.

Given the assumption of wealth equality (and other assumptions), the QF paper proves that allocating more money to art maximizes social welfare, because if people contribute more to the art, it means art it has more utility.

But given the reality of wealth inequality, and the theory of diminishing marginal utility of wealth, the wealthy may contribute more to art simply because they can afford it, and because 1,000,000 may not have any more utility to them than 100 has to a very poor person.

"the example confuses by making the group sizes different" But isn't that also realistic, since there a lot more people with little income and "small" problems than ultra-wealthy potential art patrons?

Today, if I get 1000 people to give $10 to the local library or public sport place, I have $10.000. (1000xsqrt(10))² are $10.000.000.

For me, an obvious fix for potential exploitation would be to cap the individual contribution to 10k or 100k. However, as I said I know nothing about qf and this has prob. already been discussed to death.

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.

> Pillaging these funds seems like it's almost a trivial endeavor assuming

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.

> absence of sybil attacks

It's funny that a cooky proposal originating from crypto, which is incredibly inefficient precisely because it has to defend against sybil attacks (unlike permissioned systems), assumes the absence of sybil attacks. Hilarious, really.

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.

I like TBC (Token-Bonding Curves) and friends, but the fault here is not understanding that funding public goods is a complex adaptive system, and no closed form / analytic solution with nice looking smooth curve will help to model it. These things together with the Game Theory are better left for textbooks, not real-life projects;)

There is another method of funding public goods re-surfaced by crypto folks: DAC (Dominant Assurance Contracts) which is more like SiTG (Skin in The Game), and I think many blank check companies / SPACs use some elements of it

BTW, that’s why economists can’t predict sh*t: they trying to use simple curves / closed form solutions, instead of using ABM (Agent-Based Modeling) or even more advanced simulation methods

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.

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.

QF is an awful idea. Literally every assumption it relies on is wrong... And probably it exacerbates the situation as implementing QF likely causes further degradation of the underlying assumptions... By Goodhart's law "When a measure becomes a target, it ceases to be a good measure."

It's incredible how, whenever people try to come up with some centralized framework, ideology or plan to improve things, they make things worse and the cost falls on someone else's shoulders.

I've been feeling the effects of this deeply flawed philosophy in my life literally every day yet I had no say on it.

From what I can understand, instead of funding various causes via "matching donations" QF is proposal for a funding body to do something like 'match in proportion to a blend of the donation amount with the number of people donating to the cause.' The point seems to be to smooth out any undue influence any one philanthropist or individual funder has and make the funding of public goods quasi-democratic.

However, compare these two problems: a) not enough people who can afford to do so engage in philanthropy, and b) philanthropic funding isn't quasi-democratically distributed. I have to imagine that (a) is a much, much bigger issue than (b).

I guess one could argue that because there isn't an analog of "a market" for public goods (c.f. "The Use of Knowledge in Society") somehow we aren't funding the important public goods "efficiently"? And maybe we should think about this more? Yet it's not clear that efficiency (in the economic sense) should be the goal or even applies. This is because markets are great at distilling people's the preferences for fungible goods they want to buy and fungible services they want to use when faced with multiple options for procuring some of each. But a) the vast majority of people don't have that same type of preference for which public goods should be funded, and b) public goods typically aren't fungible. (I.e., funding one scientist gives you a very different research output from funding another in the same subfield.)

> a) not enough people who can afford to do so engage in philanthropy, and b) philanthropic funding isn't quasi-democratically distributed. I have to imagine that (a) is a much, much bigger issue than (b)

Consider philanthropy funding as actions that terraform the future. The future is where all possibilities unfold, so shaping future landscape pays dividends to the worldview of those who materialize it.

I would propose that if (b) is miscalibrated and inequitable, it might affect everything, including (a), much more than we assume.

But also, I'm not trying to claim I know that one is more important, just that they're both quite important and very interrelated :)

Ah, interesting. So what (I think) you are saying is that if there is enough of the right type of philanthropic, in-kind donation more people will be able to donate in the future. I will admit the possibility that there may be a clever way of of doing in-kind donations that isn't wide-spread. Sort of akin to ranked-choice-voting but for donor matching.

Quadratic funding is a terrible idea. It doesn't make sense to separate things into quadrants. From the linked article:

> So how about non-excludable goods that are rivalrous in nature? This intersection represents common goods such as fish, timber or coal. Everyone has access to these resources but there is an inherent competition when it comes to collecting them due to potential overuse or congestion.

These are excludable in many countries. There are often regulations which prevent you from making a living selling fish or timber. There is a significant financial and time hurdle which needs to be cleared to obtain a boat + license to fish commercially. In terms or logging and coal mining, you are excluded based on lack of access to land + equipment + license. Not everyone legally has access to these in all countries. Also, it's not even possible to obtain a loan to do these in most countries. It's literally impossible to get started if you do not have the financial means.

I would also question the 'non-excludable and non-rivalous' quadrant. Not everyone has access to clean air. Many people are trapped in urban centres with low air quality and cannot afford to leave. Some literally cannot leave because they may be in prison, on probation or it's a condition of bankruptcy. Clean air is rivalous since there are a limited number of jobs available in places where the air is clean. Privacy is certainly excludale; e.g. prison and clearly it is rivalous as we have to fight to protect it constantly.

Quadrants are fine when they point to more productive re-framings of the "public X" problem. As implied by you & maybe the article you mentioned, the boundaries of the quadrants are where the theory is likely to fail..

So, if we focus on these boundaries, as honest and curious scientists & engineers, we might chance on new avenues

As somebody who is getting paid via quadratic funding almost monthly, I love it but Its also possible to cheat.

There are also issues plaguing the ecosystem like delayed or missing payments

> 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.

If crypto is an unambiguous public bad, quadratic defunding would be a worthwhile experiment?

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