# Quadratic Payments: A Primer (Vitalik Buterin, 2019)

Apr 5 20213 min read 6

# 30

## Why I'm making this linkpost

• I think this is a great summary of the theory behind "quadratic mechanisms" (e.g. quadratic funding, quadratic voting), and I'd like to create a space to discuss these mechanisms and their merits.
• I think mechanism design in general, and quadratic mechanisms specifically, may be relevant to a range of EA causes, as well as coordination within EA, so I'd like to create a space where we can propose ideas for applying them to EA.

## Key points

• Regular markets are great for providing private goods, but they fail to provide public goods because consumers have to be strategic about whether and how much they pay for them.
• Specifically, suppose I want to see a public good (e.g. a blog post) be created and I think that contributing in $1 will increase the probability that it is created by . If I value the public good at$, then I should donate if , and not donate if .
• Empirically, the author has found that when he offered to write blog posts as long as readers contribute some total dollar amount (e.g. $1000), more than half of the contributions came from a single donor. • The author compares this with one-person-one-vote (1p1v) systems, which he says fails to incorporate information about how much voters care about outcomes. • To the author, the ideal mechanism is one where the cost of buying an additional unit of influence is proportional to how many units of influence, because "your determines how much you're willing to pay for one unit of influence." • The quadratic mechanism formula: your th unit of influence costs you$. So, to "buy"  units of influence, you need to spend  units of currency (e.g. dollars or voice credits).
• In the case where two options are being voted on, casting  votes for or against either option costs you  voice credits.
• QV can be extended to the case where more than two options are being voted on, and to cases where agents are "voting" on a continuous setting, such as the temperature of a thermostat.
• However, QV assumes a fixed set of options, and the ability to decide which options are on the table gives you considerable power.
• Quadratic funding (QF): Used to collectively decide how much money to allocate to public goods by allowing individual contributions.
• QF is more open-ended than QV: "anyone can raise funds for what they claim to be a public good project."
• Suppose each individual  contributes $to a project. Then the total amount of money that will be allocated to the project will be at most$.
• "Note that if the subsidy pool is not big enough to make the full required payment to every project, we can just divide the subsidies proportionately by whatever constant makes the totals add up to the subsidy pool's budget."
• Gitcoin is a platform that allows individuals to fund public goods using QF and create their own funding pools for collections of projects.
• Public advertising is often used to pay for public goods, but it forces people to look at ads they don't want to see, and ads from wealthy actors and centralized authorities are overrepresented.
• We can use a quadratic fee schedule to enable small actors to buy ad slots for specific messages more easily: your th unit of influence costs you $. This works like quadratic voting on how long messages are displayed: you can either broadcast a new ad for minutes for$, or extend the airtime of someone else's ad by  minutes for \$.

# Reactions

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Thanks for the post. Are there concrete examples of organizations that use quadratic voting for collective decisions?

EA Hannover uses qv for choosing books for our reading club!

An online poll generator for quadratic voting is qv.geek.sg, which wasn’t too easy to find a couple months ago and might be interesting to play around with to get an impression.

Cool! This website looks good as well but I haven't tried it yet: quadraticvote.co

Colorado has been using QV to make some decisions, such as priorities for agencies and interagency groups.

Hi! I really liked this post and think there should be more discussions about these algorithms on here. I just wanted to point out what he writes in the penultimate paragraph:

One particular cause dear to me personally is what I call "entrepreneurial public goods": public goods that in the present only a few people believe are important but in the future many more people will value. In the 19th century, contributing to abolition of slavery may have been one example; in the 21st century I can't give examples that will satisfy every reader because it's the nature of these goods that their importance will only become common knowledge later down the road, but I would point to life extension and AI risk research as two possible examples.

What he says here is almost the same as what we mean when we talk about the search for "Cause X". In this lingo, cause X is a public good which is currently underfunded.

Maybe a mechanism like quadratic funding could even help us with allocating funds to researchers working on niche topics? An example could be insect suffering: Suppose that many people think that there is some chance that insect suffering might be a big deal, but very few people care deeply about it (I guess insects are hard to relate to because they are so different from us).

It would cost very little to all those people who think there is a small chance of importance, because initially the funding is cheap. Yet due to the nature of the algorithm, research into insect suffering would receive a strong subsidy.

Am I getting this right?

Yeah, it sounds right to me.

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