Quadratic Payments: A Primer (Vitalik Buterin, 2019)

By BrownHairedEevee @ 2021-04-05T18:05 (+30)

This is a linkpost to https://vitalik.ca/general/2019/12/07/quadratic.html

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.
  • See also: The Case for Promoting / Creating Public Goods Markets as a Cause Area

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 $p$. If I value the public good at $$v$, then I should donate if $pv>1$, and not donate if $pv<1$.
  • Empirically, the author has found that when he offered to write blog posts as long as readers contribute some total dollar amount (e.g. $1000), more than half of the contributions came from a single donor.
• The author compares this with one-person-one-vote (1p1v) systems, which he says fails to incorporate information about how much voters care about outcomes.
• To the author, the ideal mechanism is one where the cost of buying an additional unit of influence is proportional to how many units of influence, because "your $v$ determines how much you're willing to pay for one unit of influence."
  • The quadratic mechanism formula: your $n$th unit of influence costs you $$n$. So, to "buy" $n$ units of influence, you need to spend $n(n+1)/2=O\left(n^2\right)$ units of currency (e.g. dollars or voice credits).
• Quadratic voting (QV): No money changes hands; instead, you "pay" for votes with voice credits.
  • In the case where two options are being voted on, casting $n$ votes for or against either option costs you $O\left(n^2\right)$ 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 $i$ contributes $$c_i$ to a project. Then the total amount of money that will be allocated to the project will be at most $${\left({\sum }_{i=1}^m\sqrt{c_i}\right)}^2$.
  • "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.
• Quadratic attention purchase:
  • 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 $n$th unit of influence costs you $$n$. This works like quadratic voting on how long messages are displayed: you can either broadcast a new ad for $n$ minutes for $$O\left(n^2\right)$, or extend the airtime of someone else's ad by $n$ minutes for $$O\left(n^2\right)$.