The CityDAO Journal #2 - Quadratic Funding and the Future of Public Goods
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May 30th, 2022

Motivation

The noblest motive is the public good”Virgil

Public goods are shared goods; they act as critical social infrastructure from which we build communities and nations. Yet, despite their importance, their provision, in general, has retained the same flawed structure for decades and even centuries, in essence – pay taxes and allow governments to provide them. While adequate and certainly better than nothing, this process suffers from critical drawbacks.

The article outlines what public goods are, why traditional methods of providing them are flawed, and a better mechanism for their provision known as Quadratic Funding (QF). Relying on advancements in blockchain and Web3 technology, QF offers a potential solution to the problems that have plagued the provision of public goods for centuries.

What are Public Goods?

Public goods have two properties, they are both non-rival and non-excludable.

Non-rival means multiple people can use a good simultaneously without hurting the other's ability to use the good. Think of digital recordings, this document, radio stations, and the internet. If I am using any of the above, it doesn't affect your ability to use them; this contrasts with rival goods like an apple or a ticket to a sporting event.

Non-excludable means you can't stop people from using it; think of public spaces. It is worth noting many things are excludable in one dimension and non-excludable in another dimension. Consider a building, it is excludable in that you can prevent people from going inside, but non-excludable in that you can't stop someone from admiring its architecture.

If a good satisfies these two properties, we call it a public good; think of sunshine, air, or public highways.

Public Goods are valuable resources that societies collectively need and, unfortunately, are often expensive. While things like sunshine are free, things like highways are not. Furthermore, they typically aren't free in the sense they can be supplied by consensus. If we all agree the majority of votes determine the leader, it is so. However, everyone deciding they want clean air doesn't magically make the air cleaner. Someone has to pay for it.

Who Should Pay?

In a recent article (see link), we discussed the benefits of Quadratic Voting (QV) in reflecting the intensity of people's preferences given many options. In theory, learning the value of various public goods would be accessible via QV. At face value, QF is similar in that, like QV, it is a way to express nuanced preferences. But, the critical difference is that when you vote, you don't lose it. Rather, you exercise your preferences at no cost. In contrast, public goods require funding. Thus QF can be seen as an extension to QV that absorbs this additional complexity.

The necessity of funding induces two significant problems: (1) some will desire to try and get the goods while not paying (free-riding). (2) the wealthy will have more say in which goods are provided. Let's deal with these issues in turn.

The free-rider problem is inherently tied to the property of non-excludability and it's a rather nasty one. Simply, everyone has the motivation to say they don't want the good, then go ahead and use it after it is produced; this is a complex problem that defies an easy solution. The problem is similar to the tragedy of the commons, where everyone has an incentive to overuse common resources. If only one person does so, the resource won't be depleted. However, given everyone has the same motivation, everyone overuses the resource leading to depletion. The free-rider problem has the same dynamic. Given that everyone has the same incentive to try and free-ride, no one pays, and the public good doesn't get produced. These are types of coordination or collective action problems.

The second issue can be minor or significant, depending on the public good in question. Many public goods are provided for by the wealthy and are enjoyed by many equally. Consider large donations from philanthropists to fund public parks.

The problem is when we consider public goods where the benefits can be biased towards those that pay for them. Consider law and order as a public good. While police and the judicial system aren’t public goods, we can’t both use them simultaneously, and we can easily exclude people from using them. They provide society with relatively low levels of crime and corruption, which is a public good. However, to get this, we need the provision of police and courts, among other things. I don’t think we have to think long to realize we don’t want the rich to be able to buy the police and judges; it could easily lead to the erosion of the rule of law (also a public good).

When we consider these problems together, the best solution is to have governments provide public goods via taxes; this partially solves both problems. It solves free-riding as paying taxes isn't voluntary. It solves the issue of wealth inequalities as governments, in theory, only rely on votes that everyone gets regardless of their wealth; of course, I say in theory as there are always ways to lobby governments, but let's put that aside.

It is easy to lose sight of how valuable governments are in this capacity. If you live in a country where functioning democracies provide essential public goods, it can be easy to take for granted. However, the solution of government provision is still partial and imperfect. Governments inherently lack valuable information, limiting their capacity to provide public goods optimally.

Which Public Goods?

The solution described above answers the question of who will pay – everyone via taxes – but it doesn't answer the question of which public goods should be provided? Some public goods are rather obvious, such as clean air and national defense, but others are not.

When deciding which public good to provide, governments rely on tools that aren't information-rich, such as votes, questionnaires, census information, etc. The reality is collecting information is difficult. Essentially, we are describing a scenario of government involvement given a market failure. However, governments fail in other respects. Markets produce prices that contain valuable information reflecting relative preference. Customers have an incentive to provide such information, and governments have no easy way to obtain the same information in a non-market setting.

Imagine going to a grocery store. Instead of purchasing what you want by considering prices relative to your budget, the government asks everyone to vote for which items everyone should get. You shouldn't have to ponder long to realize the result wouldn't be informative or efficient. Though the wealthy can buy more, prices yield information. Governments wish to obtain the knowledge that a market would have produced but don't have a mechanism to uncover this information. QF offers a potential mechanism while maintaining equity and solving the free-rider problem.

Quadratic Funding

To provide public goods, we need funding to democratically and efficiently match preferences. Citizens know their preferences but can't raise funds given collective action and coordination problems. Furthermore, the ability to raise funds is directly tied to your wealth. Governments adequately solve these problems as they can enforce coordination and provide public goods regardless of your wealth, but they don't accurately know citizens' preferences and thus what public goods are the most valuable. We need a method to reveal preferences while incentivizing citizens not to free-ride.

Suppose an entity existed such that citizens could freely and publicly express their desire for a given public good, thus revealing preferences. The entity would fund the good and subsidize others to do so in a manner that induces no one to free ride and offsets wealth inequality; not a small task. Without further detail, I will discuss the notion of QF and the related concept of quadratic matching developed by DAOs such as Gitcoin. The following might seem confusing at first but will become intuitive after an example.

The idea behind Gitcoin is to create a public forum where anyone could declare the desire for a given public good - for example, clean air, solving climate change, or a public works project. Then anyone can come to the forum and pledge funding for the stated public good. Gitcoin will then match the funding in line with the following formula:

Where C is the amount funded by each person and ⅀C is the sum of all the contributions. We use i to denote each person. First, take the square root of each funded amount by each person, add them up, and square the total. Then take away the sum of funded amounts. The matched amount is the difference between the two.

To illustrate suppose there is an initiative to build a park in area A of a city; we'll call it park-A. Suppose there is also an initiative to build a park in area B of the same city; we'll call it park-B. Suppose ten people are each willing to contribute $10 to the construction of park-A. Suppose there is one wealthy investor willing to see park-B built, they will donate $400, but no one else wants the park.

The table below describes the scenario.

So how do we get the numbers? Park-B is easy. Take the square root of 400, which is 20, then square it back to 400. We take away the amount contributed, which is also $400. The matched amount is the difference which is zero (400 - 400 = 0). This is the only case where the matched amount is zero. The intuition is that there are no issues with coordination, or free-riding, with a single contributor, thus no reason for additional funding.

Park-A is a little more complicated, but not much. Each person contributes 10$, so we take the square root, roughly 3.16, and add it up ten times given each person contributes the same amount. Then we square the total, so 31.60 squared, which is 1000 (ignore rounding error). The matched funding is then $900 (1000 - 100 = 900).

Note the desirable properties. Both parks get funded. However, all matched funding goes to park-A. Park-A, after all, is desired by many more people. The matched funding reveals these preferences and accounts for differences in wealth.

Now consider the most powerful aspect of all, it solves the free-rider problem. With quadratic matching, everyone has a significant incentive for honesty and contributes in line with the park's value; this is true given the weighting of contributions. Note that each person putting in $10 saw that become $90 in terms of the matched funding  (900/10 = 90). Consider if we had the same situation, but one person was a free-rider, the total contribution would be $90, and the matched amount would fall to $720. This means that the free-rider could opt-in and get an extra $180 in matched funding for their $10 contribution. The additional value is extremely high, which isn't a coincidence. This is precisely how the formula is intended to work.

QF effectively pays people to reveal their preferences. With public goods, there is an incentive for each participant not to divulge their preferences and not pay for the good in hopes of getting it for free. QF counterbalances this incentive. It makes the market for public goods like a grocery store. In a grocery store, you have an incentive to provide information and pay for the goods you want. This is true given the good you are buying is a private good, not a public good – you can't wait for someone else to pay for it and then, without permission, use the good after. QF incentivizes you to act as if the public good were a private good. The benefit of revealing your preference is higher than the benefit of not doing so, thus solving the free-rider problem!

QF offers a way to fund public goods via a collective pool, thus similar to taxes, but also incentivizes citizens who use the public goods to pay in line with their valuation. Furthermore, regarding which public goods should be provided, QF incentivizes citizens to reveal preferences in an information-rich manner. Taken together, this would vastly increase the efficiency of every dollar spent on public goods. The potential is a much lower tax burden and higher value public goods being delivered.

In summary, quadratic funding/matching is an innovation that delivers a more optimal provision of public goods. It solves the problem of free-riding and, principally, the issue of unequal ability to fund public goods while incentivizing citizens to reveal the most valuable public goods.

Public Good in a City of the Future

CityDAO’s mission is to build a city of the future fully utilizing Web3 and blockchain technologies. In a CityDAO city, the provision of public goods would utilize such profound breakthroughs. CityDAO could fund parks or other public spaces, solve traffic congestion, reduce pollution, and reward innovation in line with the QF method described above. The result would be a city with an abundance of public goods!

Written by Scott Auriat (scotta.eth)  – This article was made possible with funding by the CityDAO Research and Education Guild

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