# A Government-Backed, Public Goods Financing Mechanism

Providing public goods is an essential role of government. Today, we face many key issues which constitute global public goods problems. These include climate change, pollution, open source software, and existential risk, to name a few. However, here I will focus on a smaller problem: how does a government choose which local public goods to finance, and in what quantity?

Finding an approach to fund public goods which is efficient, budget-balanced, and incentive-compatible has long been known to be hard or impossible under many circumstances. But as a government, it is not as important to achieve a balanced budget in the public goods financing mechanism because revenue can be raised using taxation. Here I want to demonstrate a simple system which a government can use to find public goods which are highly valuable to its citizens and efficient to fund, all while determining peoples true valuations for different goods (which could be useful information for future projects).

To start, lets examine how we would find someone’s valuation of a private good. For this, we can use the Becker-deGroot-Marshak (BDM) Mechanism. In this mechanism, a consumer is asked how much they would be willing to pay for a particular commodity. Then, their stated willingness to pay (WTP) is compared against a random bid $B$. If $B$ is higher than the WTP, the consumer gets nothing, however, if the WTP is higher than $B$, the consumer pays $B$ and receives the good. With this mechanism, the consumer is incentivized to state their true WTP. In other words, this mechanism is incentive compatible.

But how do we apply this to public goods? Unlike with the single consumer, everyone receives (or doesn’t receive) the public good simultaneously. Oftentimes, this incentivizes people to report lower WTP for a public good and hope that other people will foot the bill. This free-rider problem is a key reason for many impossibility results in public goods games.

But, what if almost nobody pays? As I mentioned before, budget balance is not important in practice, since governments often raise finances through taxation.

The new mechanism works like this:

1. each citizen is asked for their WTP for a particular public good with a known cost $C$. The government checks that total WTP is greater than $C$
2. A random citizen is chosen, and their WTP ($w$) is compared to a random bid $B$
3. If $w > B$ this citizen pays the government $B$ and the public good gets created, otherwise, the citizen pays nothing and the public good is not funded.

This mechanism essentially replicates the BDM mechanism for each citizen. Either they pay the random bid $B$ and get the good, or they pay nothing and get nothing. If they are not chosen, it does not matter what bid they report. This way, citizens are still incentivized to report their true WTP and valuable public goods (when the total WTP is greater than the cost) are funded by the government! Additionally, because the system is so simple, it could be relatively easy to convince citizens to give this new system a try. Even better, the government itself doesn’t need to determine which public goods to propose. Instead, entrepreneurs can propose different projects directly, and the government can determine which projects are actually valuable to it’s citizens.

The main drawback is that the citizens don’t fund the good themselves, but rely on (possibly inefficient) taxation. Additionally, this mechanism will often fail to fund important public goods (when $B > w$), and might need to be repeated. One solution would be to change the mechanism to chose a larger set of citizens who face a random bid. Instead of requiring that all of their WTP’s are above $B$ (they each face a different i.i.d. random bid), the mechanism could require that 90% (or some large fraction) of the WTP’s are above their bids. This runs into an issue of incentive compatibility, however, since citizens will now be incentivized to under-report their WTP slightly.

Another common objection is that this system allows for more power in the hands of the wealthy. Since wealthier people will likely have higher reported WTP for a given amount of utility obtained from the public good, they may exert an undue influence on the total WTP and likelihood of funding a public good. Overall, this doesn’t seem like a major issue to me, since wealthy people will essentially convince the government to fund more public goods than if they did not participate in the mechanism.

Of course, one could argue that this may still direct public funds towards projects favored by the rich, as these projects are more likely to have a higher total WTP and thus exceed their project costs. A simple remedy for this is to “top up” the stated WTP of poorer participants, giving them more equal influence on the mechanism. Alternatively, the government could give priority to projects which are predominantly valued by the poor.

Overall, this approach highlights the fact that, within a country, it is quite feasible to fund local public goods. The bigger issue, however, is how to fund public goods in situations without a common governance structure or on a global scale? I hope to answer this question more thoroughly in future posts. But for now, note that there is a simple modification of the above mechanism which can be applied across countries: just ask citizens from several countries their valuation of a public good (e.g. pollution reduction) and have the countries divide up the payment proportional to the citizens valuations.

For example, imagine the U.S. and Canada are deciding how to pay for a U.S.-Canada border wall. U.S. citizens are worried that illegal Canadian immigration will make U.S. politics too civil, and Canadian citizens are worried about illegal U.S. immigration for the opposite reason. They ask their citizens how much they would be willing to pay for the border wall and sum up the total WTP by country. Canadian citizens are willing to pay a total of \$100 million for the border wall while U.S. citizens only offer \$10 million. In this case, the Canadian government provides \$100 million for the wall while the U.S. provides \$10 million.

New problems arise if citizens within a country collude to misreport their WTP. Essentially, if the entire country acts like a single agent, it may be incentivized to under-report (if they want other countries to foot the bill) or over-report (if they want to ensure that the good gets funded). Behavior like this would likely necessitate a more sophisticated system such as the VCG mechanism at the country level. In practice, I cannot see this being a major issue since country-wide coordination is already hard (have you read the news lately?).

These concerns still motivate a further look into public goods financing at a global scale. It would be nice if our mechanism for public goods financing did not have to rely on an effective and efficient government (with lots of tax revenue) as these can be hard to find.