Editing Public good (section)

== Academic literature ==
[[Paul A. Samuelson]] is usually credited as the economist who articulated the modern theory of public goods in a mathematical formalism, building on earlier work of [[Knut Wicksell|Wicksell]] and [[Erik Lindahl|Lindahl]]. In his classic 1954 paper ''The Pure Theory of Public Expenditure'',<ref name=":0">{{cite journal|last=Samuelson|first=Paul A.|author-link=Paul Samuelson|year=1954|title=The Pure Theory of Public Expenditure|journal=[[Review of Economics and Statistics]]|volume=36|issue=4|pages=387–89|doi=10.2307/1925895|jstor=1925895}}<br />See also {{cite journal|last=Samuelson|first=Paul A.|year=1955|title=Diagrammatic Exposition of a Theory of Public Expenditure|journal=Review of Economics and Statistics|volume=37|issue=4|pages=350–56|doi=10.2307/1925849|jstor=1925849}}</ref> he defined a public good, or as he called it in the paper a "collective consumption good", as follows:<blockquote>[goods] which all enjoy in common in the sense that each individual's consumption of such a good leads to no subtractions from any other individual's consumption of that good...</blockquote>

Many mechanisms have been proposed to achieve efficient public goods provision in various settings and under various assumptions.

=== Lindahl tax ===
A [[Lindahl tax]] is a type of taxation brought forward by [[Erik Lindahl]], an economist from Sweden, in 1919. His idea was to tax individuals for the provision of a public good according to the marginal benefit they receive. Public goods are costly and eventually someone needs to pay the cost.<ref>{{Cite journal|last1=Gunnthorsdottir|first1=Anna|last2=Houser|first2=Daniel|last3=McCabe|first3=Kevin|date=2007|title=Disposition, history and contributions in public goods experiments|url=http://www.sciencedirect.com/science/article/pii/S0167268105002532|journal=Journal of Economic Behavior & Organization|language=en|volume=62|issue=2|pages=304–315|doi=10.1016/j.jebo.2005.03.008|issn=0167-2681}}</ref>  It is difficult to determine how much each person should pay. So, Lindahl developed a theory of how the expense of public utilities needs to be settled. His argument was that people would pay for the public goods according to the way they benefit from the good. The more a person benefits from these goods, the higher the amount they pay. People are more willing to pay for goods that they value. Taxes are needed to fund public goods and people are willing to bear the burden of taxes.<ref>{{Cite web|author=Investopedia Staff|title=Lindahl Equilibrium Definition|url=https://www.investopedia.com/terms/l/lindahl-equilibrium.asp|access-date=2020-10-28|website=Investopedia|language=en}}</ref> Additionally, the theory dwells on people's willingness to pay for the public good. From the fact that public goods are paid through taxation according to the Lindahl idea, the basic duty of the organization that should provide the people with this services and products is the government.<ref name=":1">{{Cite web|title=Public Good {{!}} Learning to Give|url=https://www.learningtogive.org/resources/public-good|access-date=2020-10-28|website=learningtogive.org}}</ref>

=== Vickrey–Clarke–Groves mechanism ===

[[Vickrey–Clarke–Groves mechanism]]s (VCG) are one of the best-studied procedures for funding public goods. VCG encompasses a wide class of similar mechanisms, but most work focuses on the Clarke Pivot Rule which ensures that all individuals pay into the public good and that the mechanism is individually rational.

The main issue with the VCG mechanism is that it requires a very large amount of information from each user. Participants may not have a detailed sense of their utility function with respect to different funding levels. Compare this with other mechanisms that only require users to provide a single contribution amount. This, among other issues,<ref>{{Cite journal|last1=Rothkopf|first1=Michael|date=2007|title=Thirteen Reasons Why the Vickrey–Clarke–Groves Process Is Not Practical|url=https://pubsonline.informs.org/doi/pdf/10.1287/opre.1070.0384|journal=Operations Research|language=en|volume=55|issue=2|pages=191–197|doi=10.1287/opre.1070.0384}}</ref> has prevented the use of VCG mechanisms in practice. However, it is still possible that VCG mechanisms could be adopted among a set of sophisticated actors.

=== Quadratic funding ===

Quadratic funding (QF) is one of the newest innovations in public goods funding mechanisms. The idea of [[Quadratic voting]] was turned into a mechanism for public goods funding by Buterin, Hitzig, and Weyl <ref>{{Cite journal|last1=Buterin|first1=Vitalik|last2=Hitzig|first2=Zoe|last3=Weyl|first3=Glen|date=2019|title=A Flexible Design for Funding Public Goods|url=https://pubsonline.informs.org/doi/abs/10.1287/mnsc.2019.3337|journal=Management Science|language=en|volume=65|issue=11|pages=5171–5187|doi=10.1287/mnsc.2019.3337|arxiv=1809.06421 |s2cid=198858039 }}</ref> and is now referred to as quadratic funding.

Quadratic funding has a close theoretical link with the VCG mechanism, and like VCG, it requires a subsidy in order to induce incentive compatibility and efficiency. Both mechanisms also fall prone to collusion between players and sybil attacks. However, in contrast to VCG, contributors only have to submit a single contribution – the total contribution to the public good is the sum of the square roots of individual contributions. It can be proved that there is always a deficit that the mechanism designer must pay.

One technique to reduce collusion is to identify groups of contributors that will likely coordinate and lower the subsidy going to their preferred causes.<ref>{{Cite journal|last1=Miller|first1=Joël|last2=Weyl|first2=Glen|last3=Erichsen|first3=Leon|date=2022|title=Beyond Collusion Resistance: Leveraging Social Information for Plural Funding and Voting|url=https://papers.ssrn.com/sol3/papers.cfm?abstract_id=4311507|journal=SSRN|language=en|doi=10.2139/ssrn.4311507|ssrn=4311507 |s2cid=255261051 }}</ref>

=== Assurance contracts ===

First proposed by Bagnoli and Lipman,<ref>{{Cite journal|last1=Bagnoli|first1=Mark|last2=Lipman|first2=Barton|date=1989|title=Provision of Public Goods: Fully Implementing the Core through Private Contributions|url=https://www.jstor.org/stable/2297502|journal=The Review of Economic Studies |volume=56|issue=4|pages=583–601|doi=10.2307/2297502|jstor=2297502 |hdl=2027.42/100743 |hdl-access=free}}</ref> In 1989, [[assurance contracts]] have each funder agree to spend a certain amount towards a public good conditional on the total funding being sufficient to produce the good. If not everyone agrees to the terms, then no money is spent on the project. Donors can feel assured that their money will only be spent if there is sufficient support for the public good. Assurance contracts work particularly well with smaller groups of easily identifiable participants, especially when the game can be repeated.

Several crowdfunding platforms such as [[Kickstarter]] and [[IndieGoGo]] have used assurance contracts to support various projects (though not all of them are public goods). Assurance contracts can be used for non-monetary coordination as well, for example, Free State Project obtained mutual commitments for 20,000 individuals to move to New Hampshire in a bid to influence the politics of the state.
Alex Tabarrok suggested a modification called dominant [[assurance contracts]] where the mechanism designer gives every contributor a refund bonus if the contract fails. {{fact|date=February 2025}} For example, in addition to returning their contributions, the mechanism designer might give all contributors an additional $5 if the total donations are not sufficient to support the project. If there is a chance that the contract will fail, a refund bonus incentivizes people to participate in the mechanism, making the all-pay equilibrium more likely. This comes with the drawback that the mechanism designer must pay the participants in some cases (e.g. when the contract fails), which is a common theme.

Zubrickas <ref>{{Cite journal|last1=Zubrickas|first1=Robertas|date=2014|title=The provision point mechanism with refund bonuses|url=https://www.sciencedirect.com/science/article/abs/pii/S0047272714002205|journal=Journal of Public Economics|language=en|volume=120|pages=231–234|doi=10.1016/j.jpubeco.2014.10.006}}</ref> proposed a simple modification of dominant assurance contracts where people are given a refund bonus proportional to the amount they offered to donate, this incentivizes larger contributions than the fixed refund from Tabarrok’s original proposal. There have been many variations on the idea of conditional donations towards a public good. For example, the Conditional Contributions Mechanism <ref>{{Cite journal|last1=Reischmann|first1=Andreas|date=2015|title=The Conditional Contribution Mechanism for the Provision of Public Goods|url=https://pubsonline.informs.org/doi/abs/10.1287/mnsc.2019.3337|journal=Discussion Paper Series No. 586|volume=65 |issue=11 |pages=5171–5187 |language=en|doi=10.11588/heidok.00018483}}</ref> allows donors to make variable sized commitments to fund the project conditional on the total amount committed. Similarly, the Binary Conditional Contributions Mechanism <ref>{{Cite journal|last1=Reischmann|first1=Andreas|last2=Oechssler|first2=Joerg|date=2018|title=The Binary Conditional Contribution Mechanism for public good provision in dynamic settings — Theory and experimental evidence|url=https://www.sciencedirect.com/science/article/abs/pii/S0047272718300355|journal=Journal of Public Economics|language=en|volume=159|pages=104–115|doi=10.1016/j.jpubeco.2018.02.009}}</ref> allows users to condition their donation on the number of unique funders. Extensions such as the Street Performer Protocol consider time-limited spending commitments.

=== Lotteries ===
[[Lotteries]] have historically been used as a means to finance public goods. Morgan <ref>{{Cite journal|last1=Morgan|first1=John|date=2000|title=Financing Public Goods by Means of Lotteries|url=https://www.jstor.org/stable/2695947|journal=The Review of Economic Studies|language=en|volume=67|issue=4|pages=761–784|doi=10.1111/1467-937X.00153|jstor=2695947 }}</ref> initiated the first formal study of lotteries as a public goods funding mechanism. Since then, lotteries have undergone extensive theoretical and experimental research. Combined with their historical success, lotteries are a promising crowdfunding mechanism. 
 
They work by using an external source of funding to provide a lottery prize. Individual “donors” buy lottery tickets for a chance to receive the cash prize, knowing that ticket sales will be spent towards the public good. A winner is selected randomly from one of the tickets and the winner receives the entire lottery prize. All lottery proceeds from ticket sales are spent towards the public good.

Like the other mechanisms, this approach requires subsidies in the form of a lottery prize in order to function. It can be shown that altruistic donors can generate more funding for the good by donating towards the lottery prize rather than buying tickets directly.

Lotteries are approximately efficient public goods funding mechanisms and the level of funding approaches the optimal level as the prize grows. However, in the limit of large populations, contributions from the lottery mechanism converge to that of voluntary contributions and should fall to zero.<ref>{{Cite journal|last1=Cabrales|first1=Antonio|last2=Lugo|first2=Haydée|date=2016|title=A public good model with lotteries in large groups|url=https://link.springer.com/article/10.1007/s10797-015-9359-y|journal=International Tax and Public Finance|language=en|volume=23|pages=218–233|doi=10.1287/mnsc.2019.3337|arxiv=1809.06421 |s2cid=198858039 }}</ref>

=== Role of non-profits ===
Public goods provision is in most cases part of governmental activities.<ref>{{Cite journal|last=Kingma|first=Bruce R.|date=1997|title=Public good theories of the non-profit sector: Weisbrod revisited|url=https://www.jstor.org/stable/27927560|journal=Voluntas: International Journal of Voluntary and Nonprofit Organizations|volume=8|issue=2|pages=135–148|doi=10.1007/BF02354191|jstor=27927560|s2cid=154163089|issn=0957-8765}}</ref> In the introductory section of his book, ''Public Good Theories of the Nonprofit Sector'', [[Bruce Kingma|Bruce R. Kingma]] stated that; <blockquote>In the Weisbrod model nonprofit organizations satisfy a demand for public goods, which is left unfilled by government provision. The government satisfies the demand of the median voters and therefore provides a level of the public good less than some citizens'-with a level of demand greater than the median voter's-desire. This unfilled demand for the public good is satisfied by nonprofit organizations. These nonprofit organizations are financed by the donations of citizens who want to increase the output of the public good.<ref>{{Citation|last=Kingma|first=Bruce R.|title=Public Good Theories of the Nonprofit Sector|date=2003|url=https://doi.org/10.1007/978-1-4615-0131-2_3|work=The Study of the Nonprofit Enterprise: Theories and Approaches|pages=53–65|editor-last=Anheier|editor-first=Helmut K.|series=Nonprofit and Civil Society Studies|place=Boston, MA|publisher=Springer US|language=en|doi=10.1007/978-1-4615-0131-2_3|isbn=978-1-4615-0131-2|access-date=2020-10-28|editor2-last=Ben-Ner|editor2-first=Avner}}</ref>          </blockquote>