Liberal Radicalism: A Flexible Design For Philanthropic Matching Funds

Quadratic Funding https://papers.ssrn.com/sol3/papers.cfm?abstract_id=3243656 Posted: 18 Sep 2018 Vitalik Buterin, Zoë Hitzig, E. Glen Weyl

We propose a design for philanthropic or publicly-funded seeding to allow (near) optimal provision of a decentralized, self-organizing ecosystem of public goods. The concept extends ideas from Quadratic Voting to a funding mechanism for endogenous community formation. Citizens make public goods contributions to projects of value to them. The amount received by the project is (proportional to) the square of the sum of the square roots of contributions received. Under the “standard model” this yields first best public goods provision. Variations can limit the cost, help protect against collusion and aid coordination. We discuss applications to campaign finance, open source software ecosystems, news media finance and urban public projects. More broadly, we relate our mechanism to political theory, discussing how this solution to the public goods problem may furnish neutral and non-authoritarian rules for society that nonetheless support collective organization. (DeepL) We propose a design for philanthropic or publicly funded seeding to (nearly) optimally provide a decentralized, self-organizing ecosystem of public goods. This concept extends ideas from the second round of voting to an endogenous community-building financing mechanism. Citizens make donations of public goods to projects that are of value to them. The amount of money the project receives is (proportionally) the square of the sum of the square roots of the donations received. Under the “standard model,” this makes the provision of public goods a good start. Variations can limit costs, protect against collusion, and aid coordination. Applications to election financing, the open source software ecosystem, news media financing, and urban utilities will be discussed. More broadly, we relate this mechanism to political theory and discuss how this solution to the public goods problem provides a neutral, non-authoritarian rule for society that may nevertheless favor collective organization. (GPT-3.5) We propose a design for philanthropic or public funding. This ensures that decentralized, self-organizing public goods ecosystems are (nearly) optimally provided. This concept extends the idea from second round of voting to an endogenous community-building financing mechanism. Citizens make public goods contributions to projects that are of value to them. The amount of money the project receives is (proportionally) the square of the sum of the square roots of the contributions received. In this “standard model,” this results in optimal public good provision. Transformation can limit costs, help protect against collusion, and support coordination. We will discuss its application to campaign finance, the open source software ecosystem, news media funding, and urban public projects. More broadly, we will relate our mechanism to political theory and discuss how a solution to this public goods problem could provide neutral, non-autocratic rules for society and yet support collective organization.

Content Description. This paper proposes “Liberal Radicalism (LR)” as a new mechanism to achieve optimal supply of public goods.

The main points are as follows

• With regard to the supply of public goods, the problem is that the capitalist voluntary donation mechanism results in underprovision, while the one-person, one-vote majority voting mechanism does not reflect the preferences of minorities.
• Under the LR mechanism, when each person makes a donation to a public good, the amount of funding for that public good is proportional to the square root of the square of the donation amount. In other words, the mechanism favors a large number of small donations over large donations.
• The standard economic model under perfect information shows that the optimal supply of public goods is achieved by the LR mechanism.
• Variants of LR are also analyzed, including cases with budget constraints, cases that allow negative contributions, and cases that change the shape of the exponential function.
• The advantage of LR is that it can deal with community formation endogenously. However, countermeasures against collusion are an issue.
• The paper discusses potential applications to campaign finance, open source software, news media, and urban utilities.
• Philosophically, LR is positioned as a framework for realizing the ideals of liberalism while responding to the criticisms of communitarianism and multiculturalism.

As described above, this is an ambitious paper that attempts to reconcile efficiency and democracy in the provision of public goods through the LR mechanism. It is thought-provoking in theory, application, and ideology.

What is the relationship between LR and QV? The LR mechanism can be understood as an application and extension of the mechanism called Quadratic Voting (QV) to the context of public goods provision.

QV is a mechanism that respects minority opinions while reflecting the strength of preferences by introducing a rule that allows each person to “buy” a vote in favor of a proposal during collective decision-making and pay an amount proportional to the square of the number of votes. For example, it costs 4 units of money to buy 2 votes; QV has been proposed and analyzed in papers such as the one by the author Weyl (2012).

The LR mechanism applies the QV concept to the public good supply problem by mapping the amount of each person’s donation to the purchase of votes in QV and setting the square root of total donations as the level of public good supply.

Thus, the development from QV to LR can be positioned as a natural extension from a collective decision rule to a public goods provision mechanism; the basic idea of LR is an application of the QV concept of having each person express his or her preferences with money.

Unlike QV, however, LR deals with the issue of financing public goods rather than decision-making, so the details of the mechanism, such as the relationship between the amount of donations and the level of supply, are different. It is also characterized by the fact that it also addresses issues specific to the supply of public goods, such as community formation.

What is your relationship with Quadratic Funding? As you pointed out, the Liberal Radicalism (LR) mechanism is also closely related to Quadratic Funding (QF), which is actually used in some Web3 projects, including Gitcoin, and is positioned as a simplified version of the LR concept. QF is a simplified version of LR.

The QF determines the amount of funding for a project by taking the sum of the square roots of each person’s donation amount and squaring it. In other words, the funding amount is proportional to the square root of the individual donation amount, which is similar to the LR mechanism.

The two main ways in which QF differs from LR are

• In a QF, the difference between the amount funded and the amount contributed by individuals is usually contributed from an external pool of funds called a “matching pool.” In contrast, LR expects the difference to be collected broadly from participants.
• The theoretical formulation and analysis of QF is not as rigorous as in LR; in the LR paper, the efficiency and robustness of the mechanism are analyzed in detail within the framework of game theory and welfare economics.

In the context of Web3, QF may be better known. On the other hand, LR is superior in terms of theoretical foundation, and QF can be regarded as a kind of application of LR.

It seems to me that LR and QF strike a balance between theoretical rigor and practicality at different points, while sharing a common problematic awareness of the democratization of the public goods supply mechanism. As to your question, I think it would be beneficial to take LR as a starting point for discussion, with a clear awareness of its relationship to QF.

What is the relationship between LR and CLR? The Liberal Radicalism (LR) mechanism and the Capital-constrained Liberal Radicalism (CLR) mechanism are closely related; CLR is positioned as a variant aimed at a realistic implementation of LR.

The basic idea of LR is to take the sum of the square roots of each person’s contributions squared as the amount of funding for public goods. However, applying this rule as is would be impractical in some cases, as it would require more funding than the total amount donated.

Therefore, CLR adjusts the gap between the amount funded by LR and the total contributions to fund it to stay within pre-determined budget constraints. Specifically, the CLR funding amount is designed to be a weighted average of the LR funding amount and the total contributions.

The main differences between LR and CLR are as follows

• In CLR, the amount of funding falls within an exogenously given budget constraint, whereas LR has no explicit budget constraint.
• The CLR funding amount will be a weighted average of the LR value and total contributions; budget constraints can be met by adjusting parameters that represent the degree of proximity to the LR.
• Theoretical analysis shows that CLR is more likely than LR to lead to underprovision of public goods, but the degree of underprovision can be controlled to some extent by adjusting LR parameters.
• In terms of realistic implementability, CLRs that incorporate budget constraints are superior.

As described above, CLR is a mechanism that incorporates responses to budget constraints with the aim of realistic implementation of LR. The key point is that while sharing the basic concept with LR, it is more feasible.

From the discussion in the paper, one can read the importance of striking a balance between the ideational advantages of LR and the practical usefulness of CLR. If we look at the implementation of the idea, CLR may be more promising. However, the parameters will need to be designed in such a way that the efficiency guarantee of LR is not compromised; LR and CLR are two important reference axes for exploring the balance between theory and practice.

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