Beyond Collusion Resistance: Leveraging Social Information for Plural Funding and Voting
December 2022
memo
o3.iconAim of the paper
Traditional Quadratic Funding (QF) assumes "independent rational individuals" and ignores social ties and cooperative behavior.
In reality, relationships among friends, organizations, communities, etc. strongly influence donation behavior, and civil attacks and collusion occur. This paper redefines "collusion resistance" and explores design principles for a Plural QF that actively exploits people's social bonds.
Reduce subsidies for similar pairs (yellow rectangles)
More accounts with more people can earn linear subsidies.
Calculate square root per group
(1) Linear increase in subsidy if one person belongs to multiple groups
(2) Can be abused even among overlapping groups
→Squared Cluster Match
Interaction term attenuates donations of "members socially close to the other group" by √c
Fully meet defined collusion tolerance
→Maintain IR (Individual Reasonableness) for each individual.
Offset Match
Estimate social centrality αᵢ and replace each contribution by √αᵢ cᵢ
Linear equations for α may not be solved; there are cases where IR is not satisfied
Sufficient condition: All members can belong to a single group as well.
Eigen Match
Cluster Match by considering eigenvectors of social graphs as "pseudo-groups
Conceptual phase (untested)
Possibility to combine the advantages of Offset and Cluster
Redefining Collusion Resistance (Summary)
The subsidy for incremental individual donations is limited to O(√cᵢ).
Subsidies for group-wide donation expansion are also O(√β), where β is the expansion rate.
The increase in subsidy due to additional members is limited to O(√x), O(√γ) for both the number of new members x and the amount of each member's contribution γ.
The appendix proves that COCM meets these three conditions.
Conclusion/Implication
Incorporating social information can better reward "consilience across differences" while reducing collusion.
The COCM and other new mechanisms will be applied not only to the allocation of public funds but also to Quadratic Voting.
Future issues include (1) robustness evaluation under incomplete or erroneous information, (2) more precise modeling of group structure, and (3) deeper exploration of unverified mechanisms such as Eigen Match.
A word summary
Re-contextualize QFs to maximize cooperation among diverse communities while preventing collusion. The key is to incorporate "who is closer to whom and how close they are" into the subsidy calculation.
AI Considerations
COCM mathematically rewards "Cooperation Across Differences" with the rule that "the closer the connection, the thinner the subsidy; the farther away, the thicker. This is a mathematical expression of Plurality's philosophy that "diversity is value. While the prediction market measures opinion strength by the amount bet on one axis, the COCM adjusts subsidies on two axes, √c × social distance, making the economic signal polyvocal. ---